A Survey of Control Mechanisms for Creative Pattern Generation

Abstract

We review recent methods in 2D creative pattern generation and their control mechanisms, focusing on procedural methods. The review is motivated by an artist's perspective and investigates interactive pattern generation as a complex design problem. While the repetitive nature of patterns is well‐suited to algorithmic creation and automation, an artist needs more flexible control mechanisms for adaptable and inventive designs. We organize the state of the art around pattern design features, such as repetition, frames, curves, directionality, and single visual accents. Within those areas, we summarize and discuss the techniques' control mechanisms for enabling artist intent. The discussion includes questions of how input is given by the artist, what type of content the artist inputs, where the input affects the canvas spatially, and when input can be given in the timeline of the creation process. We categorize the available control mechanisms on an algorithmic level and categorize their input modes based on exemplars, parameterization, handling, filling, guiding, and placing interactions. To better understand the potential of the current techniques for creative design and to make such an investigation more manageable, we motivate our discussion with how navigation, transparency, variation, and stimulation enable creativity. We conclude our review by identifying possible new directions that can inspire innovation for artist‐centered creation processes and algorithms.

Full text

EUROGRAPHICS 2021
H. Rushmeier and K. Bühler
(Guest Editors)
Volume 40 (2021), Number 2
STAR – State of The Art Report
A Survey of Control Mechanisms for Creative Pattern Generation
Lena Gieseke1, Paul Asente2, Radomír Mˇ
ech2, Bedrich Benes3, and Martin Fuchs4
1Film University Babelsberg Konrad Wolf, 2Adobe Research, 3Purdue University, 4Hochschule der Medien
Abstract
We review recent methods in 2D creative pattern generation and their control mechanisms, focusing on procedural methods.
The review is motivated by an artist’s perspective and investigates interactive pattern generation as a complex design problem.
While the repetitive nature of patterns is well-suited to algorithmic creation and automation, an artist needs more flexible
control mechanisms for adaptable and inventive designs. We organize the state of the art around pattern design features,
such as repetition, frames, curves, directionality, and single visual accents. Within those areas, we summarize and discuss the
techniques’ control mechanisms for enabling artist intent. The discussion includes questions of how input is given by the artist,
what type of content the artist inputs, where the input affects the canvas spatially, and when input can be given in the timeline of
the creation process. We categorize the available control mechanisms on an algorithmic level and categorize their input modes
based on exemplars, parameterization, handling, filling, guiding, and placing interactions. To better understand the potential
of the current techniques for creative design and to make such an investigation more manageable, we motivate our discussion
with how navigation, transparency, variation, and stimulation enable creativity. We conclude our review by identifying possible
new directions that can inspire innovation for artist-centered creation processes and algorithms.
CCS Concepts
•Computing methodologies →Computer graphics; •Human-centered computing →Interaction design process and meth-
ods; Interaction design theory, concepts and paradigms; Systems and tools for interaction design;
1. Introduction
Pattern generation in computer graphics provides a large amount
of precise and quickly-generated digital content. However, despite
more than three decades of research, supporting artists with mean-
ingful digital tools for creative content generation, for example,
those needed for ornamental pattern designs (Figure 1), is an ongo-
ing challenge. Most solutions focus on singular features and control
mechanisms, such as example-based controls or brushes, on an al-
gorithmic level. Little attention, however, has been paid to overall
creative workflows, which need to strike a balance, giving users
needed power without burdening them with unwanted details. Of-
ten, techniques that are claimed to be artist-controllable turn out not
to be so.
This may be a consequence of research often being executed
without direct and continuous collaboration with artists and without
the support of large-scale user studies. Algorithms and methods are
often developed to further the state of the art, such as building on
recent progress in deep learning research, with little understanding
of artists’ needs and how mechanisms can be validated.
Recent surveys have covered 3D generation in great detail, fo-
cusing on world building [STBB14;ADBW16], terrain model-
ing [GGP*19] and game-specific approaches [HMVI13;TYSB11].
In this report, we review recent advances in 2D pattern generation.
The underlying regularity of 2D pattern designs is based on a
repetitive and balanced distribution of elements, usually following
hierarchical structures. These characteristics can be efficiently im-
plemented by procedural approaches that arrange elements in space
according to generative rules [ŠBM*10], but developing these rules
can be tedious, non-inspiring, repetitive, and challenging. The pri-
mary motivation for inverse procedural models is to free the artist
from these tasks. Computational generation techniques can ease
these problems and also perform in a more precise and less error-
prone way than a human artist. However, the creative demands of
tasks like laying out space-specific designs and placing visual ac-
cents must also be considered. Procedural models must be aug-
mented and different approaches must be unified to combine the
control and quality of manual creation with the efficiency and ac-
curacy of computation [GALF17].
We review recent advances in 2D pattern generation and discuss
procedural models, data-driven generation, and design-specific pat-
tern generation. As theoretical grounding, we classify control
mechanisms and their characteristics from the perspective of an
artist, from global to local and from automatic to manual, with
varying levels of abstraction. As a basis for a discussion of the ca-
DOI: 10.1111/cgf.142658
© 2021 The Author(s).
Computer Graphics Forum published by Eurographics - The European Association for Computer
Graphics and John Wiley & Sons Ltd.
This is an open access article under the terms of the Creative Commons Attribution NonCommercial
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is properly cited and is not used for commercial purposes.

L. Gieseke, P. Asente, R. Mech, B. Benes, M. Fuchs / A Survey of Control Mechanisms for Creative Pattern Generation
Figure 1: Historic examples for creative pattern designs and or-
namentation. Places of origin from left to right, top to middle row:
France, China, USA, UK, Poland, Egypt, UK. Bottom row: recent
commercial examples. This figure is adapted from [GALF17], im-
age sources: [1-11].
pabilities of control mechanisms in the creative process and their
potential for innovative creation, we review relevant literature on
creativity and summarize aspects that can help to understand these
capabilities in the context of computer graphics research.
We organize contemporary techniques by design areas and the
visual features they enable. We further group related work by
commonly-used control types. Then, we specifically analyze the
artistic controls offered by each technique. We conclude the review
with a discussion of the means for enabling creativity for the differ-
ent control mechanism types. With this survey, we hope not only to
meaningfully categorize and summarize the state of the art but also
to contribute to a shared vocabulary and to establish a foundation
for incorporating artists and their creative tasks into algorithmic
content creation pipelines.
2. Terminology
The following describes how we will be using terms relevant to our
topic.
Pattern is a generic term for any type of repeated, often regular,
arrangement [Oxf17].
Artistic refers to a task with an outcome that potentially has
meaning and value beyond aesthetics and practicality. In addition to
formal skills that depend on a given domain, an artistic task usually
requires creative thinking as well as intuition, emotion and sensual
considerations.
Creative refers to a task that intentionally produces a novel, non-
standard outcome, as further discussed in Section 4.
Design space refers loosely to the range of visual results a tech-
nique can create. For example, Perlin noise [Per85] has a rather
restricted design space of noise images, only differing in few char-
acteristics. Drawing with a pen can result in many different designs,
thus resulting in a larger design space.
Expressiveness refers to the size, the variability and the open-
ness of a design space as discussed in detail in Section 4. Expres-
siveness is commonly used in the context of creative controls, but
often without a clear understanding of its meaning.
Canvas constitutes the area in which the output is generated,
similar to a canvas in a painting context.
Shape refers to the external boundary or outline on the canvas or
of an object without any restrictions on the form.
Procedural refers to the production of output by running an al-
gorithm, such as a rule-based system.
Data-driven is the production of output based on given data.
Parameterized refers to offering separately controllable charac-
teristics. It can be used with procedural pattern representations, or
data-driven approaches.
3. Taxonomy of Control Mechanisms
The following taxonomy lays groundwork for our later evaluation
of control mechanisms of the state of the art. It is difficult to derive
the discussion of means for enabling creativity directly from the
related work, as its authors have followed different motivations and
have emphasized various aspects when describing their work and
results. To classify the work in an objective and unified manner, we
analyze general characteristics of control with digital creation tools
and relate the actual presented control mechanisms to them. Based
on this analysis, we then review the related work in Section 7.
3.1. Control Characteristics
A creation process can be described by answering the questions
of how,what,where,when and who. These characteristics can be
discussed in various creation contexts and could even be translated
to traditional media such as water color on paper.
How (User Interaction) is a control executed or an input given by
an artist? How detached is it from the visual result on the canvas?
External File On-CanvasHow: UI
•File: The control is externally given, such as with code or a con-
figuration file.
•Separate UI: A separate UI is given through which an artist gives
input and activates states. Separate UIs are often in close proxim-
ity to the canvas, carefully designed and easily usable. However,
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because they detach the work from the actual output, separate
UIs have a level of indirection. An artist must actively translate
the interaction with the separate UI to the resulting output on the
canvas.
•On-Canvas: Controls are executed directly on the output canvas.
Most of them require activating or selecting a tool in a separate
UI, such as selecting a pen for drawing on a canvas. There are
cases where controls cannot clearly be classified as either sep-
arate UI or on-canvas. A pen, for example, can have different
characteristics that an artist needs to set in the UI. The adjust-
ment of settings should be as seamlessly integrated into an on-
canvas tool as possible (e.g., with choices appearing as tool tips).
What (Content) does an artist give as input? What is the level of
abstraction of the content that an artist works with?
What: Code Element
float noise()
{
...
}
Value Intermediate
•Code: Input is a syntactically structured formal language.
•Value: The input is a single value, chosen from a range—for ex-
ample, with a slider.
•Intermediate: The input is visual but abstract, such as sketching
a mask or arrows for directionality. Artists still have to interpret
how the input affects the result.
•Element: The input is a component of the resulting pattern.
Where (Canvas) does the input have an effect and what is the area
of influence?
Where: Global LocalRegional
The input can have global influence, regional, e.g., on a drawn
curve or local, e.g., on one specific element.
When (Timeline) is the input given and at what time in the cre-
ation process is the control executed?
Before AfterDuring
Input can be given before the creation process, during it when
parts of the results are already visible, or after, when the result is
visible and can be adjusted retrospectively.
Who (User) has the skill set needed to provide the input?
Who:
Technical Artistic
This category can be in part derived from the above characteris-
tics of how and what. In most general terms, this category can be
classified as the skill set of a Programmer, for giving, e.g., code
as input, requiring analytical-formal and logical thinking and the
ability to abstract. On the other end of the spectrum, the skill set
of an Artist is needed, e.g., for drawing, requiring intuitive-visual
and spatial thinking and the ability to create. The who category is
listed here for completeness. The discussion of needed competen-
cies, skills and mindsets, including the accompanying psychologi-
cal and artistic aspects, is out of the scope of this survey.
3.2. Control Mechanisms
We now classify the control mechanisms as they are described in
the state of the art. These low-level mechanisms define what an
artist can or must work with and are specified for each reference in
Table 1. Because this survey focuses on algorithms, UI specifics,
such as the layout of buttons, are not considered. For each mech-
anism we summarize the how,what,where and when characteris-
tics over all reviewed publications and with that show, in Table 3,
connections and capabilities of different control mechanisms and
potential trade-offs between approaches.
Initialization
•System Configuration: The required overall setup of the system,
such as computing caches or training a model. This is usually a
one-time investment.
•Task Initialization: A non-creative task that has to be executed
each time in order to produce an output, such as selecting the
specific optimization algorithm.
Exemplars
•Image: An example image that should be matched in its entirety.
Examples are usually pixel data.
•Element Arrangement: An example element arrangement that
should be matched in its entirety. Elements in the arrangement
are usually separate shapes and might carry additional data.
•Element: One specific, individual asset that becomes part of the
result. Elements can be shapes or pixel data.
Parameterization
•Visual Output: Parameters that can adjust visual features directly
in the output.
•System/Generation: Parameters that influence the output indi-
rectly, such as parameters for an optimization algorithm or con-
straints.
Handling
•Visualization: Any type of visual interface that goes beyond the
standard UI elements, such as sliders and buttons.
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•Image-Based: Images as indirect control input, such as pixel data
masks.
•Sketch-Based: Sketches and curves defining indirect control ele-
ments on the canvas—for example, the drawing of a mask with
a pen tool.
Filling
•Shapes: A space to fill, usually a specific shape.
•Masking: Areas within the shape to fill that should remain unaf-
fected.
•Curves: A one-dimensional curve or path to be followed with
elements of the pattern. The curve is given as a whole before the
generation starts.
Guiding
•Brushing/Strokes: A curve, usually created by mouse movements
or with a stylus pen, that is followed with output elements—often
understood as brushing.
•Directions: Visual elements such as intermediate curves, arrows
or output components that define directions for the design to fol-
low (e.g., with an underlying vector field).
Placing
•Element Placement: The direct placement of components on the
canvas as part of the final result.
•Element Drag & Drop: Drag and drop of components on the
canvas within the existing result.
4. Means For Enabling Creativity
Many content generation tasks in computer graphics involve cre-
ative considerations. Considering creativity is especially relevant
for investigating control mechanisms because the controls provide
the means for creative creation. However, creativity is ill-defined
and involves insights from various disciplines, making it a notori-
ously difficult topic to address.
On the one hand, there are efforts to develop algorithms that per-
form creatively themselves. On the other hand, there is the goal
of supporting human creativity with digital tools, which is the fo-
cus of this survey. Enabling human creativity is an established
field in the human-computer interaction (HCI) community, based
largely on the pioneering work of SHNEIDERMAN [Shn07] about
Creativity Support Tools. This topic has recently found renewed
attention [FMD18;FMR*19;RMF*20], asking for more rigorous
evaluation in regard to claimed creativity support. Among other as-
pects, FRICH et al. [FMD18] ask for “clearer definitions of creativ-
ity.” This shows that the HCI community already strives for the type
of survey this STAR proposes. However, for this survey, rooted in
the field of computer graphics, we review potentially relevant char-
acteristics of underlying algorithms that enable artists to be cre-
ative. We include interface design aspects but they are not the focus
of this survey. However, the need to bridge between developing the
core algorithms and the interface in order to support creative and
artistic intent has been voiced by past research [DHF*17;Ise16;
Sal02], and this work contributes to this effort.
CHERRY et al. [CL14] presented an evaluation technique called
the quantifiable Creativity Support Index (CSI), which has found
its way into the graphics community [SLD17]. The index measures
how well a tool enables creativity based on a psychometric survey.
The development and validation of the measurement dimensions—
namely, exploration,expressiveness,immersion,enjoyment,results
worth effort, and collaboration—are based on user tests. CHERRY
et al. [CL14] quantified the specific phrases participants used to
describe a creative process. However, a clear definition of terms
like exploration and expressiveness is missing and the meaning of
a statement such as, “I was able to be very creative,” is left open.
A quantified user study is often not feasible, for example for this
survey and for assessing the state of the art. Furthermore, doing
so would not always be meaningful because supporting creativity
is not a goal for most methods. However, most methods do offer
carefully developed control mechanisms. We propose a discussion
of how the control mechanisms of each technique, as presented by
its authors, enable creativity. Based on the given information, we
reflect on the potential for the means for enabling creativity in a
meaningful way, even if creative control was not necessarily the
authors’ intention.
We derive a working basis of such means for enabling creativity
in regard to control mechanisms in the following review of relevant
references. Our classification is meant as a step toward understand-
ing the creative control options within the current state of the art.
In terms of measurement dimensions, it can be seen as an eval-
uation on algorithmic level and a subset of the more general and
user-study-based classification with the Creativity Support Index.
4.1. Discussion Basis
WEISBERG [Wei06] states that a creative person “intentionally pro-
duces a novel product” (p.70) and explicitly decouples a possible
value of a product from it being the result of a creative process
(p.63). BODEN [Bod10] described novelty as a surprising product,
one that the creator did not directly anticipate (p.30).
The integration of intention in describing a creative process is
crucial for the development of meaningful algorithms. Weisberg
explains that a painter who accidentally stains a painting—a stain
that is later applauded by the art world as an innovative technique—
cannot be considered to have achieved a creative result. Hence, al-
gorithms need to enable artists to follow their intentions with trans-
parent and controllable mechanisms.
Weisberg argues that a creator needs domain-specific knowledge
and expertise in order to come up with something novel or surpris-
ing. He rejects the common perception of creativity as being an
“unfathomable leap of insight” and advocates its systematic acces-
sibility.
Weisberg’s argument applied in the context of control mecha-
nisms leads to requiring techniques to enable artists to fully under-
stand the domain they work with. Cause and effect of interactions
as well as the overall options to control the output must be trans-
parent and navigable.
However, there also must be a large design space for a creator
to explore. Such an increase of possible options is a core aspect
of many common creativity techniques, such as brainstorming, and
must also be used for the development of digital tools [TMNY04].
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Design spaces need to be big but also meaningful and well-framed
for the domains they represent. They must provide space to delve
into without the danger of getting lost. Therefore in a system
that offers design options, all options need to make sense, while
“enabling someone to see possibilities they hadn’t glimpsed be-
fore” [Bod10]. For the discovery of unseen results, various stimuli
can be given, for example well-designed constraints.
The target audience is also an influencing factor in enabling
creativity. Each skill level requires its own unique type of sup-
port [CL14]. In the following discussion, this survey does not ex-
plicitly investigate the appropriateness of a technique for different
skill levels unless it specifically distinguishes itself from a related
work, as, for example, in BENEDETTI et al. [BWCS14]. Instead it
focuses on the general suitability of a technique to create the design
goal with a reasonable training curve for an average artist. Also,
for this first investigation, we focus on support for a single artist,
but it is worth mentioning that enabling collaborative creative work
would be a meaningful aspect to consider in the future.
To sum up the brief review in the context of control mechanisms,
we consider the categories navigation,transparency,variation and
stimulation in the context of control mechanisms. We understand
variation as the size of the design space within the context of the
technique. For the exploration of different designs we distinguish
between the general controllability necessary for navigating a de-
sign space (“there are many different roads in the landscape”), and
the transparency of that navigation and the understanding of cause
and effect when using the tool (“I have the map to the landscape
and know how to get from one point to another”). However, at this
point, these categories can be seen as somewhat loose and experi-
mental, aiming toward a better understanding of requirements for
creative controls. For these characteristics, there is no clear transla-
tion into quantifiable metrics, such as timings or error rates, which
are standardized measurements for productivity [CL14;Shn07].
Navigation
Navigation describes both whether a creation processes is effi-
ciently manageable and the extent of the controllability.
•Interactive: Refers to the lack of noticeable delays when execut-
ing controls and computing results. Lengthy, non-creative con-
figuration requirements are potentially distracting. Hence, a thor-
ough analysis should consider the whole process an artist has to
go through to produce a result.
•Number of Controls: Indicates how flexible and controllable a
technique is by counting the number of different controls that can
be adjusted for one output. Ideally, this category would refer to
the ratio in the possible output of visual features that are relevant
to humans to controllable features. This would ensure that the
controls cover all necessary features and that they complement
each other. However, the identification of generally describable,
perceptually relevant visual features is out of the scope of this
survey and left to future work.
•Navigation History: Describes the ability to go back and forth in
one’s own creation process, such as using an eraser.
Transparency
Transparency describes how clear the understanding of cause
and effect within the system is.
•Control Domain: Refers to how well controls are mapped to vi-
sual features and how well they cover the possible design range
of each feature. A high-quality control should not have any over-
lapping effects with other controls.
•Control Communication: Describes how well controls (e.g.,
with a visualization and/or little abstraction) represent their ef-
fects on the result. For artist-centered tools this could mean that
controls should be visual and directly on the canvas.
Variation
Variation indicates how visually different the results can be.
•Size of the Design Space: This is limited if all results look rather
similar to each other and are part of a specific design class. A
large design space of one technique allows, for example, com-
bining different texture classes such as stochastic and structural
creation.
•Openness of the Design Space: Refers to the limitlessness of pos-
sible designs and that there is no attachment of the technique to
a specific design class. An open design space enables an artist to
come up with a distinctive individual style. Different artists can
create inherently different and unique results with the same tool
if it has a open design space.
We do understand that a clear definition of the available differ-
ent design classes is needed. However, these depend solely on the
design task.
Stimulation
The means of stimulation indicate how well an artist can enter a
pleasurable and stimulating workflow.
•Immersion: How natural and enjoyable the usage of a system
feels. An immersive technique needs navigation to be fluent,
controls to be intuitive, and the design space large enough to
not to hit its boundaries while using the tool.
•Stimuli: The support for finding surprising results—for example,
with design suggestions or variations of the input. Options to
support stimulation are still underrepresented but on the rise with
machine learning techniques. A clear definition of this category
is not feasible at this point.
In summary, for handling the ill-defined topic of creativity, we
follow the definition of creativity as intentionally producing a novel
and surprising product. We derive the means for enabling creative
control from recent research results and relate them to control
mechanisms. We hope to further a more objective judging of the
ability of a technique to support creativity and a detailed compari-
son of methods and give an first example for that in the following
review of the state of the art.
Various aspects of our discussion guides still leave room for in-
terpretation. Knowledge from other disciplines, for example in re-
gard to the perception of visual features, can contribute with valu-
able insights. We hope that our work inspires such research towards
a quantifiable analysis of creative control.
5. Design Features
Creative patterns usually include repetitive and ordered structures
that are often considered as textures, demanding automatic and pro-
cedural creation. But they also often have a global layout, adapting
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Figure 2: Patterns showcasing the design features 1. Distribution and Repetition, 2. Frames and Hierarchies, 3. Curves,
Lines and Brushing, 4. Connections, Branches and Directionality, and 5. Single Accents. Sources, from left to right:
[LHVT17], [SP16], [JBMR18], [GJB*20], [SKAM17], [GALF17].
to the space being filled. Furthermore, these patterns often include
visual hierarchies and highlights that were placed with creative in-
tent.
With this in mind, we categorize the analysis of the state of the
art in Section 7with the design features Distribution and Repeti-
tion;Frames and Hierarchies;Curves, Lines and Brushing;Con-
nections, Branches and Directionality; and Single Accentsn. Here
we briefly explain each design feature and give a visual example
in Figure 2for each from the related work.
Distribution and Repetition refers to an overall distribution of el-
ements and usually results in a homogeneous pattern with a texture-
like quality. A careful composition of the repeating elements can be
used to create a perception of balance and order. Compositions are
not limited to the repetition of the same element, but different visual
qualities such as size or saturation can create various relationships.
Frames and Hierarchies form compositions that further structure
a design by creating contrasts, e.g., foreground vs. background, and
accentuating spatial relationships, e.g., framing.
Curves, Lines and Brushing refer to artist-defined curved ele-
ments, which are an essential design feature for many creative pat-
tern designs. They can be used, for example, as a base element or
frame or as a distinct visual element. Brushing usually gives an in-
dividual, hand-made quality to a pattern.
Connections, Branches and Directionality between base ele-
ments are often used to further emphasize frames and hierarchies.
These structures and directionality are also often used to elaborate
and accentuate the form of the space they fill, e.g., by aligning to it,
building an pattern-space relationship [ABS06].
Single Accents refer to visually dominant elements and structures
that might not follow the underlying order of a pattern, breaking an
otherwise homogeneous appearance. This design feature is based
on the principle of contrasts and accents, which is crucial for the
overall visual appeal of a creative pattern design [War96;WZS98;
MOT99].
To analyze the state of the art, we sort all work according to the
above-discussed design areas and, within each area, by the visual
features they enable. We then discuss control mechanisms used in
that area.
6. Models
In the context of computer graphics, generation techniques are usu-
ally differentiated into procedural and data-driven approaches. This
understanding applies equally to generating geometry, animations
and texture. Procedural techniques describe the visual output by
evaluating an algorithm, while data-driven approaches rely on ex-
isting data, such as photographs. However, as the field has devel-
oped, the approaches have begun to blend and their advantages have
been combined.
This survey focuses on procedural models, but it also integrates
and highlights promising or desirable characteristics of suitable
data-driven techniques.
6.1. Procedural
EBERT et al. [EMP*02] describe procedural techniques as algo-
rithms and mathematical functions that synthesize a model or an ef-
fect. Representations based solely on equations are considered the
“purest” form of procedural modeling [STBB14]. This approach
gained immediate importance in the early days of computer graph-
ics. Analytical methods were able to reproduce natural phenomena
such as wood, stone, water, smoke and plants using only a small
amount of code, hence being memory efficient. The main appeal in-
cludes compactness combined with being continuous, scalable and
not bound to a specific resolution.
The compactness and efficiency of a procedural model also en-
able parameterization, resulting in the model being responsive and
flexible. Parameters usually represent certain visual characteristics
and their prominence. Parameterization brings the crucial benefit of
textures remaining editable throughout an entire visual effect pro-
duction pipeline.
However, the effectiveness of traditional parameterization in
helping an artist fulfill design goals is debatable. EB ERT et
al. [EMP*02] argue that parameterization brings the benefit of a
few parameters controlling many details. At the same time, this is
potentially problematic for the realization of specific designs be-
cause these often require full individual control of all visual ele-
ments. Additionally, parameters are often non-intuitive due to rep-
resenting overly abstract characteristics of the underlying func-
tions and having overlapping effects [BD04;LVLD10;GD10;
BŠMM11;LLD12b;LLD12a].
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In addition to difficulties in controlling a procedural represen-
tation, creating the procedural model itself requires considerable
effort, even though it is only a one-time investment. They re-
quire translating a visual design into a technical representation and
generalizing it. For procedural textures specifically, handling anti-
aliasing efficiently can also be challenging. EBERT et al. [EMP*02]
includes a valuable and in-detail survey of function-based design
principles of procedural models with a focus on textures.
Procedural models are not limited to purely function-
based designs. For example, the pioneering work of
PRUSINKIEWICZ [Pru90] applies the grammar-based L-system
to algorithmically model plant growth, an approach extensively
investigated by the computer graphics community.
The classifications of core mechanisms for procedural genera-
tion of HENDRIKX et al. [HMVI13] in the context of games and
the categorization of SMELIK et al. [STBB14] for virtual worlds
are equally appropriate in the context of creative pattern generation.
In the following we briefly discuss core mechanisms in the context
of creative pattern generation, based on the previously mentioned
taxonomies ([HMVI13], [STBB14]).
Stochastic Models generate models by using random values. They
can either be used in their original form as procedural models or as
noise basis functions. Visual features can be added by combining
multiple layers of noise in different resolutions. Typical noise func-
tions are lattice value noise, lattice gradient noise (e.g., Perlin noise
[Per85]), sparse convolution noise, and spectral noise [EMP*02;
LLC*10]. In the context of creative pattern generation, stochastic
models build a basis for many designs but their design spectrum
and controllability are limited.
Function-based Models extend the class of stochastic models by
layering and combining a variety of functions to form a visually
complex pattern. Typical building blocks are periodic, spline, step,
clamp and conditional functions [EMP*02] and are the basis for
regular patterns designs.
Rule-based Models are part of often quite complex generation
systems that can be context-dependent and/or design-specific.
Rule-based models are programs that relate to and partition the
space to fill and follow propagation rules. The algorithmic core
often handles proxy shapes, while for the result graphical ele-
ments, such as vector graphics, are mapped to the proxies. Rule-
based procedural models are suitable for creative pattern genera-
tion and novel control mechanisms because their iterative genera-
tion logic is open and flexible [WZS98;MM12]. They can imple-
ment many designs and include any elements. Moreover, within a
suitable pipeline, they can potentially take global constraints into
consideration and build structural hierarchies.
Grammar-based Models form grammatically-correct sentences
from individual words, based on a system of rules, and they are
related to rule-based models in that the rules are using grammars or
rewriting systems. Prominent techniques are L-systems and shape
grammars. An emerging subgroup of grammar-based models incor-
porates probabilistic inference into the derivation of correct sen-
tences from a grammar. In recent years, there have been a variety
of successful grammar-based approaches for certain aspects of cre-
ative pattern generation [BŠMM11;TLL*11;RMGH15]. However,
grammars are difficult to set up and to design [ŠBM*10]. Because
the execution process is inherently hierarchical, grammar systems
have difficulty supporting creative control from a global to local
scale.
Artificial Intelligence Models represent approaches that go be-
yond the direct execution of specific rules. For example, they au-
tomatically optimize results based on fitness or error functions, or
they apply planning steps. HENDRIKX et al. [HMVI13] group this
class into genetic algorithms, neural networks, and constraint sat-
isfaction and planning. In recent years, machine learning has been
introduced into procedural content generation with the same impact
as in all other computer science fields [SSG*17]. The potential of
machine learning techniques in regard to creative pattern genera-
tion and their control mechanisms seems almost limitless.
6.2. Data-Driven Models
We classify methods for creative pattern generation as data-driven
when they extrapolate from limited data such as the pixels from
an image. Data-driven models traditionally do not include underly-
ing design models, as procedural representations do. Consequently,
data-driven approaches are flexible in terms of possible designs and
can achieve photorealism by processing real images.
At the same time, images often include visual features such as il-
lumination effects that are unwanted and difficult to remove. More-
over, further down a production pipeline, pixel data is usually no
longer editable. Working with high-resolution images leads to high
memory requirements, and without additional algorithms, data is
fixed to a given resolution and scale.
Addressing the issue of resolution in example-based synthesis
is a well-established field of research that aims to create an infinite
amount of pixel data based on a given exemplar. The pyramid-based
texture synthesis of HEEGER et al. [HB95] is an early famous ex-
ample. WEI et al. [WLKT09], as well as BARNES et al. [BZ17]
present comprehensive summaries of such example-based texture
synthesis techniques, discussing statistical feature matching, neigh-
borhood matching, patch-based and optimization methods. Overall,
example-based methods for texture synthesis have achieved similar
results in data size, random accessibility and editing and resolution
options as procedural textures—but only within specialized con-
texts and not in a unified manner. Procedural textures offer these
capabilities as inherent characteristics.
Data-driven models are numerous and diverse because they need
no underlying procedural model. In the following survey of the
state of the art for creative pattern generation, we include various
data-driven techniques, however an overall classification is not the
focus of this work. Relevant techniques include the tiling and dis-
tribution of elements and drawing and brush mechanisms.
6.3. Specific Pattern Designs
In this section we review models that output specific pattern de-
signs, which could be the basis for creative pattern generation. The
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Figure 3: Examples of traditional Islamic (left) and Celtic pattern
designs, showing the complexity of possible pattern designs. Image
sources: [12, 13].
references in this section summarize work that solely focuses on the
output, offering little control or support for a creative creation pro-
cess. Work that produces similar aesthetics but also offers control
mechanisms (e.g., [WZS98;CSC12;ZCT16]) is reviewed in Sec-
tion 7.
Work on the generation of pattern designs is spread over vari-
ous research communities. For the development of models WHI TE -
HEAD [Whi10] differentiates between two motivations in the con-
text of generating models for ornamentation in games. First, the au-
thor identifies the goal of reproducing existing patterns such as Is-
lamic and Celtic designs. Such work is mainly found in the commu-
nities of mathematics and computer science. Second, WHITEHEAD
identifies the goal of generating novel pattern designs, which is held
mainly by algorithmic computer artists. Such designs are usually
not executed in an academic context and, beyond the presentation
of the results, are unfortunately not well documented. Only a few
exceptions, such as the work of TAKAYAMA [Tak16] in 3D-printed
ornate shapes or ALVAREZ et al. [AMM19] in randomized abstract
texture designs give much information about their underlying algo-
rithms.
For what WHITEHEAD [Whi10] calls mathematical/scientific or-
namentation in the context of games, the author describes tiling
and symmetry as the most relevant rules. Combined with interlac-
ing parts of the pattern while repeating and tiling elements, these
principles are able to systematically describe Islamic [Ost98] and
Celtic [Cro93] patterns, moving towards the traditional designs
given in Figure 3.
The seminal work of KA PL AN et al. [KS04] presents an algorith-
mic representation of Islamic star patterns, a topic of ongoing in-
terest [KB18]. Readers further interested in this line of work are re-
ferred to the extensive investigation of KAPLAN [Kap02]. ETEMAD
et al. [ESP08] and HAMEKASI et al. [HS12] also focus on Islamic
flower patterns. Celtic designs were also successfully computed
by KAPLAN et al. [KC03] and DOYL E and SE MWAL [DS13].
In addition to Islamic and Celtic designs, a variety of other
pattern designs have been algorithmically formalized, such as
Gothic window tracery [HF04], M. C. Escher patterns [DLW81;
KS04], woodwork [GTS10;GSK12], optical illusions [CYZL14],
mazes [PS06] and tile-based patterns [OZH15;Gda17].
7. Analysis of the State of the Art
This survey analyzes the control mechanisms in the state of the
art for creative pattern generation from the perspective of an artist.
Techniques are evaluated as a whole, including required configura-
tion input, what they can create, and performance times. The anal-
ysis of the control mechanisms is directly taken from the authors’
descriptions.
The analyzed works are categorized by design features they can
create. The categories are Distribution and Repetition;Frames and
Hierarchies;Curves, Lines and Brushing;Connections, Branches
and Directionality; and Single Accents (Section 5, Figure 2). Within
those design areas we investigate how an artist can create such de-
signs and how control mechanisms are clustered for each design
feature. Common clusters include example-based, field-based, and
data-driven control mechanisms. In Table 1all design features and
discussed publications are cross-linked to the following sections.
If a work belongs to several design categories, it is discussed in
detail in the most fitting area and then briefly referenced in other
applicable areas. Techniques are considered procedural unless in-
dicated otherwise. As it is the nature of procedural generation to au-
tomatically fill a space upon execution, we include the shapes cat-
egory for all procedural systems in Table 1even though this might
not be mentioned in a publication. If a publication does not specify
how the shape to be filled is provided, we consider the control to be
code given by a file.
7.1. Distribution and Repetition
Designs with a repetitive pattern and a distribution of elements can
be viewed as texturing methods. In the following, we further dif-
ferentiate between stochastic, regular-to-near-regular, and design-
specific patterns, as well as element arrangements. Texture gen-
eration mainly focuses on creating a repetitive and homogeneous
pattern as automatically as possible. These methods usually pro-
vide only part of the design space and controllability that is needed
for creative pattern generation. They are applicable to sub-parts
with a texture-like quality, such as background regions and fills.
Because texturing has been the driving force behind much of the
development of procedural representations, it produced manifold
approaches and noteworthy control mechanisms. Throughout this
section, we identify clusters of example-based, field-based, proba-
bilistic interference, and data-driven methods for the design feature
of Distribution and Repetition.
7.1.1. Stochastic Pattern
Stochastic textures have been the foundation of both research in-
vestigations and many complex models. They are generated with
noise functions, and LAGAE et al. [LLC*10] present the state of
the art for work before the year 2010. Figure 4shows a typical
visual appearance for a stochastic pattern. For controlling the tex-
tures, the authors identify three main approaches: indirect access
to the noise through controlling the power spectrum (also shown
in Figure 4), direct access to its appearance through function pa-
rameters, and example-based techniques. The first two approaches
are based on specific function characteristics and are hardly gen-
eralizable for creative pattern generation. Also, for stochastic pat-
terns, related work usually focuses on defining a new model. Then,
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INIT. EXEMPLARS PARAM. HANDLING FILLING GUIDING PLACE.
Configuration
Initialization
Image
Arrangement
Element
Visual Output
System
Visualization
Image
Sketch
Shapes
Masking
Curve
Brushing
Directions
Element
Drag & Drop
DISTRIBUTION AND REPETITION
Stochastic
GALE RNE et al. [GLLD12]× × × ×
GILE T etal. [GDG12a]× × × × ×
GILE T etal. [GSV*14]× × × × ×
PAVIE et al. [PGDG16]× × × × ×
GUINGO et al. [GSDC17]× × × × ×
KANG et al. [KH17]× × × ×
GILE T etal. [GD10]× × × × ×
Regular to Near-Regular Patterns
LEFEBVRE et al. [LP00]× × × × ×
GILE T etal. [GDG12b]× × × ×
BOUR QUE et al. [BD04]× × × × ×
GIES EKE et al. [GKHF14]× × × × × ×
HUet al. [HDR19]× × × × ×
GUEH L etal. [GAD*20]× × × × × ×
BIAN et al. [BWL18]× × × ×
LIet al. [LBMH19]× × × ×
TUet al. [TWY*20]× × × × × × ×
ZEHN DER et al. [ZCT16]× × × × × ×
CHEN et al. [CZX*16]× × × × ×
Rule- and Design-Specific Patterns
WONG et al. [WZS98]× × ×
LOI et al. [LHVT17]× × ×
TALTON et al. [TLL*11]× × × × ×
RITCHIE et al. [RMGH15]× × × × ×
LIet al. [LBZ*11]× × × ×
ŠT’AVA etal. [ŠBM*10]× × × × ×
TALTON et al. [TYK*12]× × × × ×
Element Arrangements
BARL A etal. [BBT*06]× × ×
HURTU T etal. [HLT*09]× × ×
IJIRI et al. [IMIM08]× × × × × × ×
MAet al. [MWT11]× × × × × × ×
ALMERA J etal. [AKA13]× ×
LANDES et al. [LGH13]× × × × ×
SAPU TRA et al. [SKAM17]× × × × × ×
SAPU TRA et al. [SKA18]× × ×
FRAMES AND HIERARCHIES
ANDERSON et al. [AW08]× × × × × ×
BENE S etal. [BŠMM11]× × × × ×
SANTO NI et al. [SP16]× × × × ×
GIES EKE et al. [GALF17]× × × × × × × × × × ×
CURVES AND BRUSHING
CHEN et al. [CSC12]×
XUet al. [XM09]× × × ×
MERR ELL et al. [MM10]× ×
Mˇ
ECH et al. [MM12]* × × × × × × × ×
HSU et al. [HWYZ20]× × × × × × ×
JACOB S etal. [JBMR18]× × × × × × ×
LUet al. [LBW*14]× × × × ×
ZHOU et al. [ZJL14]× × × × × ×
KAZI et al. [KIZD12]× × × × × × × ×
XING et al. [XCW14]× × × × × × × × ×
CONNECTIONS, BRANCHES AND DIRECTIONALITY
GUO et al. [GJB*20]× × × × × ×
SINGLE ACCENTS
YEH et al. [YM09]× × × ×
GUER RERO et al. [GBLM16]× × × × ×
Table 1: Recent techniques, sorted by design areas and visual features. The specific control mechanisms each work offers is marked. *Note
that Mˇ
ECH et al. [MM12] present a procedural modeling engine, which in principle can be programmed to include almost any control type.
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Figure 4: In blue, Gabor noise examples. To their right an inter-
active visualization of their power spectrum for editing the visual
characteristics. [GLLD12].
the control of that model often directly derives from that specific
model.
Example-Based Most example-based stochastic texturing tech-
niques do not offer further artist input beyond the exemplar but
focus on performance. LAGAE et al. [LVLD10] match noise band-
width for isotropic multi-resolution noise in a few milliseconds, as
described by GI LE T et al. [GDG12a]. GA LE RN E et al. [GLM17]
introduced an efficient sparse convolution noise based on textons.
The example match takes between half a second and five seconds,
depending on the resolution.
GALERNE et al. [GLLD12] add an interactive visual editor for
adjusting their Gabor noise to the example fitting, and take about
two minutes per texture. Sets of Gaussians represent the power
spectrum of the noise, which can be rotated, scaled, translated, and
cloned. Due to the abstract visual nature of a power spectrum, its
connection to the visual features of the noise is not directly intuitive
for artists. Hence, the editor has a strong exploratory nature to it.
However, as the editing itself is interactive and visually appealing,
it is inviting to do so.
GILET et al. [GDG12a] focus on increasing the expressiveness
of their model toward more structural texture designs. For that,
they introduce a noise that can approximate arbitrary spectral en-
ergy distributions. A straightforward noise-by-example computa-
tion takes up to 20 seconds, depending on the number of artist-
defined convolution noises. For greater control and expressive-
ness, a perturbation function and a multi-layer approach are pre-
sented and some configurations can be given by artist-defined im-
age maps. Further pursuing the topic of greater expressiveness and
structured noise, GI LE T et al. [GSV*14] introduce a local random
phase noise. Adjustable parameters control the visual quality of the
noise and the amount of structure in comparison to noise. The au-
thors do not report performance times for the matching step. PAVIE
et al. [PGDG16] argue for control mechanisms being more intu-
itive in the spatial domain instead of the commonly-used editing of
the power spectrum and align local random phase noise on a reg-
ular grid with a spot noise model based on a random distribution
of structured kernels. Artists have interactive control of the spatial
structures by modifying the spot functions and their distribution,
thus increasing the range of possible designs.
Figure 5: Visual examples of regular to near-regular pattern de-
signs [GKHF14].
GUINGO et al. [GSDC17] further improve on spatial varia-
tion and visual quality. They base their work on an underlying
novel noise model and separate the handling of structures. Artists
need to configure the fitting, and the performance of matching a
512×512 input image can take up to one hour with the current non-
parallelized implementation. KA NG et al. [KH17] combine pro-
cedural noise with a data-driven tiling. So-called “non-features”
are obtained by a noise-by-example method. “Features” such as
edges can be edited in the feature image and are combined with
the noise based on an artist-controlled ratio. The feature extraction
for a 257 ×257 input image, and therefore the texture matching,
ranges from few seconds to two minutes. GILET et al. [GD10] ap-
ply a more general optimization strategy for choosing the param-
eters of a noise-based model. With a given estimated light source
direction in the input, GI LE T et al. [GD10] can create displacement
map textures, with the parameter computation taking from one to
three hours. With a given rough approximation of the geometry and
a representative pattern patch in the input, even volumetric repre-
sentations can be created from the exemplar.
7.1.2. Regular to Near-Regular Patterns
All the above discussed noise-based methods control a single
stochastic procedural model. Even though recent advances greatly
increase their expressiveness, the design space of noise-based mod-
els is too limited for creative pattern generation. Procedural models
featuring regular to near-regular pattern designs (for a definition of
the texture spectrum see LIN, HAYS, WU, et al. [LHW*06]) are
usually optimized for specific design goals or even support a va-
riety of procedural models within this class of designs. Figure 5
shows several regular to near-regular patterns.
Example-Based For brick and wood textures, the early work of
LEFEBVRE et al. [LP00] presents example-based control by trans-
ferring specific measured properties of an input to corresponding
parameters for the procedural representation. The authors describe
the matching performance as taking from a few minutes up to an
hour. Expanding the design range notably, GILET, DISCHLER, and
GHAZANFARPOUR [GDG12b] focus on the interactive creation of
procedural semi-structured texture models and their visual features.
Random variations of artist input pattern are generated considering
hierarchical spatial relationships, . In order to do so, an artist needs
to give multiple exemplary object distributions.
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BOURQUE et al. [BD04] allow for the whole procedural tex-
ture spectrum with a parameter retrieval technique. For the fitting,
artists need to chose a configuration from two types of similarity
metrics and two types of optimization strategies. As initialization
for the optimization, the authors propose “on the order of 200” pre-
computed random choices. The authors report an average optimiza-
tion time of 12 minutes, not specifying for how many parameters.
However, GILET et al. [GDG12a] report more than an hour run-
time. With a higher number of parameters the current form of the
approach quickly becomes unfeasible. GI ES EK E et al. [GKHF14]
build up on the work of BOURQUE et al. [BD04] and interpret
the parameter matching as retrieval task. Based on precomputed
caches and a perceptually motivated image metric, their technique
achieves interactive performance for fitting a 256×256 exemplar.
An artist has to chose the texture model to be matched. A similar
approach by HUet al. [HDR19] trains convolutional neural net-
works for the parameter retrieval. A style transfer step in the pixel
domain is added for fitting visual details. The user has to chose
from four high level texture classes presented next to the given in-
put example. With the precomputed caches ready, the fitting is in-
teractive, with performances around one second, depending on tex-
ture resolution. The style transfer itself takes several minutes. Over-
all, for parameter retrieval methods the parameter count is highly
influential on the performance for both visual quality and compu-
tation time. Heavy one-time investments must be made to compute
the caches or train the network, which then determine the possible
design spaces. Artists could use such techniques for computing a
reasonable starting point for their creative work.
While focusing on stochastic patterns, the semi-procedural ap-
proach of GU EH L et al. [GAD*20] offers a much larger design
space than related methods by enabling the combination of pat-
terns. The technique generates textures based on input exemplars
and gives an artist the option for manual editing and database
browsing to shape the output (Figure 6) At its core the system is
based on a noise-by-example approach. The appearance space of
the noise can be explored with an interactive 2D map and brows-
ing a database of preview images, which are unusual options for
example-based modeling. The interactive 2D map is visually ab-
stract and not suitable for reaching a specific output quickly but
is helpful for exploring the design space. Data-driven details are
smoothly combined with the noise and the user can adjust the out-
put with different parameters. The system is interactive with re-
ported synthesis times below one second.
Data-Driven By adding appearance as an objective when
optimizing for a structurally sound topology, MART ÍN EZ et
al. [MDLW15] offer a data-driven example-based approach. Exam-
ple patterns are given as raster images. The authors report on perfor-
mances between 1 and 15 minutes for exemplars up to 330×330.
BIAN et al. [BWL18] build upon that work by controlling topol-
ogy appearance with custom-made vector pattern tilings. The tech-
nique is worth pointing out for automatically helping an artist create
structurally sound connections between manually drawn tiles. Tiles
can be drawn from scratch. The interactive interface gives hints and
corrections for the construction of structurally sound designs, such
as previews of the pattern on the canvas, snapping to proper cor-
rection points, and automatic corrections near tile boundaries. Sim-
Figure 6: GUEHL et al. [GAD*20] offer various control mecha-
nisms for a semi-procedural generation of stochastic patterns. Ex-
amples are from the supplemental video. With the different controls,
an artist can work exploratively as well as implement a specific de-
sign goal efficiently.
ilarly, LIet al. [LBMH19] optimize for structural soundness when
putting decorative elements together to generate quilting patterns.
A user inputs the decorative element, a region boundary and config-
uration values. Then a quilting pattern is generated automatically.
There are no further adjustments of the result possible. The perfor-
mance is below ten seconds.
Similar to the interactive authoring of BIAN et al. [BWL18], TU
et al. [TWY*20] merge automation with manual creation. The algo-
rithm synthesizes continuous curve patterns from exemplars made
of BÃl’zier curves, replicating not only on the position of the el-
ements but also on their connectivity. The authors report match-
ing times of 160 seconds depending on the sampling density. The
example-based generation process is supported by various artist-
controllable interactions before, during and after the creation pro-
cess. Connections are continuously recomputed. An artist can also
draw the example and connections directly on the canvas from
scratch.
ZEHNDER et al. [ZCT16] provide artists with a tool to directly
assemble structurally sound curve networks on a three-dimensional
surface in 3D. The components of the network are spline curves
defined by the artist. Components can be placed manually or are
repeated semi-automatically. The curves can be moved on the sur-
face while having an elastic quality to them, which seems to be a
quite engaging task. To prevent structural weaknesses, the system
indicates problematic areas and suggests improvements, seamlessly
combining the design task with engineering requirements. The per-
formance of the automatic packing highly depends in the number
of curves and ranges from seconds up to 15 minutes on average for
the presented examples. For filigrees, which are thinly structured
repetitive patterns, CHEN et al. [CZX*16] present a mainly data-
driven approach. Their method automatically distributes and as-
sembles a set of suitable input elements. The filigrees are mechan-
ically strengthened through the optimization of a packing problem,
which must be configured by the artist. Additionally, a directional
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stroke field can be drawn on the canvas, controlling element orien-
tation and size. Element distribution percentages can be given when
multiple elements are combined into one common pattern. The per-
formance in two-dimensional space runs from 6 to 26 seconds.
Within their specific design spaces, the example-based data-
driven techniques of BIAN et al. [BWL18], TUet al. [TWY*20],
and ZEHNDER et al. [ZCT16] highlight the promising direction of
automating filling and repetition, and computing, e.g., structural
constraints, while giving an artist enough interactivity for creative
exploration.
7.1.3. Rule-based and Design-Specific Patterns
In the following we summarize designs that are based on a specific
set of rules or grammars, as for example the ornamental patterns
shown in Figure 7or the tangles pattern in Figure 9. Hence, there
are no limits to their expressiveness other than their underlying cre-
ation logic. Also, the following section discusses techniques that
focus on filling global shapes, often supporting masks.
WONG et al. [WZS98] introduced a programmable procedural
system that employs a greedy rule-based strategy to generate or-
namental patterns. A procedural model is created with decorative
elements and with a set of growth rules that handle the selection,
appearance and connections of the elements. The process iterates,
finding tentative places for elements by testing them against con-
straints in the procedural model and, where suitable, placing ele-
ments in the found spaces, optionally connecting them to existing
elements. Possible ornament designs are technically restricted only
by this iterative creation logic. All adjustments to the design and
layout of an ornament have to be done by writing code. The au-
thors do not report any performance times.
SANTON I et al. [SP16] and GIESEKE et al. [GALF17] present
rule-based and design specific patterns. These techniques feature
frames and hierarchies and are discussed in Section 7.2). LOI et
al. [LHVT17] present a custom-made procedural framework that
can create a large variety of element texture designs. The authors
aim for designs that are unrelated to their spatial location and the
Figure 7: Visual examples for the rule-based iterative space filling
model from WONG et al. [WZS98].
space they fill, calling it stationary. Their programmable method is
developed for technical artists and requires programming expertise.
Pattern scripts are built with partitioning, mapping and merging op-
erators. These operators enable both global and local design con-
trol and the composition of designs. The operator-based technique
would enable a node-based interface design, which is not explicitly
demonstrated in the article. The execution time for most designs
is a few seconds, with some examples taking more than 1 minute.
A user study with technical artists carefully evaluates the system’s
scripting interface, concluding positive results overall.
Probabilistic Interference Other systems provide the control to
fill an outlining shape by interpreting the procedural modeling task
as a probabilistic inference problem.
TALTON et al. [TLL*11] extend grammar-based procedural
models by decoupling the growth control from the grammar itself.
Their flexible analytic objective functions take images and volumes
as global controls. The authors discuss that some experimentation
might be needed to achieve a desired design goal, making the ap-
proach less transparent. Performance depends on the complexity of
the grammar and the number of optimization steps needed. The au-
thors report performance times ranging from a few seconds to sev-
eral hours. For their examples, the authors manually terminated the
optimization iteration. Similarly, RITCHIE et al. [RMGH15] con-
trol rule-based hierarchical and iterative procedural models with
image-based matching and target volumes. The work improves
convergence behavior and final scores. The reported performances
range from around 3 seconds to 12 minutes, and the authors show
that the number of included primitives scales reasonably. RITCHIE
et al. [RTHG16] uses machine learning to improve the performance
even further, increasing performance up to 10 times by integrating
a neural network and sampling a learned constraint-satisfying ap-
proximation. Reported performances are overall below 3 seconds.
As interactive performance is the foundation of creative control,
this is of great importance.
Fields Fields have been used to creatively control the appearance
of patterns with great success for several design features, meriting a
separate discussion of them as control mechanisms in Section 8.3.
In the present context, for repeating structures and filling shapes,
LIet al. [LBZ*11] present a shape grammar that is guided by ei-
ther a vector or tensor field. The field can influence the grammar’s
translation command, potentially leading to globally pronounced
structures. The field can furthermore guide rotation, scaling, and
color parameters. The artist can specify a priori field constraints,
such as regular and singular field elements, on the surface to be
filled. Once the field is computed, local Laplacian smoothing can
be applied. The authors report a synthesis performance for geomet-
ric surfaces from less than a second up to 3 minutes. Recently, by
applying a parameter field and a density field for controlling the
appearance, ETIENNE et al. [EL20] present the procedural genera-
tion of band patterns as pixel shader in real time. Both fields can be
controlled by image input.
Example-Based ŠT’AVA et al. [ŠBM*10] present a context-free
L-System that is able to recreate a given two-dimensional vector
image consisting of groups of line segments. The algorithm creates
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similarity groups of these basic elements, computes spatial rela-
tionship clusters and iteratively translates these into rules. An artist
is required to define a similarity threshold and significance weights
for the different clusters, such as element distance or similarity,
for example, thus guiding their representation according to the L-
system rules. The time needed for the inverse step, depending on
the number of elements in the input, is reported to range from a few
seconds up to 20 minutes. TALTON et al. [TYK*12] further gener-
alize the idea of inverse grammar generation and interpret it as a
probabilistic interference problem. Their system induces a proba-
bilistic formal grammar from a hierarchy of labeled components.
The authors demonstrate their technique on scene graphs for ge-
ometry models as well as DOM trees for web layouts. The authors
do not report any performance times for learning design patterns.
7.1.4. Element Arrangements
Element arrangements, such as shown in Figure 8, have individ-
ual and unconnected visual entities as their smallest unit. The ele-
ments themselves usually come from separate input data, such as
vector graphics. In its broadest sense, the underlying distribution
models for the arrangements can be seen as a procedural model.
Even though there are no generative rules, characteristics of the
discrete elements and their distribution can often be parameterized,
and changes can be automatically processed and reproduced in the
output. When filling a shape with elements or masking areas on the
canvas, elements ideally should not be cut and should align them-
selves to evenly fill the shape.
Example-Based For an example-based generation of element ar-
rangements, relationships between elements are usually extracted
from example arrangements and reproduced for the synthesis. In
the following, we only include techniques with some form of user
input beyond non-creative system configuration parameters. Much
previous work [PH19;CXL19] focuses mainly on point distribu-
tions.
BARLA et al. [BBT*06] and HURTUT et al. [HLT*09] focus on
example-based element arrangements of stroke-based vector ele-
ments. BAR LA et al. [BBT*06] synthesize arrangements by match-
ing local neighborhoods to a global seed distribution computed by
Lloyd relaxation. Computing arrangements takes up to 10 seconds,
and artist input is used in addition to the stroke patterns. Further
visual adjustments are possible in a post-processing step. HU RTU T
Figure 8: An example for a pattern in 3D made of discrete ele-
ments [MWT11]. MAet al. also offer extensive editing options such
as the propagation of the edit of a single element to the overall pat-
tern.
et al. [HLT*09] can capture non-uniform distributions and improve
the performance to the order of seconds. As a possible artist input,
one exemplary shape input and density map are shown, and other
input options are discussed in principle. The authors clearly state
their focus to be on automation.
IJIRI et al. [IMIM08] combine data-driven texture synthesis with
procedural generation. Their technique analyzes a given element
distribution with local neighborhood comparisons and synthesizes
new arrangements with interactive performance with incremental
rule-based local growth. Element attributes that go beyond the po-
sitions of the elements and orientation cannot be controlled. Artists
have a variety of design options with element orientation modes,
an interactive spray tool to define areas to grow in, a flow field
tool to define overall alignments and a boundary tool. Moreover,
the reconstructed topology can be manually adjusted. This work is
an early example of combining a data-driven with a procedural ap-
proach. The tools allow artists to work on the canvas directly and
to focus on the actual output, even with procedural models.
The technique of MAet al. [MWT11] is based on a sample of
a discrete element distribution and a shape to fill, both in two and
three dimensions. The exemplar has to contain the actual elements
in their domain and cannot be pixel data. In order to fill the output
shape with elements, an energy optimization is processed with a
novel neighborhood similarity metric. In addition to element posi-
tions, the metric includes variable features referring to orientation,
geometry, appearance and type, for example. Hence, the metric is
capable of reproducing global aggregate distributions that go be-
yond local element placements. The authors also extended their
work to the spatial-temporal domain [MWLT13]. Necessary in-
puts are the exemplary element distribution, the neighborhood size
to consider and the output shape. Further distribution constraints
based on element attributes are optional. Examples for the inclu-
sion of a vector field and element drag and drop are given. The au-
thors report performance times between one and ten minutes with
a non-optimized implementation.
ALMERAJ et al. [AKA13] base their example-based geometric
texture generation technique on how such textures were manually
created in a previous user study [AKAL11]. The idea of developing
a generation algorithm based on a systematic study of how artists
manually create patterns is worth further investigation. The authors
identify tiling, structure and randomness as the prominently used
creation strategies. The patch-based algorithm, which focuses on
eliminating the appearance of regularity, doesn’t seem to allow for
any user interaction. The authors do not report on the performance.
LANDES et al. [LGH13] present an element distribution technique
in 2D as well as 3D that improves on collision-free and anisotropic
distributions with spatial relationship measurements. Next to the
exemplar, there are several possible user inputs, such as a gradient
image for the distribution intensity and parameters for the fitting
algorithm. Even though these can control a visual range, their com-
munication is quite abstract. Performance ranges from seconds to
several minutes depending on the complexity of the arrangement.
Fields SAPUTRA et al. [SKAM17] optimize a flow-based orna-
mental packing of elements into a two-dimensional outline. For
each element, a predefined spine controls the element’s deforma-
tion. The artist defines direction guides and optionally fixed ele-
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Figure 9: An example for a tangle pattern from SANTO NI et
al. [SP16]. On the left, the automatically generated tangle pattern
and on the right the pattern is further edited by an artist.
ments that control the computation of evenly placed streamlines.
Elements are placed and deformed along streamlines. An iterative
refinement step optimizes for a dense and balanced filling. An av-
erage packing takes about an hour. SAPUTRA et al. [SKA18] build
up on their previous work substituting the flow-based packing with
a mass-spring system. An additional secondary packing step fur-
ther fills gaps with simpler shapes. With that the technique achieves
denser and more even packings. A user provides primary and op-
tionally secondary elements, the closed shape to fill and a distance
for the spacing between elements. Packings take between 2 to 20
minutes, including both the packing of the primary and secondary
elements.
HSU et al. [HWYZ20] present an interactive brushing system
for placing aggregations of elements directly. As the work stands
out through its brush-based control mechanisms, we discuss it in
Section 7.3.
Data-Driven PHAN et al. [PLA*16] offer a data-driven rec-
ommendation system for circular ornamentation, employing a
machine-learned style and composition feature vector. Based on
a custom ring-based layout system that represents, for example,
plates and vases, and an initial decorative element chosen by the
artist, the system completes a design. The artist can also chose to in-
crementally add elements manually, while the system accompanies
this by suggesting suitable elements and placements. This work in-
dicates the promising direction of using learned characteristics for
tools that stimulate with, e.g., meaningful design suggestions.
7.2. Frames and Hierarchies
For the design feature of Frames and Hierarchies, results usually
consist of different patterns in different areas (Figure 9). Frames are
either based on filling a frame-shaped space or on lines and curves.
This type of control usually gives an artist more direct visual con-
trol than the previously discussed methods, which mainly focus on
filling a shape. In addition to the visual output being further struc-
tured, the control is put onto the actual canvas.In the following, we
cluster this work based on curves, shapes, and masks.
Curves ANDERSON et al. [AW08] place discrete elements on the
sides of an artist-given curve based on techniques from WONG et
al. [WZS98]. The artist can input masks and use proxies to control
the size and type of elements to be placed next to the curve. Two
interfaces exist, the interactive view and the buffer view. The au-
thors do not report a user study or specific performance times but
call their system interactive.
Shapes and Masks BE NE S et al. [BŠMM11] offer a complex
shape-filling and masking system for procedural L-system models
by dividing a target space into artist-editable guide shapes. Seeds
for the L-system are interactively given by an artist as a position
and orientation. The guide shapes determine what types of patterns
grow in different areas. The connections between the shapes are
manually specified by the artist and in turn guide the connections
between elements, possibly creating frames and emphasizing hi-
erarchies. Based on a mass-spring system, the guides can be intu-
itively edited as a whole. The authors report 30 minutes to one hour
for inferring the L-systems. The generation times for most pattern
examples are less than a second, with up to 45 seconds for only one
complex scenario.
SANTON I et al. [SP16] present the design-specific generation
of tangles with a stochastic shape grammar. Tangles are repeti-
tive black-and-white hand-drawn patterns made from dots, straight
lines, simple curves and circles (Figure 9). The visual elements
of Tangle patterns can align to the shape they fill and this align-
ment can create borders, frames and hierarchies automatically. A
tangle generation usually takes a few seconds, with a complex ex-
ample taking about 3 minutes. The authors present an interactive
system for creation based on a parameterized artist interface, in-
cluding rule re-expansion and sketch-based operator modification.
The presented system is a powerful combination of editing opera-
tions with procedural generation. The work also includes naviga-
tion through the editing history, which is noteworthy as this basic
operation needed for creative control is usually overlooked. A user
study evaluates the system as accurate, controllable and easy to use
after a reasonable training time.
Curves, Shapes and Masks Also building upon WON G et
al. [WZS98], GIESEKE et al. [GALF17] offer, among other fea-
tures, several mechanisms to create frames and hierarchies for pro-
cedural models. The authors specifically focus on generating pro-
cedural ornamentation. At the core of their system, procedural el-
ement placement can be combined with custom-made placement
functions that enable global design constraints such as symmetry.
An artist can control the overall growth of the pattern as well as the
connectivity of the elements by drawing frames and paths directly
onto the canvas or by designing a vector field by sketching its direc-
tions. While all editing steps are interactive, more complex designs
can have computation times up to several minutes, depending on
the chosen placement functions.
7.3. Curves and Brushing
For the design feature of Curves and Brushing, we consider curves
and brushing as visual elements, as well as an overall control mech-
anism, which in turn leads to a distinct visual style. Figure 10 give a
visual example of both approaches. For brushing, we further cluster
data-driven mechanisms and feature-exploration techniques.
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Figure 10: Left, an example for curves used as control mechanism
for a data-driven approach [LBW*14] and on the right for proce-
dural pattern generation [MM12].
Formed curves such as circles, spirals or hearts are essential
components for many pattern designs, including ornamentation,
and are discussed first. Incorporating an artist-defined curve as
the spine of a pattern, CH EN et al. [CSC12] use an interactive L-
system to attach decorative spiral designs to the curve given by an
artist. XUet al. [XM09] use the space-filling algorithm of WON G
et al. [WZS98] in combination with particle tracing in simulated
magnetic forces for the generation of decorative curves. Physical
properties and the initialization of the particles are the parameters
for designing the curves. The computation takes less than five sec-
onds. The authors acknowledge the non-intuitive parameterization
of the system and give an example timing of two minutes for finding
the parameters of a specific design goal. ME RR EL L et al. [MM10]
generated a set of curves in the same style of a given parametric
example curve. A style is defined by local properties, such as tan-
gents and curvatures, that are derived from a local shape analysis.
The new curves are computed with a rule-based system that allows
artists to interactively edit the result. Interactivity is somewhat di-
minished by computation times of up to minutes for a curve set.
For more individual designs, brushing methods create output
along curves but do so directly without taking an a priori com-
pleted curve into consideration, as if using a spray can or a brush.
Brushing techniques usually include a brush diameter, giving the
size of the area to be filled along the curve. M ˇ
ECH et al. [MM12]
present the flexible Deco procedural engine and examples of brush-
ing methods for different aspects of generating procedural models,
from brushing growth constraints, such as masks, to having a pat-
tern grow along the strokes. This discussion only refers to the ac-
tual examples given by the authors. However, the engine opens up
and generalizes environments for interactive control mechanisms
for various types of procedural models. For the programming of
decorative pattern models within the engine, helpful functionali-
ties, such as symmetry objects and control guides, are predefined.
All artist control mechanisms have interactive performance. Over-
all, performance mainly depends on the pattern generation scripts.
The engine can load pattern codes as a dynamic library, optimizing
performance.
For texture generation, there are various methods that have
successfully combined texture synthesis with a brushing inter-
face. For example, LU KÁ ˇ
Cet al. [LFA*15] present an interactive
example-based brushing system that processes user-given shapes
and directions for the features of the synthesised texture. HS U et
al. [HWYZ20] builds on this, presenting an interactive brushing
system for placing aggregations of elements directly. The work fo-
cuses on an even distribution and on resolving collisions. An artist
can do add, erase and replace operations with the brush and also
sketch a density map. The brushing is combined with an autocom-
plete functionality with element fields to control the automatically
filled elements’ alignment based on brushed directions. Filling is
computed by iteratively optimizing the scale, orientation and posi-
tion of the elements. Elements can be rigid or be deformed through
the packing. The technique is applicable for 2D planes, 3D surfaces
and 3D volumes. Performance is below 30 seconds for 2D repre-
sentations. Overall, this work is a convincing combination of man-
ual creation with automation for creating creative element arrange-
ments. DAVISON et al. [DSJ19] add to the work with a brushing
technique that employs several example arrangements as palettes,
which can be freely combined.
More painting-like methods can be found, for example, in proce-
dural botanical modeling [APS08;CNX*08;PHL*09], procedural
landscape generation [EVC*15], as part of a procedural water color
engine [DKMI13] or for dynamic effects [XKG*16].
Going far beyond simple curve structures, JACOBS et
al. [JBMR18] developed the programming and drawing environ-
ment Dynamic Brushes, in which an artist can create individual
procedural brushes for a stylus pen. General programming logic
and relevant mathematical functions for creating patterns are trans-
lated into a visual programming interface. The evaluation of the
system by two professional artists shows that once initial struggles
to learn the system were mastered, the artists were able to capture
their personal analog styles with the procedural brushes. Overall,
the authors and the artists open many valuable questions about the
usage of current tools and about alternative approaches that seek
to seamlessly blend manual and procedural creation processes. De-
mystified Dynamic Brushes [LBM*20] expands on this by giving
an artist further options, e.g., with visualizations on the canvas to
investigate the linking between the procedural modelling and the
visual output. Also, the creation history is recorded and can be nav-
igated. Overall the evaluation of the system with artists indicates
that a tighter bond between visual work and programming tasks
make procedural modelling more accessible to artists.
Data-Driven LUet al. [LBW*14] create a pattern along a sketched
curve with a data-driven approach. Vector pattern exemplars are
placed and deformed along the curve using optimized visual sound-
ness. For the exemplars, an artist has to define the start and end
point of their spines. The artist can refine results with “add” and
“erase” constraints that are drawn on the canvas. The authors re-
port a performance of an average of eight seconds per stroke for
the examples given. A related data-driven approach for synthesiz-
ing example-based vector patterns along a curve was presented by
ZHOU et al. [ZJL14] in the same year. In this work, the authors
focus on ensuring a structurally sound output pattern. Artists can
input topological constraints, local pattern orientations and a value
for variation. Once a pattern is generated, an artist can interactively
adjust the underlying curve, with the pattern being updated accord-
ingly. Generation performance is reported as below one second up
to a little more than two minutes for complex models.
Creating textures from pen-and-ink drawings, KAZI et
al. [KIZD12] present a multifaceted tool, mixing data-driven and
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Figure 11: Visual examples for branching structures from GUO et
al. [GJB*20], who recreate a user sketch (left) with a procedural
L-system (right) through inverse modeling.
procedural modeling. Simple manually-created drawings can be
automatically repeated along paths and brush strokes, and can be
used to fill regions. Edits of the original drawing can be propa-
gated to all repeated elements. A user study confirms the system’s
usefulness for efficiently creating repetitive textures while main-
taining the natural workflow and artistic control of an artist. XING
et al. [XCW14] build upon that work by automatically detecting
and suggesting possible repetitions to the artist, aiming for a less
regular, more painting-like quality. The presented system also of-
fers various brush options and navigation tools in order to combine
automation with artist control. Neither of these two articles report
on performance times for the computation of the strokes and edits.
More data-driven painting-like methods can be found, for
example, for hand-drawn animations [XWSY15], creating mo-
saics [Iga10;AGYS14] and data visualization [XHC*18].
Feature Exploration Even though not a generating technique in
itself, exploration is an important characteristic of a creative pro-
cess. TOD I et al. [TWO16] present a tool for exploring common
layout types with sketched input. With the method of CHE N et
al. [CFA16], an artist can browse a collection of texture images by
sketching highly abstracted pattern features. The represented struc-
tural features of reflection, rotation, and translation symmetries ad-
here to important design principles for visually pleasing patterns.
One could imagine a similar intuitive approach for exploring the
parameter space of an ornamental procedural representation, for
example.
In the context of 3D modelling, TALTON et al. [TGY*09] inves-
tigate a collaborative 3D modeling system by crowd-sourcing pos-
sible models and feeding the results back to the system for others
to explore in a structured manner.
7.4. Connections, Branches and Directionality
While some already-discussed work [CSC12;XM09;MM10] en-
ables branching in a limited way, the systems described here in-
clude the design feature of Connections, Branches and Direction-
ality more generally. The general category includes the already-
discussed technique of BE NE S et al. [BŠMM11]. Even though their
work focuses on structuring a space with shapes, an artist can also
control the connecting points between those shapes. In the follow-
ing, we identify the mechanism clusters of fields, example-based,
and data-driven.
Fields The already-discussed work of GI ES EK E et al. [GALF17]
(Section 7.2) enables a sense of directionality by controlling the
growth of a pattern through vector fields and directing the connec-
tivity and branching of elements along user-specified paths. Con-
nections between single elements can be designed through drag
and drop. Patterns align to the space they are filling by auto-
matically growing around obstacles, implemented with a shortest-
pathfinding approach. Of the systems described in Section 7.1.4,
IJIRI et al. [IMIM08] employ vector fields to define the overall
growth direction and alignment of elements within an example-
guided arrangement, enabling the design of directionality. Simi-
larly, SAPU TR A et al. [SKAM17] optimize a flow-based ornamen-
tal packing of elements into a two-dimensional outline.
Vector fields are further employed in various other specific
procedural modeling contexts, including procedural street mod-
eling [CEW*08], micrography [MBS*11] and botanical mod-
els [XM15].
Example-based GUO et al. [GJB*20] focus specifically on creat-
ing branching structures with an inverse modeling process for in-
ferring a generating L-system. The technique is robust and takes a
variety of input designs such as real-world images or hand-drawn
sketches of the branching. The inverse modeling employs convo-
lutional neural networks, a tree graph for representing transforma-
tions and greedy optimization. Beside the exemplar, a user can in-
put the length of the rules and the frequency of the repetition. Once
the network is trained, the inference take a fraction of a second.
Data-Driven Even though the energy-brushes of XING et
al. [XKG*16] are intended for creating animations, and hence are
not included in the table, they could also be used in a pattern gener-
ation process. The technique could be used to deform given visuals
in an aesthetic manner, perhaps under certain design constraints for
pattern generation. Their brushes let an artist roughly sketch di-
rections that shape smoke, swirl, and wind velocity fields, which in
turn control the animation of the illustration. An abstracted preview
of the type of brush is given on the canvas letting an artist translate
abstract strokes into the desired animation. The user interface gives
all basic interactions of a drawing tools, such as layers and undo.
In contrast, HUet al. [HXF*19] solve the design of velocity fields
by freely sketching all possible scene elements, such as boundaries,
obstacles and specific types of flow, offering more freedom but also
leading to less-structured results.
7.5. Single Accents
The design feature of Single Accents breaks with the underly-
ing principle of procedural generation, which is to repeat certain
rules and thereby visual features. This overall principle is demon-
strated in Figure 12. However, for creative pattern generation, it is
worthwhile to investigate how to combine the execution of rules
with occasionally breaking such rules. For example, GIESEKE et
al. [GALF17] claim this to be necessary for ornamentation to break
“an otherwise too-homogeneous appearance.” Because of the small
amount of work matching this design feature, there are no mecha-
nism clusters.
Even though the required functionality can be compared to using
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Figure 12: While the pattern exploration technique of GUERRERO
et al. [GBLM16] focuses on exploring design variations with repet-
itive visual characteristics, e.g., based on symmetry, as shown on
the left, the technique also enables the placement of single elements
as shown on the right. The example is from the supplemental video.
the tip of a brush, paint-like procedural modeling techniques such
as M ˇ
ECH et al. [MM12] often have a more spray-can-like quality
and do not explicitly include the option to place single elements.
GIESEKE et al. [GALF17] (Section 7.2) explicitly provide local
editing options, including deleting and placing single elements and
connections and dragging and dropping existing ones. SAPUTRA
et al. [SKAM17] also support accent elements in their field-based
ornamental packing generation. The system-generated elements au-
tomatically flow around the placed accents.
YEH et al. [YM09] allow for separating single elements by
combining a manual data-driven design process with procedural-
modeling-like editing options. Based on detected symmetries and
curvilinear element arrangements in a given vector pattern, an artist
can adjust the spacing, location and scale of one element and prop-
agate that change to the all other elements in the group. The au-
thors also offer a brush that recreates recognized element groups.
The technique is interactive for the examples shown but interactive
performance does not scale to more complex input patterns.
The vector pattern generation technique of GUERRERO et
al. [GBLM16] also supports single accents while the artist is ex-
ploring design variations. An artist can select and continue with
one of the offered alternatives. The system constantly re-selects
from large space of relevant variations based on the artist’s modifi-
cations. The user interface is carefully laid out to offer design vari-
ations in an intuitive and efficient manner while not hindering the
artist’s own workflow. The authors thoroughly evaluate their sys-
tem quantitatively and qualitatively, including a user study. Overall,
participants agreed on the usefulness of technique.
8. Discussion of Means for Enabling Creativity
Table 2compares performance timings as reported by the origi-
nal authors. As the works discussed here come from a time frame
spanning more than 20 years, older techniques can be expected to
significantly outperform their original implementations on current
platforms. Accordingly, we categorize them coarsely into realtime,
interactive,synchronous,asynchronous, and offline to indicate how
one would work with the proposed techniques, and how their origi-
nal application may have been intended. To relate the control mech-
(2D)
Table 2: A rough categorization of timings in realtime, interactive,
synchronous, asynchronous, and offline. Timings are taken from the
authors’ descriptions. An ×is used for work that the authors call
interactive without giving specific timings.
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anisms to the control characteristics, we considered the same pub-
lications in Table 3. Due to the diversity of the underlying methods
and the different design goals of the considered body of work, we
believe this to be a representative summary.
The categories in Table 1show a highly uneven distribution. The
largest category is Distribution and Repetition, which focuses on
repetitive pattern designs and filling a space, usually automatically.
Another large group is Curves and Brushing, which lets artist man-
ually create distinct but potentially unstructured designs. However,
creative pattern designs, such as the historic and commercial pat-
terns in Figure 1, are rarely uniform or unstructured, so additional
control is needed to let artists create structure and work with de-
sign rules. The table categories of Frames and Hierarchies; Con-
nections, Branches, and Directionality; and Single Accents include
systems that attempt to address this need. These include algorithms
that have a greater understanding of the space being filled and offer
global planning to the artist.
In addition, there are domains closely related to pattern gener-
ation for which there are few creatively controllable algorithms.
The interwoven structures in the Celtic pattern design in Figure 3
could be computed algorithmically while an artist controls the
overall design, but systems that generate similar designs automati-
cally [KC03;DS13] have limited controllability.
Table 3shows that global control is most commonly enabled
through intermediate representations, such as example images. At
the other end of the spectrum, placing elements as part of the ac-
tual output is most often local and manual with little automation
supporting the artist throughout the creation process. The domi-
nant control mechanisms in the Parameterization category, File and
Value, both require abstracted input from an artist, such as a text
value or the use of a slider. Sketch-based controls move the interac-
tion onto the canvas and can make small-scale adjustments. Spaces
to fill, curves to follow, and masking areas are also usually done di-
rectly on the canvas, but only influence the output indirectly. Brush-
ing creates the output directly on the canvas, but can only do so in
a limited region depending on the brush size, unless used to brush
intermediate control lines. All other inputs are typically given be-
fore or after the generation of the output. The classification under-
lines that a focus on one control type, as is often done in computer
graphics research, leads to the common trade-off between global
automation and local manual manufacturing.
We now discuss various techniques’ potential to support a cre-
ative workflow, clustered into the most common types of control.
This discussion of the means for enabling creativity, namely Navi-
gation, Transparency, Variation and Stimulation (Section 4), is in-
terpretive and somewhat subjective. However, we strive to combine
a realistic discussion of terms like “artist-usable” and “creatively
controllable” with steps towards defining them more objectively.
8.1. Example-Based Control
As the state of the art shows, the most prominently investigated
techniques for texturing are example-based and inverse approaches.
Example-based control mechanisms provide goal-oriented control.
The motivation behind using these techniques is mainly to gener-
ate a specific and predictable output as efficiently as possible. This
HOW WHAT WHERE WHEN
Total (out of 50)
File
UI
Canvas
Code
Value
Intermediate
Element
Global
Region
Local
Before
During
After
Setup
Configuration 13 13 9 4 13 2 13
Initalization 20 18 3 3 16 8 2 19 3 20
Exemplars
←− Decreasing Automation
Image 13 11 1 12 2 13 2 13
Arrangement 13 11 1 3 4 3 10 13 4 13 1
Element 11 7 3 1 5 6 9 3 11 1
Parameterization
Visual Output 36 26 8 5 30 2 34 2 19 1 19
System 22 14 8 21 1 23 4 22 1
Handling
Visual UI 10 4 4 1 7 4 7 6 5 3 5
Image 11 11 2 9 11 5 11
Sketch 10 1 9 10 5 6 9 2 8 3 2
Filling
Shapes 41 32 11 26 14 40 15 41 3
Masking 11 5 8 2 9 8 11 11 2
Curve 9 9 7 2 1 9 8 2
Guiding
Brushing 8 1 7 2 6 2 8 2 7
Directions 9 1 8 8 1 8 8 9
Placing
Element 9 9 9 1 9 9 2 1
Drag&Drop 7 7 7 1 5 6 6 3
Table 3: Prevalence of control mechanisms in the literature: In
total, 50 publications are included (the discussed state of the art
in Section 7). Please note that the total for each step (how, what,
where, when) can exceed the total of that category because the cat-
egory can be implemented in multiple ways.
type of control stands in contrast to exploration. Example-based
approaches change the design task into a data-driven image gen-
eration task, such as taking a photograph or designing a sample
in an application such as Adobe Photoshop or Illustrator. Relevant
factors for differentiating example-based techniques are the size of
the design space and hence their expressiveness, performance and
initialization requirements.
The investigation of example-based techniques shows valuable
achievements in goal-oriented control and in increasing design
space size within specific contexts. With regard to creative control,
crucial steps are increasing variability and improving navigability
with interactive performance. However, many techniques still re-
quire considerable non-creative effort for an artist, such as working
with a power spectrum or predicting how changes in the exemplar,
such as element arrangements, affect the output.
TUet al. [TWY*20] and BIAN et al. [BWL18] combine drawing
a tile with an automatic tiling system, a promising direction that
offers transparent navigation. Also, drawing tiles leads to a design
space that is fairly open within the scope of the specific pattern
type, which is further limited by fabrication constraints in BIAN
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L. Gieseke, P. Asente, R. Mech, B. Benes, M. Fuchs / A Survey of Control Mechanisms for Creative Pattern Generation
et al. [BWL18]. Both techniques offer direct canvas interactions
such as editing options on the tiling itself [TWY*20] and preview
and snapping functionalities that make it easy for an artist to create
structurally sound patterns [BWL18].
The potential of example-based methods for creative control lies
in improving interactive performance, reducing initialization re-
quirements, and experimenting with the spatial influence of the
input, such as introduced by GU EH L et al. [GAD*20] with their
semi-procedural generation of stochastic textures (Figure 6). Over-
all, the presented work focuses on global designs, such as the whole
canvas and repeating regions. Methods for which regions could be
defined, models layered or the placement of single elements inte-
grated constitute valuable directions for example-based methods as
creative control.
8.2. Shapes and Masks
Sophisticated masks and growth constraints lead to visually inter-
esting and complex designs, such as the packing patterns from SA-
PUTRA et al. [SKA18]. However, it is not completely predictable
exactly how a space will be filled. Because the interactive perfor-
mance of many of the presented methods is quite limited, even
a basic trial and error exploration is hardly feasible. The naviga-
tion of the design space becomes cumbersome, and stimulation be-
comes hindered. The one technique (SA NT ONI et al. [SP16]) that
offers transparent navigation is also the one with a severely re-
stricted design space, but their inclusion of a navigation history
stands out from the related work in this survey. In terms of stim-
uli, the mass-spring system for editing control guides offered by
BENES et al. [BŠMM11] and the elastic curves from ZEHNDER et
al. [ZCT16] (Figure 13) are promising directions because they are
intuitive and enjoyable to use and encourage exploration. Overall,
the control mechanisms of ZE HN DE R et al. [ZCT16] are a convinc-
ing solution for enabling artists to adhere to structural constraints
while still offering a fully navigable, transparent and stimulating
creative workflow.
In terms of control mechanisms for a more complex design goal,
shapes and masks do not permit hierarchical or element-level local
controls or the control of element connections needed by artists
who want to generate patterns creatively without having to write
code.
8.3. Fields
Fields (in the context of this survey, usually vector fields) constitute
a powerful tool for combining automatic procedural filling with the
option to direct the process in specific regions, usually with direct
control on the canvas. As HSU et al. [HWYZ20], SAPUTRA et
al. [SKAM17] and GI ES EK E et al. [GALF17] show (Figure 14),
the streamlines of a field can structure how a space is filled. Using
a vector field to control, e.g., directionality, can greatly decrease
the manual work needed to fill a space in its entirety because a
few curves can define the entire field. Other global design choices,
such as an overall growth direction or the alignment of elements,
are simple to translate from a vector field to procedural generation
rules.
The discussed work shows that fields allow for greater visual
Figure 13: ZEHNDER et al. [ZCT16] offer various control mecha-
nisms, from creating the base elements (top-left) to combining and
editing them on the surface, while ensuring structural soundness
(bottom). Examples are from the supplemental video.
variation by opening the design space and providing transparent
control for filling a space automatically. While fields are still a
level of abstraction away from the pattern itself, they are intuitive to
understand, e.g., through a visual representation. Their abstraction
translates to the model in a straightforward manner. Thus, using
flow within a vector field to design is a suitable control mecha-
nism, especially for designs that aims to align their elements to the
space.
8.4. Curves and Brushing
Curves and hand-drawn paths give an artist direct control over the
final result, putting the control directly onto the canvas. Curves are
needed for tasks such as creating a decorative frame or structuring a
space. Some techniques consider the whole curve before computing
the ornament and optimize the filling of the curve based on certain
design goals. This can be understood as a form of global planning.
Curves and sketch-like methods offer well-communicated, trans-
parent navigation. The discussed techniques are mostly interactive,
and artists are familiar with their functionality from the real world
and how they work directly on the canvas. The ease and directness
of usage also constitute a foundation for possible immersive flow
of work. Painting-like methods can support smoother navigation by
integrating brush settings and increasing the quantity of controls.
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L. Gieseke, P. Asente, R. Mech, B. Benes, M. Fuchs / A Survey of Control Mechanisms for Creative Pattern Generation
Figure 14: Different approaches to using vector fields for creative pattern generation. 1. GIE SE KE et al. [GALF17] (example from the
supplemental video), 2. HSU et al. [HWYZ20], 3. SAP UT RA et al. [SKAM17].
Figure 15: XING et al. [XCW14] propagate user sketches (right,
black strokes) to fill an outline automatically (right, red strokes).
On the downside, curves and brushing could lead to tedious man-
ual creation requirements for patterns and unstructured results. To
balance this, KA ZI et al. [KIZD12] and XING et al. [XCW14]
(Figure 15) incorporate procedural creation principles into a data-
driven process. HSU et al. [HWYZ20] offer an intuitive and trans-
parent navigation through a brushing system, letting artists realize
their design goals for element arrangements. The approach of LIet
al. [LBM*20] combines visual curve creation, code, and data in a
unique manner by showing textual and numeric information about
the underlying procedural algorithm on the canvas. The technique
might increases a transparent and navigable workflow once an artist
has learned the workflow. This novel approach calls for further in-
vestigation and verification.
In summary, brushes let artists draw almost anything, depending
only on their drawing capabilities. For creative pattern generation,
however, structure, pattern hierarchies, and distribution techniques
also need to be supported.
8.5. Element Placement
Placing single elements onto the canvas maximizes artist control
and is on its own a trivial data-driven control principle. However,
this mechanism becomes interesting in combination with procedu-
ral modeling. Separately placed elements that do not follow any
rules should be integrated and processed to remain part of the un-
Figure 16: GUERRERO et al. [GBLM16] combine the exploration
of pattern variations with manual editing of single elements, e.g.,
by drag and drop.
derlying global scene structure, as demonstrated by GI ES EK E et
al. [GALF17]. Element placement control mechanisms are closely
related to data-driven sketch-based techniques and represent a
promising approach for integrating procedural modeling function-
alities into a data-driven process. GUERR ERO et al. [GBLM16]
present an overall transparently navigable and stimulating control
mechanism (Figure 16). The carefully designed workflow fosters
artist stimulation by offering novel but suitable design variations.
9. Outlook
This analysis shows various possibilities for future work within the
specific contexts of creative pattern generation. Here we highlight
directions that we have not mentioned yet but that have great po-
tential for creative control mechanisms.
Collaboration is a valuable future line of investigation for en-
abling creative work. Many aspects of common tools are either
fully browser-based, or are in some way connected to cloud-based
storage of assets, settings and results; therefore, they function on-
line and are easily shared. Collaboration is closely connected to
the previously-discussed issue of navigation histories. This is rele-
vant not only for individual work processes but also for more gen-
eral production pipelines in a commercial context. In this regard,
sharing and collaborative work on iterations, involving multiple
persons referencing different versions, is essential. Work has been
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L. Gieseke, P. Asente, R. Mech, B. Benes, M. Fuchs / A Survey of Control Mechanisms for Creative Pattern Generation
done [TGY*09;SSTP15;OWL*18] but further investigations of
collaboration for creative control are called for.
The procedural content generation (PCG) community for games
is pushing the general integration of artificial intelligence (AI) into
a procedural creation process. A new discipline of mixed-initiative
creative interfaces is rising as, e.g., an ACM CHI workshop un-
der the same name in 2017 [DHF*17]. The workshop summary
states as its goal to “put human and computer in a tight interactive
loop where each suggests, produces, evaluates, modifies, and se-
lects creative outputs in response to the other.” To achieve this, AI
enables computer agency, and novel interfaces enable collaboration
between computers and human users. On the topic of agency and
automation, HEER [Hee19] discusses three case studies and poses
several open questions for further developments.
Semantic attributes present a highly intuitive navigation tech-
nique, which so far has been successfully applied in the context
of shape modifications, for example by YUMER et al. [YCHK15].
For procedural textures, these attributes can be based on the anal-
ysis and description of texture with regard to human perception,
which has a long research tradition, starting with textons from
JULESZ [Jul81]. Since then, this line of research has continued,
and texture descriptions with perceptual [LDC*15] and seman-
tic [MNN13;CMK*14] attributes have been investigated. DONG et
al. [DWLS17] and LIU et al. [LGD*18] employed such features for
navigating a procedural texture space and generating suitable tex-
tures by given features. However, the results of such studies are still
limited and of varying quality—the authors themselves [LGD*18]
call their results experimental. Nonetheless, these works present an
interesting approach that is worth further investigation, especially
in combination with machine learning algorithms. Because many
pattern designs are structured and follow an internal logic, it seems
feasible to come up with a collection of suitable attributes. For ex-
ample an ornamental design space is much smaller in comparison
to all “textures in the wild” [CMK*14], and ornamentation could
constitute a valuable context for further investigations into the in-
corporation of semantic attributes into a creative creation process.
As discussed in Section 6, control techniques are closely inter-
related with the representation of the underlying models. Further
automation for the creation of complex models also poses interest-
ing challenges, such as abstraction [NSX*11], symmetry computa-
tion [CO11] and design space variations.
10. Conclusion
The overall challenge addressed in this survey is to show how to
support artists in their work with meaningful control mechanisms.
The investigation of controllability is put into the context of two-
dimensional creative pattern designs. Procedural models and the
computation of designs offer novel approaches to create content
and provide benefits over traditional manual manufacturing. How-
ever, providing control mechanisms that are intuitive to use and al-
low individual designs is an ongoing research challenge. For more
complete and meaningful solutions aspects of both data-driven and
procedural techniques are needed and must be merged into a unified
whole.
The reviewed techniques could complement each other and we
hope to have furthered the direction of bringing different ap-
proaches together and to have carefully analyzed and emphasized
an artist-centered perspective. This is the basis for developing in-
novative tools that further the ability of artists to create and to cre-
atively express themselves.
Acknowledgements
Open Access funding enabled and organized by Projekt DEAL.
[Correction added on 15.10.2021, after first online publication: Pro-
jekt Deal funding statement has been added.]
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