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Implementation of shape embedding in 2D CAD systems
Abstract
The process of shape embedding, that is, the inquiry whether for two shapes u and w there is a transformation f that embeds the shape f(u) in w is the most critical – and elusive – process for all shape grammar interpreters implemented within CAD systems. This paper identifies three major challenges underlying the implementation of shape embedding within a CAD environment and proposes three corresponding solutions. The focus is given here in the calculation of shape embedding for shapes made up of lines in a 2D CAD environment to provide the testbed for the mechanisms proposed. The integration of these three sets of algorithms into one coherent framework produces the blueprint of Shape Machine, a general-purpose shape grammar interpreter implemented in Rhinoceros, a NURBS 2D/3D CAD software. Some preliminary thoughts regarding the impact of the proposed shape-rewrite modeler in CAD industry and more broadly, in design education are given in the end.
... The automation of isovist calculations is achieved by implementing a general isovist grammar in Shape Machine, a visual rewriting system that enables shape rule applications with shape embedding and replacement (Hong and Economou, 2023). Shape Machine has been used in multiple studies, especially in research focused on visual, spatial, and geometric concerns, to demonstrate how visual rewriting systems reduce complexity while developing spatial algorithms for visual problems in design (Park 2023, Economou and Hong, 2022;Okhoya et al, 2022;Yu et al, 2021;Ligler, 2021;Economou et al, 2020). ...
... The grammar to derive isovist fields is implemented with 25 shape rules categorized in four steps that follow the process introduced in the previous section. All shape rules are applied under linear transformations, including: 1) isometric transformation, that is, translation, rotation, and reflection; 2) similar transformation, that is, uniform scaling and all isometric transformations; and 3) affine transformation, that is, stretching, compressing, shearing and all the similar transformations (Hong and Economou, 2023). In this study, the initial shape contains three parts: a) an observer, which is represented as a blue vantage point; b) a design environment, which is a configuration of multiple spatial obstacles with each represented as a rectangle consisting of four black lines; and c) an infinite boundary which is represented as a dashed square where the observer and all obstacles are contained. ...
Isovists and isovist fields are used to analyze spatial factors of an architectural design according to connective qualities of spaces. Still, the automation of isovist calculations requires significant translation from the visual to the numerical. This research presents a shape grammar that formalizes the visual framework of isovist calculations through visual means. More specifically, the graphical calculation of isovists is formalized by the graphic definition of rules, allowing for a mapping from the manual drafting of an isovist field to the digital automation of the same logic, providing a general framework for producing isovist fields visually. The isovist grammar is implemented in Shape Machine, a visual rewriting system that automates shape rule applications to verify and test the visual calculations. The results and discussion suggest how this allows for the furthering of isovist techniques to inform the analysis and synthesis of architectural designs.
... The utilization of parametric shape grammar allows for the dynamic modification of designs, effectively balancing the integration of new ideas respecting to the traditional principles. This makes it an important tool for communicating design ideas across disciplines [3][4][5][6][7]. ...
... The work here addresses the identified shortcomings in the literature review by reworking and significantly expanding the existing shape grammars into a new set of shape rules in Shape Machine -a general purpose shape grammar interpreter implemented in Rhino. Shape Machine has successfully tackled the complex task of shape embedding, redefining CAD representations, and enabling direct application of shape rules to 2D or 3D models [3,5]. Its ability to transform shapes under various geometric transformations expands its use in diverse design applications, offering versatile modes of interaction from manual to automated workflows [4,22]. ...
... Their rules incorporate this graph to identify a shape by matching its graph structure and its topological patterns, such as point order, parallelism, and line length. The SS and SG methods have been widely studied, and they have been digitally automated as software plugins for space planning or shape matching (e.g., SG interpreter) [35][36][37][38]. Additionally, the graph has been used to navigate rules, rule iterations, and design outputs in design space [39][40][41]. ...
... Incorporating these other features could help increase design variety and separate the useful and useless results. Further studies could include resolution enhancement of the diagrammatic outputs with tools such as those mentioned in [36,38,71,72], and function descriptions can be organised into an ontological structure in semantic modelling [73][74][75]. ...
This paper presents a method to synthesise functional relationships and spatial configuration simultaneously using shape and graph computation from shape grammar and space syntax theories. The study revisits seminal works and summarises the compatibilities between shape and graph computation as a set of rules. The rule computation is demonstrated in two cases from hospitality and retail, where current applications, opportunities, and limitations are discussed. The results from the study show that incorporating graph and shape rules allows sequences of functions and spatial arrangements to be developed in parallel. The method could help the designer anticipate the impact on the users’ flow of activities more explicitly during the early design process and could also assist in generating new functional configurations to provide alternative spatial strategies in broader applications.
A shape grammar is a formal rewriting system for producing languages of shapes. While initially defined to operate over line segments and labeled points, the theory of shape grammars has numerously been extended to include other spatial and non-spatial entities, including, planar segments and volumes, some types of curves, weights, colors and descriptions. Over the years, also a number of shape grammar interpreters have been developed, implementations that support the specification and application of shape rules. However, each of these implementations has adhered to a single shape grammar formalism, even if the exact formalism may differ from one implementation to another. This paper reports on the development and application of a shape grammar interpreter supporting multiple shape grammar formalisms. This is achieved in two ways, first, by supporting a variety of representational structures as compositions of basic data types, and second, by providing two alternative matching mechanisms for spatial elements, a non-parametric and a parametric-associative mechanism. Together, this provides for a flexible and extensible interpreter for the specification and application of shape rules, which has been implemented in the Python programming language and is accessible from Rhino and Grasshopper.
Shape queries based on shape embedding under a given Euclidean, affine, or linear transformation are absent from current CAD systems. The only systems that have attempted to implement shape embedding are the shape grammar interpreters albeit with promising but inconclusive results. The work here identifies all possible 14 cases of shape embedding with respect to the number of available registration points, four for determinate cases and ten for indeterminate ones, and an approach is sketched to take on the complexities underlying the indeterminate cases. All visual calculations are done with shapes consisting of straight lines in the Euclidean plane within the algebra U ij for i = 1 the dimension of lines and j = 2 the dimension of space in which the lines are defined, transformed and combined. Aspects of interface design and integration to current work design workflows are deliberately left aside.
Shape grammar interpreters have been studied for more than forty years addressing several areas of design research including architectural, engineering, and product design. At the core of all these implementations, the operation of embedding—the ability of a shape grammar interpreter to search for subshapes in a geometry model even if they are not explicitly encoded in the database of the system—resists a general solution. Here, a detailed account on various constructions of embedding is provided, including determinate and indeterminate ones, to give a sense of the rising complexity of their implementation in a shape grammar interpreter, and to provide a visual map of the work accomplished in the field so far, and the work ahead too.
A persistent challenge to the more widespread use of shape grammars in architectural research is the creation of rules and rule sets for application in design contexts, while leaving space for design creativity despite the limitations of a rule-based system. A hybrid of associative and rule-based approaches may alleviate this. We present one such development, a Grasshopper shape grammar plug-in that embeds a rule-based approach within a parametric modelling environment. It supports shape emergence, visual enumeration of rule application results, and the parametric definition of shapes and shape rules even when selecting a non-parametric rule matching mechanism. Grasshopper's ability to handle geometries and text together allows for external descriptions and labels as attributes to points, enabling definition and application of compound, geometric and description rules. Well-known examples from shape grammar literature are implemented using the plug-in, with a focus on rule definition and application in the context of interaction between the parametric modelling environment and the rule-based interpreter, and simultaneous use of geometry, descriptions, and descriptions as attributes in rules.
Two formal exercises in hotel composition are presented. In both, the hospitality work of the architect John Portman is the focus. His language of hollow forms is addressed following his unique claim on the organizing principles found in his 1964 house, Entelechy I. The first exercise outlines a generative specification for his atrium hotel language in a parametric shape grammar informed by the logic of the house that generates an atrium hotel prototype. The second exercise speculates with a sketch on how transformation grammars can yield various configurations to explore Portman’s atrium hotel language for a series of initial shapes.
We present a shape grammar plug-in for Grasshopper that allows shapes and shape rules to be defined in a parametric manner, even if the rule matching mechanism does not support parametric rules. The plug-in supports shape emergence and provides support for visually enumerating rule applications. We reflect on the interaction between parametric or associative modelling and rule-based generation within the context of using this plug-in.
This paper introduces the special issue “Advances in Implemented Shape Grammars: Solutions and Applications” and frames the topic of computer implementations of shape grammars, both with a theoretical and an applied focus. This special issue focuses on the current state of the art regarding computer implementations of shape grammars and brings a discussion about how those systems can evolve in the coming years so that they can be used in real life design scenarios. This paper presents a brief state of the art of shape grammars implementation and an overview of the papers included in the current special issue categorized under technical design, interpreters and interface design, and uses cases. The paper ends with a comprehensive outlook into the future of shape grammars implementations.
As a general plane sweeps through space it counts the various types of regions produced by a given collection of planes.
This article is respectfully dedicated to George Poly a on the occasion of his 90th day, December 13, 1977.
The geometric design of the exterior appearance of consumer products is a principal consideration to retain brand identity. Architectural and engineering shape grammars had demonstrated shape computation as a formal and viable approach for supporting style conformance. However, most existing shape grammar implementations operated in limited experimental domains, and lacked support for complex three dimensional geometry, shape emergence and parametric shape rules. The aim of the reported research is to address these issues. Shape algebras are reduced in terms of shape operations with their basic elements which is generally applicable to shape computation. Specifically for algebra U 13 , exhaustive cases were enumerated for shape sum and shape difference operations. A U 13 shape grammar implementation was developed to support both rectilinear and curvilinear basic elements in three dimensional space. Mathematical representations of basic elements were based on non-uniform rational b-splines and their reduced form. This allowed a simple yet exact notation which simplified support for maximal representation and its computation. Two cases studies, a Coca-Cola bottle grammar and a Head & Shoulder bottle grammar, were used to test the implementation.
A method for implementing parametric shape grammars is presented. Subgraph detection is used to find subshapes. Parametric shapes are described by restricting topologies.
The design of the computer program SGI (pronounced sigi) for the generative specification of shapes using the shape grammar formalism (Stiny, 1980) is outlined. The program interprets commands from the SGI language. The commands which are described in detail allow for shape grammars to be defined interactively, and for shapes defined by these shape grammars to be generated via user-specified sequences of shape rule application. The program has graphics capability which permits line drawings of shapes to be displayed on the screen and drawn on the graphics plotter. Examples of shape grammars defined using this program, and plotter line drawings of shapes generated by the grammars are illustrated.
Currently available computer-aided design tools provide strong support for the later stages of product development processes where the structure and shape of the design have been fixed. Support for earlier stages of product development, when both the structure and shape of the design are still fluid, demands conceptual design tools that support designers’ ways of thinking and working, and enhance creativity, for example, by offering design alternatives, difficult or not, possible without the use of such tools. The potential of spatial grammars as a technology to support such design tools has been demonstrated through experimental research prototypes since the 1970s. In this paper, we provide a review of recent spatial grammar implementations, which were presented in the Design Computing and Cognition 2010 workshop on which this paper is based, in the light of requirements for conceptual design tools and identify future research directions in both research and design education.
Recent developments in techniques for modeling, digitizing and visualizing 3D shapes has led to an explosion in the number
of available 3D models on the Internet and in domain-specific databases. This has led to the development of 3D shape retrieval
systems that, given a query object, retrieve similar 3D objects. For visualization, 3D shapes are often represented as a surface,
in particular polygonal meshes, for example in VRML format. Often these models contain holes, intersecting polygons, are not
manifold, and do not enclose a volume unambiguously. On the contrary, 3D volume models, such as solid models produced by CAD
systems, or voxels models, enclose a volume properly. This paper surveys the literature on methods for content based 3D retrieval,
taking into account the applicability to surface models as well as to volume models. The methods are evaluated with respect
to several requirements of content based 3D shape retrieval, such as: (1) shape representation requirements, (2) properties
of dissimilarity measures, (3) efficiency, (4) discrimination abilities, (5) ability to perform partial matching, (6) robustness,
and (7) necessity of pose normalization. Finally, the advantages and limitations of the several approaches in content based
3D shape retrieval are discussed.
Shape grammars play an important role in a new generation of tools for the analysis and design of products. In this work we present a general tool named Shape Grammar Interpreter (SGI) for the automatic generation of designs. The developed shape grammar framework allows designers to obtain automatically generated designs and to participate in the design process. In that way the generated design complies with both the desired functionality and an attractive aspect. Great effort has been devoted on having a comfortable way of defining shapes and later using them in shape grammar rules and designs' generation process. We have also implemented and incorporated in the tool an optimized subshape detection algorithm. Hence, subshapes of the existing shapes can be detected in the generation process obtaining more appealing designs.
Spatial composition can be viewed as computation involving spatial changes each expressed as s - f( a )+f( b ), where s is a shape, and f( a ) is a representation of the emergent part (shape) that is altered by replacing it with the shape f( b ). We examine this formula in three distinct but related ways. We begin by exploring the conditions under which a sequence of spatial changes is continuous. We next consider the conditions under which such changes are reversible. We conclude with the recognition of emergent shapes, that is, the determination of transformations f that make f( a ) a part of s . We enumerate the cases for shape recognition within algebras Uij , 0 <= i <= j <= 3, and within Cartesian products of these algebras.
The subshape recognition problem for three-dimensional shapes under linear transformations is considered. The problem is analysed in a series of cases, some that provide a determinate number of solutions and others that have indeterminately many solutions. Procedures for its solution for general shapes are developed. Difficulties posed by strict adherence to rational transformations are examined. As a corollary, an outline of a procedure for determining the symmetries of a shape is presented.
The geometry of shapes made up of finite planes is considered in detail. Algorithms on maximal planes for performing shape arithmetic are developed.
A fundamental problem in editing shapes is the recognition of partial shapes in a drawing to which changes are to be made. In this paper the possibility of using shape rules as a mechanism for effecting such changes is explored. Shape rules represent spatial relationships between two shapes α and β with the interpretation that any instance of α in a shape can be replaced by a 'similar' instance of β. A shape generation system implemented in PROLOG is described.
This paper deals with the matching of geometric shapes, with an emphasis on techniques from computational geometry. We are concerned with geometric patterns such as nite point sets, curves, and regions. For an overview of more general shape analysis, see [Lon98]
Visual calculating in shape grammars aligns with art and design, bridging the gap between seeing (Coleridge's “imagination”) and combinatoric play (Coleridge's “fancy”).
In Shapes of Imagination, George Stiny runs visual calculating in shape grammars through art and design—incorporating Samuel Taylor Coleridge's poetic imagination and Oscar Wilde's corollary to see things as they aren't. Many assume that calculating limits art and design to suit computers, but shape grammars rely on seeing to prove otherwise. Rules that change what they see extend calculating to overtake what computers can do, in logic and with data and learning. Shape grammars bridge the divide between seeing (Coleridge's “imagination, or esemplastic power”) and combinatoric play (Coleridge's “fancy”).
Stiny shows that calculating without seeing excludes art and design. Seeing is key for calculating to augment creative activity with aesthetic insight and value. Shape grammars go by appearances, in a full-fledged aesthetic enterprise for the inconstant eye; they answer the question of what calculating would be like if Turing and von Neumann were artists instead of logicians. Art and design are calculating in all their splendid detail.
Three computer implementations of one of the earliest and most iconic shape grammars are given to showcase different ways to use shape rules in Shape Machine. These three modes of working with shape rules-manual, automatic and conditional-are used interchangeably to produce three skeuomorphic variations of the original checkerboard lattice grammar in different design domains-3D prints, origami and kerfing-and showcase the versatility and applicability of the shape rules for the specification of diverse artifacts for different scales, materials and functions. Some initial remarks on the extension of the shape grammar formalism to include programming constructs including states, loops, jumps, and conditionals are discussed.
As a ubiquitous paper folding art, origami has promising applications in science and engineering. Many software and parameterized methods have been proposed to draw, analyze and design origami patterns. Here we focus on the shape grammar formalism and the Shape Machine, a shape grammar interpreter that has managed to automate the seamless shape calculations that the shape grammar formalism advocates. Different from other origami pattern generation methods, the shape grammar considers the origami pattern as a combination of different shapes (such as lines and curves). Based on this concept, the transformations between some common origami patterns are reorganized following visual cues and reasoning. Four examples of generating origami pattern are presented to show the capability of shape machine in origami design, including construction, modification and programming of an origami pattern. The new origami designs inspired by this work prove that shape grammar and shape machine provide a perspective and modeling technique for creating origami tessellation patterns.
Shapes are considered as finite arrangements of spatial elements from among points, line and plane segments, circles and ellipses, (circular) arcs, quadratic Bezier curves, of limited but non-zero measure, in 2D and 3D. Augmented shapes are defined as shapes augmented with attributes, e.g., labels, weights, colors, enumerative values, and (parametric) descriptions. Different attribute types specify different behaviors under operations of sum, product and difference and a part relationship. We review different shape–attribute propositions from the shape grammar literature and characterize them uniformly. This uniform characterization of augmented shapes is intended to assist in formalizing new shape–attribute propositions that may have been visually conceived.
The shape grammar formalism has been discussed theoretically extensively. Recently there has been increased activity in implementing shape grammar interpreters, yet there is a lack of implementations that support parametric rules and emergence. Here the structure of a general parametric shape grammar interpreter is discussed in detail. The interpreter is based on graph grammars. It supports emergence, parametric rules, and numerous types of geometric objects. The shape grammar engine, an agent-based rule selection system and several implementations based on the engine are discussed.
This paper explores the relationships between geometric constructability, numbers, shapes and shape grammars. Shapes are based compositional constructs in geometry, which rely upon drawing instruments. Implementing shape grammars relies upon numeric encodings, properties of which specify whether shape algorithms are decidable and/or tractable.
A general purpose computer vision system must be capable of recognizing three-dimensional (3-D) objects. This paper proposes a precise definition of the 3-D object recognition problem, discusses basic concepts associated with this problem, and reviews the relevant literature. Because range images (or depth maps) are often used as sensor input instead of intensity images, techniques for obtaining, processing, and characterizing range data are also surveyed.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1974. Includes bibliographical references (leaves 135-139). Vita.
In this article we propose a computer-aided conceptual design system to assist modelling at the early stages of design. More precisely, we address the problem of providing the designer with design alternatives that can be used as starting points of the design process. To guide the generation of such alternatives according to a given set of design requirements, the designer can express both visual knowledge in the form of basic geometric transformation rules, and also logic constraints that guide the modelling process. Our approach is based on the formalism of shape grammars, and supplements the basic algorithms with procedures that integrate logic design constraints and goals. Additionally, we introduce a layered scheme for shape grammars that can greatly reduce the computational cost of shape generation. Shape grammars, constraints, goals and layers can be handled through a graphic environment. We illustrate the functionalities of ShaDe through two use cases taken from the architectural design and video games domains, and also evaluate the performance of the system.
Large image databases are used in an extraordinary number of multimedia applications in fields such as entertainment, business, art, engineering, and science. Retrieving images by their content, as opposed to external features, has become an important operation. A fundamental ingredient for content-based image retrieval is the technique used for comparing images. There are two general methods for image comparison: intensity based (color and texture) and geometry based (shape). A recent user survey about cognition aspects of image retrieval shows that users are more interested in retrieval by shape than by color and texture [62]. However, retrieval by shape is still considered one of the most difficult aspects of content-based search. Indeed, systems such as IBM’s Query By Image Content, QBIC [57], perhaps one of the most advanced image retrieval systems to date, is relatively successful in retrieving by color and texture, but performs poorly when searching on shape. A similar behavior is exhibited in the new Alta Vista photo finder [10].
GRAPPA, an implementation of the Palladian grammar, is introduced. Graphs are used for the underlying representation, graph grammars take over the computation. Once a set of graph grammar rules equivalent to the original set of shape rules is defined, derivations, in the form of attributed graphs, are generated. These graphs contain all necessary information to output floor plans of Palladian villas using an appropriate mapping.
Winner, Reference Category, 2007 AAUP Book Jacket and Journal Show. In Shape, George Stiny argues that seeing shapeswith all their changeability and ambiguityis an inexhaustible source of creative ideas. Understanding shapes, he says, is a useful way to understand what is possible in design. Shapes are devices for visual expression just as symbols are devices for verbal expression. Stiny develops a unified scheme that includes both visual expression with shapes and verbal expression with signs. The relationshipsand equivalenciesbetween the two kinds of expressive devices make design comparable to other professional practices that rely more on verbal than visual expression. Design uses shapes while business, engineering, law, mathematics, and philosophy turn mainly to symbols, but the difference, says Stiny, isn't categorical. Designing is a way of thinking. Designing, Stiny argues, is calculating with shapes, calculating without equations and numbers but still according to rules. Stiny shows that the mechanical process of calculation is actually a creative process when you calculate with shapeswhen you can reason with your eyes, when you learn to see instead of count. The book takes the idea of design as calculation from mere heuristic or metaphor to a rigorous relationship in which design and calculation each inform and enhance the other. Stiny first demonstrates how seeing and counting differ when you use rulesthat is, what it means to calculate with your eyesthen shows how to calculate with shapes, providing formal details. He gives practical applications in design with specific visual examples. The book is extraordinarily visual, with many drawings throughoutdrawings punctuated with words. You have to see this book in order to read it.
Research into shape grammar implementation has been largely concerned with rectilinear shapes and there has been limited research into implementation on shapes composed of curves. This reflects developments of the shape grammar formalism which has been defined largely according to straight lines, planes, and associated volumes. In this paper, implementation of shape grammars on curved shapes is examined using algorithms for shape operations on shapes composed of parametric curves. These algorithms have been implemented in a shape grammar interpreter for shapes composed of quadratic Bézier curves, which is illustrated via application of a shape grammar that generates Celtic knotwork patterns. Implementing shape grammars on shapes composed of Bézier curves highlights difficulties that arise when the shape grammar formalism is applied to curved shapes, and the paper concludes with a discussion that explores these difficulties and indicates potential implications for the shape grammar formalism.
Shapes made up either of points, lines, planes, or solids belong to algebras that separately and in Cartesian products provide the main objects and devices used in shape grammars.
Advances in computer speed, memory capacity, and hardware graphics acceleration have made the interactive manipulation and visualization of complex, detailed (and therefore large) three-dimensional models feasible. These models are either painstakingly designed through an elaborate CAD process or reverse engineered from sculpted prototypes using modern scanning technologies and integration methods. The availability of detailed data describing the shape of an object offers the computer vision practitioner new ways to recognize and localize free-form objects. This survey reviews recent literature on both the 3D model building process and techniques used to match and identify free-form objects from imagery.
This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Research in shape analysis has been motivated, in part, by studies of human visual form perception systems. Several theories of visual form perception are briefly mentioned. Shape analysis methods are classified into several groups. Classification is determined according to the use of shape boundary or interior, and according to the type of result. An overview of the most representative methods is presented.
Shape similarity assessment is a fundamental geometric reasoning problem that finds application in several different product design and manufacturing applications. A computationally efficient way to assess shape similarity is to first abstract 3D object shapes into shape signatures and use shape signatures to perform similarity assessment. Several different types of shape signatures have been developed in the past. This paper provides a survey of existing algorithms for computing and comparing shape signatures. Our survey consists of a description of the desired properties of shape signatures, a scheme for classifying different types of shape signatures, and descriptions of representative algorithms for computing and comparing shape signatures. This survey concludes by identifying directions for future research.
Thesis (doctoral)--Swiss Federal Institute of Technology Zurich, 2001.
The conventions used to construct traditional Chinese ice-ray lattice designs are investigated. Parametric shape grammars are defined for the recursive generation of these patterns.
Shape grammars specify a mechanism for performing recursive shape computations. A general paradigm is established for a computer implementation supporting this computation in the algebras of points and lines in two dimensions ( U 0 2 and U 1 2 ). The guiding principles and the actual implementation are described.
Shapes and shape grammars use algebras of subshapes in the description and generation of designs. Different types of boundary, including element boundaries, closure boundaries, and specially defined boundary shapes, are defined in shape algebra descriptions. These are compared to boundaries in point set topologies used in geometric modelling for computer-aided design. It is shown that boundaries emerge in shape algebra descriptions but are inherited from the underlying topology in point set representations.
Shape grammars, a well-structured method of generating designs, are suitable for computer implementation. In this paper, a formal representation of shapes as individuals is developed; some binary operations and relations are then defined upon shapes. The formal mechanisms of shape grammars are presented, with some of the computational problems illustrated. Algorithms to solve some of these problems are given. A Prolog implementation of a generic shape grammar system is demonstrated.
3D architecture form synthesizer. Massachusetts Institute of Technology
- Wang