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Real-Time Rendering of Water Surfaces with Cartography-Oriented Design
Amir Semmo
1
Jan Eric Kyprianidis
2
Matthias Trapp
1
J
¨
urgen D
¨
ollner
1
1
Hasso-Plattner-Institut, Germany
*
2
TU Berlin, Germany
*
Stipples
Input
Lines
Lines
Strokes
Figure 1: Illustrative rendering techniques implemented in our system: waterlining, contour-hatching, water stippling, and labeling.
Abstract
More than 70% of the Earth’s surface is covered by oceans, seas,
and lakes, making water surfaces one of the primary elements in
geospatial visualization. Traditional approaches in computer graph-
ics simulate and animate water surfaces in the most realistic ways.
However, to improve orientation, navigation, and analysis tasks
within 3D virtual environments, these surfaces need to be carefully
designed to enhance shape perception and land-water distinction.
We present an interactive system that renders water surfaces with
cartography-oriented design using the conventions of mapmakers.
Our approach is based on the observation that hand-drawn maps uti-
lize and align texture features to shorelines with non-linear distance
to improve figure-ground perception and express motion. To obtain
local orientation and principal curvature directions, first, our system
computes distance and feature-aligned distance maps. Given these
maps, waterlining, water stippling, contour-hatching, and labeling
are applied in real-time with spatial and temporal coherence. The
presented methods can be useful for map exploration, landscaping,
urban planning, and disaster management, which is demonstrated by
various real-world virtual 3D city and landscape models.
CR Categories:
I.3.3 [Computer Graphics]: Picture/Image
Generation—Display Algorithms
Keywords:
water surfaces, illustrative rendering, cartography-
oriented design, contour-hatching, waterlining, water stippling
1 Introduction
Water surfaces represent key elements in mapmaking and surveying
because they shape our world and convey important information
*
http://www.hpi3d.de | http://www.cg.tu-berlin.de
to a number of domains, including hydrology, urban planning and
environmental sciences. Hand-drawn illustrations of such surfaces
are often carefully designed to help a viewer explore the geospatial
environment. Usually, these designs effectively establish land-water
distinction to facilitate orientation, navigation, or analysis tasks.
Yet the many different shapes of water surfaces pose a number of
challenges that have required contemporary craftsmanship and de-
sign skills. Typical challenges include (1) the symbolization of the
land-water interface using (2) design elements (e.g., strokes) that
exactly align with the shorelines to effectively provide figure-ground
and express motion. Over centuries, cartographers have developed
illustration techniques and design principles that address these chal-
lenges [Imhof 1972; Robinson et al
.
1995; Merian 2005]. Certain
techniques have become abundantly used in modern cartography,
such as waterlining, hatching, or water stippling; and most of them
express aesthetical appeal, provide excellent figure-ground balance,
and establish a sense of motion [Christensen 2008; Huffman 2010].
For instance, fine solid lines are placed parallel to shorelines to
effectively communicate shoreline distances (Figure 1 left).
To date, computer-generated illustrations of water surfaces are
mainly based on photorealistic rendering techniques [Darles et al
.
2011]. Approaches in illustrative rendering have been subject to
cartoon-like water effects [Eden et al
.
2007; Yu et al
.
2007] or other
primary cartographic elements, such as terrain [Bratkova et al
.
2009;
Buchin et al
.
2004], vegetation [Deussen and Strothotte 2000; Co-
conu et al
.
2006], or buildings [D
¨
ollner and Walther 2003], but have
neglected the many challenges water exhibits for map design.
This paper presents an interactive system for rendering water sur-
faces with cartography-oriented design that addresses the aforemen-
tioned challenges. For this, our work makes the following contribu-
tions. First, we identify and describe design principles from tradi-
tional and modern cartography to create more effective illustrations
of water surfaces. Based on these findings, Euclidean distance maps
are computed using a novel feature-aligned distance transform to
derive principal curvature directions of complex water shapes. Using
this information, we contribute real-time rendering techniques for
waterlining, contour-hatching, water stippling and labeling (Figure 1)
that facilitate a view-dependent level-of-abstraction [Semmo et al
.
2012]. Finally, we tested these rendering techniques with various
© ACM, 2013. This is the authors' version of the work. It is posted here by
permission of ACM for your personal use. Not for redistribution. The definitive
version will be published in Proceedings of the International Symposium on
Computational Aesthetics in Graphics, Visualization, and Imaging (CAe'13).
CAe'13, July 19 - 21 2013, Anaheim, CA, USA.
real-world virtual 3D city and landscape models. Our results reveal
potential applications within 3D geovirtual environments for map
exploration, landscaping, urban planning, and flooding simulation.
The remainder of this paper is structured as follows. Section 2
summarizes design principles derived from hand-drawn maps and
textbooks on map design. Section 3 reviews related works on texture
synthesis and illustrative rendering. Section 4 presents our methods
used for rendering water surfaces according to the identified design
principles, whose implementation details and results are presented
in Section 5. Finally, Section 6 concludes this paper.
2 Design Principles from Cartography
Well-designed illustrations of water surfaces provide figure-ground,
establish a sense of motion, and communicate meta-information
(e.g., water names). A variety of illustration techniques have been
developed by cartographers whose design principles address feature-
aligned texturing and symbolization. However, most cartographers
develop and vary their own illustration styles. Therefore, we ana-
lyzed the work by famous cartographers like Matth
¨
aus Merian and
Jouvin de Rochefort printed in map collections (e.g., [Merian 2005]),
and textbooks on map design and thematic cartography [French
1918; Imhof 1975; MacEachren 1995; Kraak and Ormeling 2003;
Tyner 2010]. From this analysis, we extracted the following design
principles, which we used for our illustrative rendering techniques:
Waterlining
. Waterlining became popu-
lar in the first half of the 20
th
century for
lithographed maps, because areas of solid
color tones could not be produced at that
time. With this technique, (P1) fine solid
lines are drawn parallel to shorelines,
and the spacing between succeeding lines
gradually increase [French 1918]. A com-
mon mistake is to “make the lines exces-
sively wavy or rippled” [French 1918] or the distance between lines
with insufficient continuity. If drawn with care, waterlining pro-
vides dynamism and effectively propagates distance information
[Christensen 2008; Huffman 2010].
Water Stippling
. Another conventional
technique for hand-drawn black-and-
white maps is water stippling [Tyner
2010]. Similar to waterlining, distance
information is propagated by aligning
small dots with non-linear distances to
shorelines. Compared to stippling in tra-
ditional artwork, water surfaces are de-
picted by (P2) stipples with varying den-
sity that irregularly overlap along streamlines to establish a sense of
motion. In perspective views, some cartographers draw (P3) stipples
with higher density at occluded areas (e.g., near bridges) to improve
depth perception, or with varying density to symbolize flow velocity.
Contour-Hatching and Vignetting.
Contour-hatching has been widely used to
balance the accurate propagation of dis-
tance information and establishment of
motion: by using (P4) individual strokes
that are placed with high density near
shorelines and complemented by loose
lines placed with increasing irregularity
towards the middle stream. In contrast to
waterlines, (P5) excessively wavy strokes are drawn to express mo-
tion. Alternative illustrations use non-feature-aligned cross-hatches
for land-water distinction. These methods have been replaced in
the second half of the 20
th
century by color tones and drop shad-
ows [Tyner 2010]. Today, coastal vignettes with solid color tones are
used to establish figure-ground but, in contrast to contour-hatching,
fail to express water movements.
Labeling
. Labels are design elements
used in cartography to enrich maps
with meta-information. By conven-
tion, (P6) cartographers depict names of
water features with italic (slanted) letters
to distinguish them from land features
for which upright letters are used [Tyner
2010]. Typically, (P7) names follow prin-
cipal curvature directions and are placed
within water surfaces [Imhof 1975] to ensure legibility.
Symbolization
. Symbolization is a com-
mon practice in cartography to reflect data
and phenomena [Imhof 1972]. To date,
standardized symbolization for water sur-
faces has not been established. However,
certain conventions have been used over
the years, including (P8) the irregular
placement of signatures with area-wide
coverage to communicate water features
(e.g., wetland, saltwater vs. freshwater), or the placement of glyphs
along streamlines to symbolize the flow direction of rivers.
For map design, blue is established as a conventional color tone, and
our work considers the identified design principles.
3 Related Work
Our work is related to previous works on texture synthesis, illustra-
tive rendering, and cartography-oriented design.
Feature-guided Texture Synthesis.
From our analysis in Sec-
tion 2, we observed that texture features are aligned with shorelines
to symbolize the land-water interface. Geometric properties of com-
plex shapes can be reconstructed quite effectively using distance
fields [Frisken et al
.
2000]. Our work uses distance maps to syn-
thesize waterlines and align stipples with shorelines in real-time.
Most algorithms use vector propagation to compute these maps by
an approximate Euclidean distance transform [Danielsson 1980]
(e.g., jump-flooding [Rong and Tan 2006]). We use the fast, work-
load efficient Parallel Banding Algorithm (PBA) to compute exact
distance maps on the GPU [Cao et al. 2010].
Feature-guided texturing based on principal curvature directions can
significantly improve shape recognition [Girshick et al
.
2000]. For
an overview on this topic we refer to the survey by Wei et al. [2009].
Recent approaches use normal-ray differential geometry [Kim et al
.
2008b] or diffusion techniques [Xu et al
.
2009] to derive principal
curvature directions, or use learning-based approaches [Kalogerakis
et al
.
2012; Gerl and Isenberg 2013] to align textures to salient
feature curves. However, these methods either require significant
(pre-)processing time or do not provide spatial and temporal co-
herence. By contrast, we present the concept of a feature-aligned
distance transform that provides continuous Euclidean distance val-
ues in a tangential direction to the shorelines. We use a GPU-based
flooding algorithm to compute a feature-aligned distance map in
real-time. Together with bilinear texture interpolation [Green 2007],
this map can be used to parameterize and place texture features along
shorelines with frame-to-frame coherence.
Non-Photorealistic Rendering.
Coastal vignettes and waterlines
are used for cartographic line generalization [Christensen 1999] and
in geoinformation systems to improve figure-ground perception.
surface masking
Water Surfaces
Euclidean Distance
Local Orientation Medial Axis
Feature-aligned Distance
3D Models
iterate over water surfaces
Strokes Glyphs
Cartography-Oriented Shading
Quantitative Surface Analysis
Texture Features
Hatches
Water Stippling
Waterlining
Contour-
Hatching
Cross-Hatching
texture mapping
Labels
Output
Figure 2:
Schematic overview of our system, which implements cartography-oriented shading using the results of quantitative surface analysis.
Stippling is a well-studied field in illustrative rendering for digital
half-toning. Conventional approaches represent local tone by a well-
spaced placement of small dots [Kyprianidis et al
.
2012]. Previous
work proposed feature-guided image stippling [Kim et al
.
2008a;
Kim et al
.
2010] that is adapted to the gradient direction of distance
maps. Water stippling works similarly, but does not match density
distributions to local tones (e.g., by blue noise) because dots irreg-
ularly overlap with varying density (P2). For this, we propose an
enhancement to Glanville’s [2004] texture bombing algorithm that
aligns water stipples with waterlines and renders them in real-time.
Feature-guided hatching has received significant attention in previ-
ous works and comprises user-defined [Salisbury et al
.
1997], patch-
based [Praun et al
.
2000; Webb et al
.
2002], shading-based [Praun
et al
.
2001], or learning-based [Kalogerakis et al
.
2012; Gerl and
Isenberg 2013] algorithms. The main difference to our approach
is that texture coordinates are obtained by Euclidean and feature-
aligned distance maps, which gives us more artistic control over
parameterizing individual strokes within real-time shaders. For
cross-hatching, tonal art maps [Praun et al
.
2001] are aligned to
Euclidean distance maps according to the view distance. This way, a
continuous level-of-abstraction [Semmo et al
.
2012] can be achieved
that significantly reduces visual clutter at high view distances. A
level-of-abstraction may also be combined with shape simplifica-
tions to produce aesthetic renditions of digital maps [Isenberg 2013].
Cartography-Oriented Design.
Illustrative rendering of water
surfaces is not a new approach. Previous works used colorization,
edge enhancement, and texturing for cartoon-like water effects (e.g.,
ripples) and to emphasize liquid movement [Eden et al
.
2007; Yu
et al
.
2007]. However, these rendering styles do not relate to tradi-
tional map design in terms of figure-ground organization for map
exploration, navigation, or landscaping. Rendering with cartography-
oriented design has been subject to other primary map elements,
such as terrain [Bratkova et al
.
2009], trees [Deussen and Strothotte
2000], and buildings [D
¨
ollner and Walther 2003], as well as land-
scape [Coconu et al
.
2006] and city models [Jobst and D
¨
ollner 2008].
We complement these techniques by our work on water surfaces
and exemplify how cartography-oriented visualization of 3D geovir-
tual environments can be achieved by combining our results with
traditional relief presentations of landscapes [Buchin et al. 2004].
Internal labeling has been addressed in the visualization of virtual
3D scenes. Previous works compute geometric hulls [Maass and
D
¨
ollner 2008] or derive medial axes based on a distance transform
[G
¨
otzelmann et al
.
2005; Ropinski et al
.
2007; Cipriano and Gleicher
2008] for shape-aligned labeling. Our work also uses distance maps
to align font glyphs with the shoreline distance and orientation.
4 Method
An overview of our system is shown in Figure 2. The input data
consists of a set of 2D or 3D water surfaces that are typically defined
as triangular irregular networks. Using orthographic projections, the
models’ shapes were captured in 2D binary masks to facilitate quan-
titative surface analysis that works in image-space. This analysis
includes the computation of Euclidean and feature-aligned distance
maps by iteratively propagating distance information in the normal
and tangent directions of shorelines. This information was used
for cartography-oriented shading, including waterlining, contour-
hatching, water stippling, and labeling. To enable a continuous
level-of-abstraction [Semmo et al
.
2012], the shading results were
parameterized, blended, and mapped onto the surfaces according to
the view distance. Because water surfaces are processed separately,
our system can be seamlessly embedded into existing rendering
systems, or combined with rendering techniques that pre-process the
3D virtual environment (e.g., terrain [Buchin et al. 2004]).
4.1 Quantitative Surface Analysis
Our goal is to provide quality, interactive illustrations of water sur-
faces that comply with the identified design principles (Section 2).
This section provides background on how geometric properties of
water surfaces can be derived using distance transforms. It includes
a novel feature-aligned distance transform that is used to align indi-
vidual strokes with the orientation of shorelines.
4.1.1 Euclidean Distance Transform
Euclidean distance information was computed to determine parts of
a water surface with equal shoreline distance. Let
I : R
2
→ {0, 1}
denote a water surface captured as a binary image, with
I(p) = 0
marking water areas, and
I(p) = 1
marking land areas by pixels
p ∈ I
D
(see Figure 2 top left). A distance transform of
I
defined as:
ω
I
(p) = min
q∈I
D
||p − q|| +χ(q)
with χ(q) =
(
0 if I(q) = 1
∞ otherwise
obtains the minimum Euclidean distance of each pixel to a shoreline.
A fast, parallel implementation to compute this information as a
distance map
D
(Figure 3a) is based on the PBA [Cao et al
.
2010].
Iteratively propagating distance information with the PBA was also
performed to obtain the nearest shoreline position as directional
information (Figure 3b). Subsequently,
D(p)
was used as a lookup
function for shoreline distances
d ∈ R
+
, and
D
b
(p)
to lookup the
nearest shoreline position b ∈ I
D
.
(a) shoreline distance (b) shoreline direction
Figure 3:
Exemplary visualization of normalized shoreline distances
and shoreline directions for a given water surface.
4.1.2 Local Orientation Estimation
Sobel Filter Structure Tensor
Figure 4: Tangential field.
The estimation of local orienta-
tion is based on the image gra-
dients of the distance map
D
.
A popular choice to approximate
the directional derivatives in
x
-
and
y
-direction is the Sobel fil-
ter which, however, yields non-
smooth tangent information on
the medial axes because opposite
gradients cancel out (Figure 4 left). A simple alternative is to use
the smoothed structure tensor [Brox et al
.
2006] and perform an
eigenanalysis to obtain gradient and tangent information. This leads
to more stable estimates of the local orientation (Figure 4 right).
4.1.3 Medial Axes Computation
θ=0.75π δ=0.0 θ=0.75π δ=0.8
Figure 5: Medial axes.
The medial axes were derived
from the distance map
D
[Cao
et al
.
2010] to align design el-
ements (e.g., labels) along the
middle stream of water sur-
faces. Basically, the medial axes
were obtained by comparing and
thresholding the directions to the
nearest shorelines in the local
neighborhood for each
p ∈ I
D
. For this, the unsigned gradient
orientation n ∈ R
2
of the smoothed structure tensor is used:
b
+
= ||p − D
b
(p + n)|| , b
−
= ||p − D
b
(p − n)|| .
Thresholding the angle between
b
+
and
b
−
then yields an approxi-
mate of the medial axes:
arccos (b
+
· b
−
) > θ ∈ [0, π].
In addition, the shoreline distance was thresholded by
δ ∈ R
+
to
avoid placing design elements too close to shorelines. For all the
examples in this paper, we use θ = 0.75π and δ = 0.8 (Figure 5).
4.1.4 Feature-aligned Distance Transform
u
vu
u
D
Contour-hatching for water surfaces is a com-
plex problem, since the properties of individ-
ual strokes (e.g., length, spacing) vary with the
shoreline distance (P4). A typical approach is
to define orientation fields on a surface to guide
an example-based texture synthesis to salient
feature curves [Wei et al
.
2009]. Yet animat-
ing individual strokes on water surfaces requires fine control over
the parameterization and placement per rendering pass, in partic-
ular to simulate water movements. Our approach parameterizes
the level-set curves of distance map
D
to obtain Euclidean dis-
tance values along its tangential field. By parameterizing these
Shoreline Distance
Feature-aligned Distance
Texture Coordinates
Surface Mask
Figure 6: Exemplary distance maps computed by our system.
feature-aligned distances (
v
-coordinate) and the shoreline distances
(
u
-coordinate), they are directly used as texture coordinates within
real-time shaders (Figure 6).
Seed Non-Seed
Flooding Direction
Algorithm.
For computing a feature-
aligned distance map
T
, we use an approach
similar to vector propagation [Danielsson
1980]. Using the non-normalized distance
map
D
, level sets correspond to the integral
part of the shoreline distances (e.g.,
bdc = 0
for the zero level sets). Starting with the
shorelines, random pixels are selected as
seed points from which (1) Euclidean dis-
tances are propagated along the level sets,
and (2) seed point information is propagated to the inner level sets.
These two steps are repeated for each level set until no more pixels
are available for processing. We implemented a parallel algorithm
by iteratively flooding distance information within the local neigh-
borhood (e.g.,
3 × 3
) of a pixel, which dynamically propagates
seed points during distance map construction (Figure 7). An effi-
cient parallel algorithm for normalization of this map is based on a
reduction [Nehab et al. 2011].
Figure 7:
Intermediate results of our algorithm that iteratively
computes a feature-aligned distance map on a GPU (
256 × 256
pixels, 503 iterations in total).
Discussion.
Exemplary results show that our approach provides
continuous feature-aligned distance values (Figure 6/7). Contrary
to texture synthesis based on energy minimization (e.g., [Xu et al
.
2009]), ours does not provide continuity across the level sets of
a surface. But since individual texture features (e.g., hatches) are
aligned with the level-set curves, no such constraint is required.
This allows us to perform an exact distance transform since no
compression or stretching is required to meet continuity in all major
directions of a surface. Because texture features can only be placed
on the level sets, choosing an adequate distance map resolution is
important to balance rendering quality and performance. On the one
d
(a) discrete input + distance lines
t
(b) continuous output
Figure 8: Bilinear filtering of a feature-aligned distance map.
hand, vector propagation along the level sets performs non-linearly
with the map resolution, and optimization techniques known from
jump flooding [Rong and Tan 2006] are less helpful since highly
curved sections require small step widths. On the other hand, too low
map resolutions insufficiently approximate the shorelines’ directions.
As a compromise, we utilized bilinear sampling for a piecewise-
linear approximation of shoreline and feature-aligned distances. This
approach has been proven effective for the magnification of glyph
contours, even with low-resolution distance maps [Green 2007].
Because bilinear sampling is able to accurately reconstruct distance
information, feature-aligned distance maps of up to
256×256
pixels
can be used for rendering and computed in real-time using our GPU-
based flooding algorithm (Section 5).
δ
δ
p
x
y
d+1
d
d+2
p
1
p
0
p
2
p
3
Bilinear Sampling.
In contrast to
signed distance maps, the accurate recon-
struction of feature-aligned distance val-
ues requires a modified version of bilinear
sampling to avoid filtering across the level
sets of
D
. For this, the shoreline distance
d
for a point
p ∈ I
D
is determined and
compared to the distance information of
the four samples p
0
to p
3
:
T (p) = A + B − ((1 − δ
y
)Bg(A) + δ
y
Ag(B))
A = (1 − u
1
)p
0
+ u
1
p
1
u
1
= (g(p
0
)(δ
x
− 1) + 1)g(p
1
)
B = (1 − u
2
)p
2
+ u
2
p
3
u
2
= (g(p
2
)(δ
x
− 1) + 1)g(p
3
)
where
g(q) = 0
with
q ∈ {p
0
, p
1
, p
2
, p
3
}
if
p, q
correspond to
different level sets to omit a pixel from interpolation, otherwise
g(q) = 1
. As is shown in Figure 8, this modified version provides
continuous feature-aligned distance values on the level sets.
4.2 Shading Techniques
The results of the quantitative surface analysis are utilized for
cartography-oriented shading (Section 2). The following techniques
utilize pixel shaders and texturing combined with bilinear sampling
to accurately reconstruct distance information. These techniques
can be parameterized in terms of tone and density to provide a
view-dependent level-of-abstraction (see the Appendix).
Waterline Color
Fade-Out
0
Body Color
Fade-In
Shoreline
d
Figure 10: Waterlining parameterized by shoreline distance.
4.2.1 Waterlining and Water Stippling
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
d
φ
(d)
s=40, e=0.6, h=0
Id
φ
Figure 9:
Non-linear step
function ϕ(d).
In the following, a non-normalized ver-
sion of distance map
D
is used to
independently apply waterlining and
stippling from a water surface’s scale
(e.g., oceans vs. lakes). To comply
with non-equidistant interspaces (P1),
target distance values
ϕ(d)
are com-
puted using a non-linear step function:
ϕ(d) =
(b(s · d)
e
+ hc − h)
1.0/e
s
.
The spacing of
ϕ
can be parameterized by
e, s ∈ R
+
to define a
corresponding number of steps in the interval of
D
(Figure 9). In
addition, these steps can be shifted along d using h ∈ [0, 1].
Waterlining.
Waterlines correspond to shaded areas of a water
surface with equal shoreline distance. To render waterlines, the dis-
tances
τ ∈ R
+
between the positions obtained by
ϕ(d)
are thresh-
olded by a corresponding width
ψ ∈ R
+
, and padded by fade-in and
fade-out intervals (Figure 10) for antialiasing, and to provide smooth
transitions. For a continuous level-of-abstraction,
ϕ(d)
and
ψ
are
parameterized by the view distance. At high view distances, this
significantly reduces the number of rendered waterlines and provides
a smooth transition while zooming in (see the accompanying video).
Water Stippling.
Water stippling refers to placing small dots with
irregular distribution along waterlines to convey shape and motion.
Our algorithm uses an enhanced variant of Glanville’s [2004] texture
bombing to place water stipples with feature-aligned distribution and
irregular density. The basic idea of texture bombing is to randomly
place glyphs in regularly distributed grid cells. We extend this algo-
rithm by three phases; stipple selection, stipple displacement, and
stipple filtering (Figure 11). Instead of using a random placement
of stipples, offsets are computed that align them with the waterlines
of
D
. Our algorithm starts with stipples that are centered in regularly
distributed grid cells and mapped onto a water surface (Figure 11a).
1. Stipple Selection:
Stipples within grid cells that cross a waterline
were selected for further processing (Figure 11a). For this, the
distance to the next waterline (d − ϕ(d)) is thresholded.
2. Stipple Displacement:
The gradient direction of
D
was used to
compute the approximate target position to the nearest waterline.
If origin and target positions correspond to the same grid cell (first
phase), a stipple was displaced towards the target position. This
results in stipples lined up with the waterlines (Figure 11b).
3. Stipple Filtering:
The displacement of stipples in the gradient di-
rection of
D
increased the irregular distribution along waterlines. To
render stipples with non-regular intervals, noise or pseudo-random
numbers were used for additional filtering (Figure 11c). Figure 12
exemplifies that this improves randomness.
Up to this point, stipples might be rendered with low density because
waterlines force them to split into multiple directions. To regular-
ize the density near coastal areas, the phases 1-3 were repeated to
place additional layers of stipples within slightly shifted grid cells.
We found that two layers were sufficient to meet this requirement
(Figure 12c). We experimented with different parameterizations to
locally vary the stipple density and tone, for example using tonal art
maps to symbolize flow velocity (P3). In addition, iterative appli-
cation of our algorithm with shifted step functions can be used to
indicate highlights or shadowed areas. For instance, a second pass
with
ϕ(d)
shifted halfway by
h = 0.5
was used to place additional
stipples at occluded areas (e.g., near bridges, Figure 19) to improve
depth perception of a virtual 3D scene (P3).
(a) selection (b) displacement (c) filtering
Figure 11:
Schematic overview of the water stippling phases. Wa-
terlines are marked as red lines, rendered stipples as black dots.
4.2.2 Contour-Hatching
To symbolize water movements, we developed a novel contour-
hatching technique. Once a feature-aligned distance map was com-
puted, individual stroke maps were irregularly placed with non-
linear distance to shorelines to express motion. Similar to Kaloger-
akis et al. [2012], parameters were defined to provide artistic control
over this placement:
• Length (l ∈ R
+
) defines the length of a stroke.
• Thickness (t ∈ [0, 1]) defines the width of a stroke.
• Spacing (s ∈ [0, 1]) controls the stroke density.
• Randomness (r ∈ [0, 1]) controls the stroke irregularity.
v
φ(d)+t
u
φ(d-1) φ(d)
s
d
...
v
φ(d)+
t
u
s
s
d
d
The main idea is to derive texture
coordinates
u, v
for each rendering
fragment by bilinearly sampling the
distance maps
D
and
T
. To obtain
the
u
-coordinate, waterline positions
and the stroke width
t
were used
to compute the fraction
u = (d −
ϕ(d))/t
. To obtain the correspond-
ing
v
-coordinate, feature-aligned dis-
tance values of the sampled distance map
T
were scaled by
l
to
match the desired stroke length. In addition, noise was used to
clamp the
v
-coordinate for an irregular placement of individual
strokes, and the
s
and
r
parameters for density control and filtering.
To render contour-hatches excessively wavy (P5), texture maps were
used that had been digitized from hand-drawn strokes. Because the
stroke placement works in object-space, it provides frame-to-frame
coherence, and avoids the shower door effect known from techniques
that work in image-space (e.g., [Kim et al. 2008b]).
From our analysis in Section 2, we observed that stroke layers
of varying tone and density are used based on the shoreline dis-
tance (P4). This observation can be modeled by our algorithm
using 3 layers with different parameter sets: dense, solid strokes
near shorelines, loose strokes with irregular density, and strokes with
shorter lengths near the medial axes (see Figure 13). Because our
technique is texture-based, water movements can be modeled quite
easily by shifting individual strokes along the major directions of
Figure 13:
Contour-hatching for water surfaces: (left) dense, wavy
strokes near shorelines, (right) loose strokes near the medial axes.
(a) overview (b) middle stream (c) coastal area
Figure 12:
A result of our water stippling technique showing a
non-linear, feature-aligned, and irregular distribution of stipples.
the distance maps D or T , for instance by a temporal displacement
of the v-coordinate using a sine function to animate rivers.
4.2.3 Water Vignetting and Cross-Hatching
In modern cartography, water vignettes are based on color gradi-
ents. A simple approach is to threshold the shoreline distance and
interpolate between a shoreline and water body’s color. We used
this effect to complement our waterlining technique (Figure 1 left).
A similar effect can be achieved by cross-hatching the shoreline
areas by a tonal art map [Praun et al
.
2001]. We used a map of five
varying levels of stroke size and density, which were blended and
mapped on water surfaces according to the shoreline distance, and
parameterized according to the view distance to create a continuous
level-of-abstraction [Semmo et al
.
2012]. In contrast to tone-based
shading, this approach does not affect shading of landmass (Fig-
ure 15), which allows us to visualize additional geospatial features,
such as terrain.
4.2.4 Thematic Visualization
Figure 14:
Symbol-
izing flooded areas.
We used distance maps for an automated, in-
ternal labeling that complies with the design
principles of cartographers (P6/P7). The
main idea is to derive piecewise cubic B
´
ezier
curves from the medial axes of the distance
map
D
and warp text to these curves ac-
cordingly [Ropinski et al
.
2007; Cipriano
and Gleicher 2008]. To obtain the control
points, pixels of the medial axes were traced
and iteratively downsampled in image-space
by nearest-neighbor interpolation. Together
with the tangent information of the structure tensor, arc-length pa-
rameterization was used to warp text with the flow direction of water
surfaces, and orient it with the viewing direction (Figure 16).
For symbolization, texture bombing was used and parameterized
so that signatures always face the view direction when viewed in
3D (Figure 14) and comply with (P8). Alternatively, an example-
based approach may be used to arrange signatures with more artistic
control, for which we refer to the work by Hurtut et al. [2009].
Figure 15:
A globe shaded by crosshatched strokes: (left) binary
mask, (middle) result of [Webb et al. 2002], (right) our result.
Figure 16:
Exemplary result of our labeling algorithm which aligns
font glyphs according to the shoreline distance and orientation.
5 Results
We have implemented our system using C++ and OpenGL/GLSL.
OpenSceneGraph is used as the rendering engine to handle 3D data
sets. The operations of the quantitative surface analysis are designed
for parallel execution, and we have implemented them in CUDA to
significantly improve overall performance. In particular, the PBA al-
gorithm is used for the computation of Euclidean distance maps [Cao
et al
.
2010], together with a reduction for normalization [Nehab et al
.
2011]. For text rendering, NVidia’s
NV path rendering
exten-
sion is used to enable the rendering and transforming of high quality,
instance-based text in a single pass. In the following, we demon-
strate the usefulness and flexibility of our rendering techniques for
different real-world data sets and potential usage scenarios.
5.1 Applications
Figure 17 shows a comparison of our rendering techniques using the
example of Spirit Lake (at Mount St. Helens, USA). We observed that
waterlining is a functional illustration technique that is able to com-
municate distance information quite effectively. The effects of water
stippling and contour-hatching are similar but add a sense of motion
and uncertainty. Coastal vignetting, by contrast, primarily focuses on
the land-water interface itself to improve figure-ground perception.
These techniques complement other cartography-oriented shading
techniques quite well. This is demonstrated by shading the terrain
in the environment with hachures of varying thickness according to
the slope steepness [Buchin et al
.
2004]. Moreover, our rendering
techniques provide a level-of-abstraction (see the Appendix), which
is exemplarily shown in the right image of Figure 17 where more
or less waterlines are depicted according to the view distance to
avoid visual clutter. The accompanying video demonstrates that
this parameterization yields a smooth, continuous transition while
zooming in and out. This example also demonstrates the ability of
our system to handle 3D scenes and provide a spatial and temporal
coherence. Because the rendering techniques are texture-based, they
are independent from a model’s geometric complexity. Finally, we
experimented with using our rendering techniques concurrently. For
instance, water stipples can be seamlessly blended with waterlines
according to the view distance; or coastal vignetting to complement
waterlining (Figure 1).
Our waterlining technique may be useful in flooding simula-
tions, i.e., to assess distances to the nearest safety zones for evacua-
tion planning. When performed over time, waterlines dynamically
shift with the flood distribution to convey motion and enhance the
depiction of land cover. This effect is demonstrated in the supple-
mentary video and is exemplarily shown in Figure 18 for the city of
Boston (USA). Here, a plane is used and temporally shifted upwards
to represent the change in the mean sea level. Using this plane as a
clipping mask with an orthographic projection, the corresponding
flooded areas are obtained and shaded in real-time.
Table 1:
Performance evaluation (in ms): distance / feature-aligned
distance transform (
D/T
), orientation and medial axis computation.
Image Res. D T Orient. M. Axes Total
128 × 128 1.6 26.6 0.1 0.7 29.0
256 × 256 2.2 96.3 0.2 0.8 99.5
512 × 512 4.5 371.6 0.6 0.9 377.6
Table 2: Performance evaluation of our illustrative rendering tech-
niques for different screen resolutions (in frames-per-second).
Screen Res. waterlining stippling contour-hatching
800 × 600 534 162 159
1280 × 720 523 88 84
1600 × 900 521 59 55
1920 × 1080 514 42 41
Figure 19 demonstrates the usefulness of our rendering techniques
in urban planning and cultural heritage. Within these domains, it is
often desired to avoid authentic impressions, in particular because
of missing evidence in the (re)construction or because construction
plans may be altered in the future. The top image shows a topograph-
ical reconstruction of ancient Cologne, in which contour-hatching
is used to express uncertainty. We animated the individual strokes
to express water movements. In addition, symbolization is used to
highlight those river areas that were flooded in ancient times. The
bottom image shows a bridge construction, where water stippling
is used to add expressiveness. As can be seen, the stipple density is
increased in the shadowed areas to improve depth perception.
5.2 Performance Evaluation
The performance tests of our system were conducted on an In-
tel
®
Xeon
™ 4×
3.06 GHz with 6 GByte RAM and NVidia
®
GTX
660 Ti GPU with 2 GByte VRAM. We used Spirit Lake (Figure 17)
as a test model. The results in Table 1 show the run-time of the
quantitative surface analysis scales with the resolution of a distance
map. The feature-aligned distance transform is shown to be a lim-
iting factor; however, its implementation is not heavily optimized
and we see potential to increase the performance. We compared
different sizes of distance maps for our illustrative rendering tech-
niques. Similar to signed distance maps [Green 2007], we achieve
stable results when bilinearly sampling a low resolution of a feature-
aligned distance map (
128 × 128
pixels). Note that the timings for
the distance maps include normalization. Table 2 shows that our
illustrative rendering techniques perform at real-time frame-rates
in HD resolution. During rendering, we observe that our shading
techniques are fill-limited and achieve, in SD resolution, twice the
performance of an HD resolution. We conclude that our system
for feature-aligned waterlining, stippling, and hatching performs in
real-time, and therefore is applicable to render animated 3D scenes.
5.3 Limitations
Our shading techniques work in object-space and the computation
of distance maps requires closed polygons for processing. For large-
scale water surfaces with complex courses, distance maps of high
resolution are required to achieve quality shading results. Here,
memory resources limit the distance map sizes that can be processed
by a GPU; for our system
≈ 16
Megapixels (MP) with 2 GByte
VRAM. Moreover, we observed that our feature-aligned distance
transform does not perform in real-time when computing distance
maps with
> 0.25
MP. Nonetheless, we observed that distance maps
of
256 × 256
pixels are sufficient for most water surfaces when
using bilinear filtering.
Figure 17:
Exemplary results of our rendering techniques for 3D mapping, (left) compared with each other within the environment of Mount St.
Helens, (right) waterlining applied to a globe that provides a continuous level-of-abstraction when zooming in and out.
Figure 18:
Flooding simulation for the city of Boston enhanced by our waterlining technique and illustrative rendering to express uncertainty.
Figure 19:
Further results of our rendering techniques for urban planning and landscaping: (top) contour-hatching used to express uncertainty
in a reconstructed topographical model of ancient Cologne (Germany), which served as the basis for the 3D reconstruction shown to the right,
(bottom) water stippling used to enhance the rendering of a bridge construction.
6 Conclusions and Future Work
We present a system for rendering water surfaces with cartography-
oriented design. Our real-time rendering techniques adopt design
principles from traditional cartography to improve figure-ground
perception and express a sense of motion. For contour-hatching,
we propose a novel feature-aligned distance transform to align indi-
vidual strokes with the shorelines of water surfaces. Results show
that our techniques provide temporal and spatial coherence, can be
parameterized for a view-dependent level-of-abstraction, and can be
useful within 3D geovirtual environments for map exploration, urban
planning, landscaping, and disaster management. Because of their
application to geospatial data, we plan to elaborate on the usefulness
of our techniques for geovisualization. Further, we plan to conduct
a user study to confirm significant effects in orientation, navigation,
and analysis tasks performed within 3D geovirtual environments.
Acknowledgments
The authors would like to thank the anonymous reviewers for their
valuable comments. This work was partly funded by the Federal
Ministry of Education and Research (BMBF), Germany, within the
InnoProfile Transfer research group “4DnDVis”, and was partly
supported by the ERC-2010-StG 259550 XSHAPE grant.
References
BRATKOVA, M., SHIRLEY, P., AND THOMPSON, W. B. 2009.
Artistic rendering of mountainous terrain. ACM Trans. Graph.
28, 102:1–102:17.
BROX, T., BOOMGAARD, R., LAUZE, F., WEIJER, J., WEICKERT,
J., MR
´
AZEK, P., AND KORNPROBST, P. 2006. Adaptive Struc-
ture Tensors and their Applications. Visualization and Processing
of Tensor Fields, 17–47.
BUCHIN, K., SOUSA, M. C., D
¨
OLLNER, J., SAMAVATI, F., AND
WALTHER, M. 2004. Illustrating Terrains using Direction of
Slope and Lighting. In ICA Mountain Carthography Workshop,
259–269.
CAO, T.-T., TANG, K., MOHAMED, A., AND TAN, T.-S. 2010.
Parallel Banding Algorithm to compute exact distance transform
with the GPU. In Proc. I3D, 83–90.
CHRISTENSEN, A. H. 1999. Cartographic Line Generalization
with Waterlines and Medial-Axes. Cartography and Geographic
Information Science 26, 1, 19–32.
CHRISTENSEN, A. H. 2008. A Reflection on the Waterlining
Technique in Relation to the History of Map Ornamentation. The
Cartographic Journal 45, 1, 68–78.
CIPRIANO, G., AND GLEICHER, M. 2008. Text Scaffolds for
Effective Surface Labeling. IEEE Trans. Vis. Comput. Graphics
14, 6, 1675–1682.
COCONU, L., DEUSSEN, O., AND HEGE, H. 2006. Real-time
pen-and-ink illustration of landscapes. In Proc. NPAR, 27–35.
DANIELSSON, P.-E. 1980. Euclidean distance mapping. Computer
Graphics and Image Processing 14, 3, 227–248.
DARLES, E., CRESPIN, B., GHAZANFARPOUR, D., AND GON-
ZATO, J. 2011. A Survey of Ocean Simulation and Rendering
Techniques in Computer Graphics. Comput. Graph. Forum 30, 1,
43–60.
DEUSSEN, O., AND STROTHOTTE, T. 2000. Computer-generated
pen-and-ink illustration of trees. In Proc. ACM SIGGRAPH,
13–18.
D
¨
OLLNER, J., AND WALTHER, M. 2003. Real-time expressive
rendering of city models. In Proc. IEEE IV, 245–250.
EDEN, A. M., BARGTEIL, A. W., GOKTEKIN, T. G., EISINGER,
S. B., AND O’BRIEN, J. F. 2007. A Method for Cartoon-
Style Rendering of Liquid Animations. In Proc. ACM Graphics
Interface, 51–55.
FRENCH, T. 1918. A manual of engineering drawing for students
and draftsmen. McGraw-Hill book company.
FRISKEN, S. F., PERRY, R. N., ROCKWOOD, A. P., AND JONES,
T. R. 2000. Adaptively sampled distance fields: a general
representation of shape for computer graphics. In Proc. ACM
SIGGRAPH, 249–254.
GERL, M., AND ISENBERG, T. 2013. Interactive example-based
hatching. Computers & Graphics 37, 1-2, 65–80.
GIRSHICK, A., INTERRANTE, V., HAKER, S., AND LEMOINE, T.
2000. Line direction matters: an argument for the use of principal
directions in 3D line drawings. In Proc. NPAR, 43–52.
GLANVILLE, R. S. 2004. Texture Bombing. In GPU Gems.
Addison-Wesley, 323–338.
G
¨
OTZELMANN, T., ALI, K., HARTMANN, K., AND STROTHOTTE,
T. 2005. Form Follows Function: Aesthetic Interactive Labels.
In Proc. CAe, 193–200.
GREEN, C. 2007. Improved alpha-tested magnification for vector
textures and special effects. In ACM SIGGRAPH Courses, 9–18.
HUFFMAN, D. P. 2010. On Waterlines: Arguments for their Em-
ployment, Advice on their Generation. Cartographic Perspectives,
NACIS 66, 23–30.
HURTUT, T., LANDES, P.-E., THOLLOT, J., GOUSSEAU, Y.,
DROUILLHET, R., AND COEURJOLLY, J.-F. 2009. Appearance-
guided Synthesis of Element Arrangements by Example. In Proc.
NPAR, 51–60.
IMHOF, E. 1972. Thematische Kartographie, vol. 10. Walter de
Gruyter.
IMHOF, E. 1975. Positioning names on maps. The American
Cartographer 2, 2, 128–144.
ISENBERG, T. 2013. Visual Abstraction and Stylisation of Maps.
The Cartographic Journal 50, 1, 8–18.
JOBST, M., AND D
¨
OLLNER, J. 2008. 3D City Model Visualization
with Cartography-Oriented Design. In Proc. REAL CORP, 507–
516.
KALOGERAKIS, E., NOWROUZEZAHRAI, D., BRESLAV, S., AND
HERTZMANN, A. 2012. Learning hatching for pen-and-ink
illustration of surfaces. ACM Trans. Graph. 31, 1, 1:1–1:17.
KIM, D., SON, M., LEE, Y., KANG, H., AND LEE, S. 2008.
Feature-guided Image Stippling. Comput. Graph. Forum 27, 4,
1209–1216.
KIM, Y., YU, J., YU, X., AND LEE, S. 2008. Line-art illustration
of dynamic and specular surfaces. ACM Trans. Graph. 27, 5,
156:1–156:10.
KIM, S., WOO, I., MACIEJEWSKI, R., AND EBERT, D. 2010.
Automated Hedcut Illustration Using Isophotes. In Proc. Smart
Graphics, 172–183.
KRAAK, M., AND ORMELING, F. 2003. Cartography: Visualiza-
tion of Geospatial Data. Pearson Education.
KYPRIANIDIS, J. E., COLLOMOSSE, J., WANG, T., AND ISEN-
BERG, T. 2012. State of the ’Art’: A Taxonomy of Artistic
Stylization Techniques for Images and Video. IEEE Trans. Vis.
Comput. Graphics 19, 5, 866–885.
MAASS, S., AND D
¨
OLLNER, J. 2008. Seamless Integration of
Labels into Interactive Virtual 3D Environments Using Parame-
terized Hulls. In Proc. CAe, 33–40.
MACEACHREN, A. 1995. How Maps Work. Guilford Press.
MERIAN, M. 2005. Topographia Germaniae.
NEHAB, D., MAXIMO, A., LIMA, R. S., AND HOPPE, H. 2011.
GPU-efficient recursive filtering and summed-area tables. ACM
Trans. Graph. 30, 176:1–176:12.
PRAUN, E., FINKELSTEIN, A., AND HOPPE, H. 2000. Lapped
textures. In Proc. ACM SIGGRAPH, 465–470.
PRAUN, E., HOPPE, H., WEBB, M., AND FINKELSTEIN, A. 2001.
Real-time hatching. In Proc. ACM SIGGRAPH, 581–586.
ROBINSON, A. H., MORRISON, J. L., MUEHRCKE, P. C., KIMER-
LING, A. J., AND GUPTILL, S. C. 1995. Elements of cartogra-
phy. New York: John Wiley & Sons.
RONG, G., AND TAN, T.-S. 2006. Jump flooding in GPU with
applications to Voronoi diagram and distance transform. In Proc.
ACM I3D, 109–116.
ROPINSKI, T., PRASSNI, J.-S., ROTERS, J., AND HINRICHS, K.
2007. Internal Labels as Shape Cues for Medical Illustration. In
Proc. VMV, 203–212.
SALISBURY, M. P., WONG, M. T., HUGHES, J. F., AND SALESIN,
D. H. 1997. Orientable textures for image-based pen-and-ink
illustration. In Proc. ACM SIGGRAPH, 401–406.
SEMMO, A., TRAPP, M., KYPRIANIDIS, J. E., AND D
¨
OLLNER, J.
2012. Interactive Visualization of Generalized Virtual 3D City
Models using Level-of-Abstraction Transitions. Comput. Graph.
Forum 31, 885–894.
TYNER, J. 2010. Principles of map design. Guilford Press.
WEBB, M., PRAUN, E., FINKELSTEIN, A., AND HOPPE, H. 2002.
Fine tone control in hardware hatching. In Proc. NPAR, 53–58.
WEI, L., LEFEBVRE, S., KWATRA, V., TURK, G., ET AL. 2009.
State of the Art in Example-based Texture Synthesis. In Euro-
graphics 2009 State of the Art Report, 93–117.
XU, K., COHEN-OR, D., JU, T., LIU, L., ZHANG, H., ZHOU, S.,
AND XIONG, Y. 2009. Feature-aligned shape texturing. ACM
Trans. Graph. 28, 108:1–108:7.
YU, J., JIANG, X., CHEN, H., AND YAO, C. 2007. Real-time
cartoon water animation. Computer Animation and Virtual Worlds
18, 4-5, 405–414.
Appendix
Level-of-Abstraction 2 Level-of-Abstraction 1 Level-of-Abstraction 0
WaterliningWater StipplingContour-HatchingCross-Hatching
Figure 20:
Exemplary parameterization results of our rendering techniques for a view-dependent level-of-abstraction. In order to reduce
visual clutter at high view distances (bottom row), the number of rendered waterlines, stipples and hatches are reduced significantly. Once
these parameterizations have been authored by our system, blending between them is performed in real-time using OpenGL fragment shaders.
