The concept of clipping planes is well known in computer graphics and can be used to create cut-away views. But clipping against just analytical defined planes is not always suitable for communicating every aspect of such visualization. For example, in hand-drawn technical illustrations, artists tend to communicate the difference between a cut and a model feature by using non-regular, sketchy cut lines instead of straight ones. To enable this functionality in computer graphics, this paper presents a technique for applying 2.5D clip-surfaces in real-time. Therefore, the clip plane equation is extended with an additional offset map, which can be represented by a texture map that contains height values. Clipping is then performed by varying the clip plane equation with respect to such an offset map. Further, a capping technique is proposed that enables the rendering of caps onto the clipped area to convey the impression of solid material. It avoids a re-meshing of a solid polygonal mesh after clipping is performed. Our approach is pixel precise, applicable in real-time, and takes fully advantage of graphics accelerators.

1. 2.5D Clip-Surfaces for Technical Visualization
Matthias Trapp & Jürgen Döllner
Hasso-Plattner-Institut, University of Potsdam, Germany
WSCG 2013
21st International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, 2013

2. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner2
Clippling-Plane vs. 2.5D Clip-Surface
Original Mesh
w/o Clipping
Clipping using
Half-Space Test
Clipping using a
2.5D Clip-Surface (CS)
h

3. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner3
Motivation

4. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner4
Exemplary Result

5. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner5
Motivation – Wrap Up
2.5 Clip-Surfaces (CS):
 Enables non-planar cut-surfaces
 Create more sophisticated cut-away views
Contributions:
 Extended clipping-plane parameterization
 Automatic cap-surface generation
Implementation Goals:
 Hardware-accelerated rendering
 Interactive configuration
 Material
 Silhouettes
 Lighting & Shading

6. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner6
Outline
Clipping using 2.5D Clip-Surfaces
Creating & Rendering of Cap-Surfaces

7. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner7
2.5D Clip-Surface Parameterization
 O Plane Origin
 U, V Direction Vectors
 S = (sx,sy,sz) Scaling Vector
 OM Offsetmap
VectorScaling
TexturemapOffset
NormalPlane
VectorsDirection,
Origin
,,,,,
3
3
3
RS
OM
VUN
RVU
RO
SOMVUOCS

8. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner8
Clipping Equation
y
N
x
N
N
zsample
s
V
VOP
s
U
UOP
T
NNOPPP
otherwisefalse
sTOMfONNPtrue
PCSclip
,
0,
,

9. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner9
GLSL Implementation
bool clipReliefPlane(in mat4 config, // configuration matrix
in vec4 point, // position in eye-space
in sampler2D reliefSampler) // 2D relief texture
{ // compute plane in eye space...
vec3 O = (gl_ModelViewMatrix * vec4(config[0].xyz, 1.0)).xyz;
vec3 A = normalize( gl_NormalMatrix * normalize(config[1].xyz) );
vec3 B = normalize( gl_NormalMatrix * normalize(config[2].xyz) );
vec3 N = cross(A, B);
// project current fragment coordinate on plane
vec3 pV = point.xyz - dot(point.xyz - O, N) * N;
// compute offset texture coordinates
float s = dot(pV - O, A) / length(config[1].xyz);
float t = dot(pV - O, B) / length(config[2].xyz);
// fetch height... maybe zero
float height = texture2D(reliefSampler, vec2(s,t) * config[3].st).x;
// compute reference plane
float plane = dot(point.xyz, N) - dot(N, O) + (height * config[3].z );
// perform clipping
return (plane < 0.0 && bool(config[3].w));
}

10. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner10
Multiple 2.5D Clip-Surfaces

11. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner
Capping Openings – Real-World Example

12. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner12
Capping Approach
Goals:
 Convey material / inner structure of the input mesh
 Enable assisted modeling of cap-surface appearance
Approach:
 Compute polygonal cap-surface from 2.5D clip-surface
 Subsequent rendering after the clipping pass
=+
Clipped Mesh Cap-Surface Final Result

13. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner13
Generating the Cap-Surface
A B
CS Derived Surface Clipped Surface
A: Generate Cap-Surface:
 Use Dynamic Mesh Refinement or Tessellation Shader
 Perform displacement, shading, texturing,…
B: Clip Cap-Surface to Opening of the Clipped Mesh:
 Clip “outside” parts of the cap-surface

14. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner14
Clipping the Cap-Surface

15. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner15
Capping – Challenges for 2.5D Surfaces
Cap
Capping Clipping Planes:
Render planar mesh using back-face
information and stencil test
Capping 2.5D Clip-Surfaces:
Back-face information does not
determine non-planar surface
completely
Back Faces CapCap

16. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner16
Decision Problem
Is a point P on the cap-surface inside a solid mesh S ?
Volumetric depth-test approach [Trapp08] :
Additional data structure required:
 Layered Depth Image (LDI) [Shade98]
 Image-based representation of shape volume
 Computed in pre-processing using depth-peeling [Everitt01]
SPOutside
SPInside
SPVDT ,

17. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner17
Example of a Layered Depth Image

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Volumetric Depth Test

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Volumetric Depth Test – Performance
2 FS 2 BS
2 LS
4 FS 4 BS
4 LS
8 FS 8 BS
8 LS
10 FS 10 BS
10 LS
14 FS 14 BS
14 LS
16 FS 16 BS
16 LS
400
500
600
700
800
900
1000
1100
640x480
800x600
1024x768
1600x1200

20. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner20
Application Examples

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Application Examples

22. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner22
Wrap-Up

23. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner23
Conclusions
Summary
 Advanced clipping approach for non-planar surfaces
 Multi-pass real-time rendering technique
 Fully implemented on GPU
Drawbacks
 Requires additional data structure
 Requires high-tessellated cap-surface
Future Work
 Direct manipulation techniques
 Stencil-routed A-Buffer [Myers07] instead of LDI

24. 2.5D Clip-Surfaces for Technical Visualization :: Matthias Trapp & Jürgen Döllner24
Thank You ! - Questions ?
Contact:
Matthias Trapp
matthias.trapp@hpi.uni.potsdam.de
Jürgen Döllner
juergen.doellner@hpi.uni.potsdam.de
Computer Graphics Systems Group
http://www.hpi.uni-potsdam.de/doellner/