Architectural geometry

Research 2009.03.05 17:29
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H. Pottmann, A. Asperl, M. Hofer and A. Kilian: Architectural Geometry. Bentley Institute Press (2007)


Source

Content

Chapter 1. Creating a Digital 3D Model
Chapter 2. Projections
Chapter 3. Polyhedra and Polyhedral Surfaces
Chapter 4. Boolean Operations
Chapter 5. Planar Transformations
Chapter 6. Spatial Transformations
Chapter 7. Curves and Surfaces
Chapter 8. Freeform Curves
Chapter 9. Traditional Surface Classes
Chapter 10. Offsets
Chapter 11. Freeform Surfaces
Chapter 12. Motions, Sweeping, and Shape Evolution
Chapter 13. Deformations
Chapter 14. Visualization and Analysis of Shapes
Chapter 15. Developable Surfaces and Unfoldings
Chapter 16. Digital Prototyping and Fabrication
Chapter 17. Geometry for Digital Reconstruction
Chapter 18. Shape Optimization Problems
Chapter 19. Discrete Freeform Structures

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Source: 1. Advanced graphics programming using OpenGL (Morgan Kaufmann)            
            2. OpenGL porgramming guide (Addison-Wesley Professional)

We assume that triangle mesh is rendered and then, we can draw the corresponding wireframe objects with their hidden lines removed as follows.

1. Disable writing to the color buffer with glColorMask.
2. Set the depth function to GL_LEQUAL.
3. Enable depth testing with glEnable(GL_DEPTH_TEST).
4. Render the object as triangles.
5. Enable writing to the color buffer.
6. Render the object as edges using such as GL_LINES, GL_LINE_LOOP, GL_LINE_STRIP, or method using glBegin(GL_POLYGON) and glPolygonMode(GL_FRONT_AND_BACK, GL_LINE).

The above algorithm works for the almost cases. However, depth rasterization artifacts from quantization errors may happen since the pixels at the edges of triangles rendered as polygon and the pixels from the edges rendered as line have depth values that are numerically close. To handel this problem, we may use the glPolygonOffset command which move the lines and polygons relative to each other.

- glEnable(GL_POLYGON_OFFSET_LINE): to offset the lines in front of the polygons
- glEnable(GL_POLYGON_OFFSET_FILL): to move polygon surfaces behind the lines

Example code fragments using glEnable(GL_POLYGON_OFFSET_FILL) are as follows.

 glColorMask(GL_FALSE, GL_FALSE, GL_FALSE, GL_FALSE);
 glDepthFunc(GL_LEQUAL);
 glEnable(GL_DEPTH_TEST);
 glEnable(GL_POLYGON_OFFSET_FILL);
 glPolygonOffset(1.0, 1.0);
// Draw triangles
glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE);
// Draw edges

Otherwise, we may accomplish the same effect by drawing line segments for edges and drawing filled triangles as follows.

glDisable(GL_LIGHTING);
glEnable (GL_DEPTH_TEST);
glPolygonMode(GL_FRONT, GL_LINE); 
glColor3f(FOREGROUND_COLOR);

// Draw triangle edges
glLineWidth(PRE_DEFINED_LINE_WIDTH);
glBegin(GL_LINES);
// ...
glEnd();
////////////////////////

glPolygonMode(GL_FRONT, GL_FILL);
glEnable(GL_POLYGON_OFFSET_FILL);
glPolygonOffset(1.0, 1.0);
glColor3f(BACKGROUND_COLOR);

// Draw filled triangles
glBegin(GL_TRIANGLES);
// ...
glEnd();
////////////////////////
glDisable(GL_POLYGON_OFFSET_FILL);

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T-splines and T-NURCCs

by Thomas W. Sederberg, Jianmin Zheng, Almaz Bakenov and Ahmad Nasri


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Visual Analysis of Biomolecular Surfaces

by Vijay Natarajan1, Patrice Koehl2, Yusu Wang3 and Bernd Hamann3

In: Visualization in Medicine and Life Sciences,
Lars Linsen, Hans Hagen (Eds.), Springer, 2007

1: Indian Institute of Science, India
2: University of California, USA
3: The Ohio State University, USA

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