1. Hidden Surface Removal
고려대학교 컴퓨터 그래픽스 연구실

2. 3D Rendering Pipeline Hidden surface removal can be inserted in...
3D Primitives
3D Modeling Coordinates
Model Transformation
3D World Coordinates
Lighting
3D World Coordinates
Viewing Transformation
3D Viewing Coordinates
Projection Transformation
Hidden surface removal can be inserted in...
2D Projection Coordinates
Clipping
2D Projection Coordinates
Viewport Transformation
2D Device Coordinates
Scan Conversion
2D Device Coordinates
Image

3. Table of Contents Motivation Algorithms for hidden surface removal
Back-face detection
Painter’s algorithm
Ray casting
Scan-line
Z-buffer
Area subdivision

4. Motivation Surfaces may be back-facing Surfaces may be occluded
Polygon
Viewer
Viewer
Occluding
Polygon
Occluded
Polygon

5. Motivation Surfaces may be overlapping Surfaces may be intersecting
Viewer
Viewer

6. Algorithms Back-face detection Painter’s algorithm Ray casting
Scan-line
Z-buffer
Area subdivision

7. Viewing Transformation
Back-face Detection
Do not render any surfaces oriented away from viewer
Back-facing
Polygon V N
3D Primitives
Viewer
Model Transformation
Lighting
Polygon is back-facing to the viewer if V•N > 0
Viewing Transformation

8. Viewport Transformation
Painter’s Algorithm
Sort surfaces
In order of decreasing depth
Scan convert surfaces
Back to front processing A D E
Viewer C
Viewport Transformation
View
Plane B
Scan Conversion
Depth Sort
Image

9. Painter’s Algorithm Determine zmax, zmin Sort on zmax
Start with polygon with the greatest depth (S)
Compare S to all other polygons in order as below
There is no depth overlap
The bounding rectangles in the xy plane for the two surfaces do not overlap
Surface S is completely behind the overlapping surface relative to the viewing position
The overlapping surface is completely in front of S relative to the viewing position
The projections of the two surfaces onto the view plane do not overlap

10. Painter’s Algorithm

11. Painter’s Algorithm If all four fails, interchange S and S’
but, can we sure ?
finished? wrong!
good!
We need to test for each surface
reordered in the list

12. Painter’s Algorithm We can fail in this case occurring infinite loop
 surfaces need to be subdivided

13. Viewing Transformation
Ray Casting
Cast ray from viewpoint through each pixel
To find front-most surface
Comments
O(plogn) for p pixels
Conceptually simple, but not generally used A D E
3D Primitives
Model Transformation
Viewer C
Lighting
View
Plane B
Viewing Transformation

14. Z-Buffer (Depth Buffer)
Store depth of closest surface for each pixel
In z-buffer
As scan convert
Update only pixels whose (interpolated) depth is closer than the depth stored in the frame buffer
z=3
Viewport Transformation
Scan Conversion
Image
z=1
z=5
z=4
z=2
z=5
z=5

15. Z-Buffer Comments Polygons can be rasterized in any order
Requires more memory, generally twice
Requires per pixel processing
Commonly implemented in hardware

16. Viewport Transformation
Scan-Line
For each scan line
Construct intersection edge table
Sort by depth
z=3
z=1
z=5
Scan
Line
z=4
Viewport Transformation
Scan Conversion
Image
z=2
z=5
z=5
z=1.8
z=3.8
Example:
Spans
z=5
z=5

17. Scan-Line Comments Fully compute only front-most pixels
Coherence along scan lines
Can use incremental algorithm
Commonly implemented in software

18. Area Subdivision Fill area if Otherwise, subdivide
All surfaces are outside
Only one surface intersects
One surface occludes other surfaces within area.
Otherwise, subdivide

19. Conclusion Hidden surface algorithms Hardware-implemented
Back-face detection
Depth sort
Ray casting
Z-buffer
Scan-line
Area subdivision
Hardware-implemented