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Principles of Computer Graphics and Image Processing
Visibility, Culling, Clipping (05)
- RNDr. Martin Madaras, PhD.
martin.madaras@stuba.sk
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Visibility, Culling, Clipping (05) RNDr. Martin Madaras, PhD. - - PowerPoint PPT Presentation
Visibility, Culling, Clipping (05) RNDr. Martin Madaras, PhD. - - PowerPoint PPT Presentation
Principles of Computer Graphics and Image Processing Visibility, Culling, Clipping (05) RNDr. Martin Madaras, PhD. martin.madaras@stuba.sk Overview Clipping Point Clipping Line Clipping Polygon Clipping Hidden Surface Removal
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3D rendering pipeline
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3D polygons Modeling Transformation Lighting Viewing Transformation Projection Transformation Clipping Scan Conversion 2D Image
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Rasterization (05)
Clip polygons outside of camera’s view
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- Ask questions, please!!!
- Be communicative
- www.slido.com #PPGSO05
- More active you are, the better for you!
How the lectures should look like #1
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2D rendering pipeline
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2D geometry Clipping Viewport Transformation Scan Conversion 2D Image
Clip and remove geometry outside of the
window
Transform from screen coordinates to image
coordinates
Fill pixels on the screen
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2D rendering pipeline
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2D geometry Clipping Viewport Transformation Scan Conversion 2D Image
Clip and remove geometry outside of the
window
Transform from screen coordinates to image
coordinates
Fill pixels on the screen
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Avoid drawing parts of primitives outside window
Window defines part of scene being viewed Must draw geometric primitives only inside window
Screen Coordinates
Clipping
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Avoid drawing parts of primitives outside window
Window defines part of scene being viewed Must draw geometric primitives only inside window
Clipping
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Avoid drawing parts of primitives outside window
Points, Lines, Polygons, Circles etc.
Clipping
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Is point (x,y) inside clip window ?
Point Clipping
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Find the part of a line inside the clip window Before Clipping
Line Clipping
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Find the part of a line inside the clip window After Clipping
Line Clipping
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Use simple test to classify easy cases first Danny Cohen, Ivan Sutherland 1967
Cohen-Shutherland Line Clipping
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Classify lines quickly by AND of bit codes representing
regions of two endpoints (test for 0)
Cohen-Shutherland Line Clipping
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Classify lines quickly by AND of bit codes representing
regions of two endpoints (test for 0)
Cohen-Shutherland Line Clipping
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Classify lines quickly by AND of bit codes representing
regions of two endpoints (test for 0)
Cohen-Shutherland Line Clipping
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Compute intersections with window boundary for
remaining lines
Cohen-Shutherland Line Clipping
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Intersect with boundary determined by the bits of the
non zero point
Cohen-Shutherland Line Clipping
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Create new point on the boundary
Cohen-Shutherland Line Clipping
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Check using the AND operation again
Cohen-Shutherland Line Clipping
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Do the same for the next line
Cohen-Shutherland Line Clipping
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Clip using the boundary determined by P7
Cohen-Shutherland Line Clipping
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Clip using the boundary determined by P7
Cohen-Shutherland Line Clipping
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Clip using the boundary determined by P8
Cohen-Shutherland Line Clipping
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Test the line again using AND
Cohen-Shutherland Line Clipping
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Again for the last line
Cohen-Shutherland Line Clipping
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P9 AND P10 no longer zero
Cohen-Shutherland Line Clipping
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Final result
Cohen-Shutherland Line Clipping
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Find the part of a polygon inside the clip window? Before Clipping
Polygon Clipping
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Find the part of a polygon inside the clip window? After Clipping
Polygon Clipping
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Clip to each window boundary one at a time
Sutherland–Hodgman Clipping
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Clip to each window boundary one at a time
Sutherland–Hodgman Clipping
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Clip to each window boundary one at a time
Sutherland–Hodgman Clipping
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Clip to each window boundary one at a time
Sutherland–Hodgman Clipping
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Clip to each window boundary one at a time
Sutherland–Hodgman Clipping
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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Do inside test for each point in sequence Insert new points when crossing the boundary Remove points outside of boundary
Clipping to a Boundary
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2D rendering pipeline
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2D geometry Clipping Viewport Transformation Scan Conversion 2D Image
Clip and remove geometry outside of the
window
Transform from screen coordinates to image
coordinates
Fill pixels on the screen
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Window to viewport mapping
Viewport Transformation
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Clipping
Point Clipping Line Clipping Polygon Clipping
Hidden Surface Removal
Overview
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wireframe model front faces silhouette visible faces, edges
Visibility
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Surfaces may be back-facing Surfaces may be occluded Surfaces may overlap in the image plane Surfaces may intersect
Motivation
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3D rendering pipeline
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3D polygons Modeling Transformation Lighting Viewing Transformation Projection Transformation Clipping Scan Conversion 2D Image
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Somewhere here we have to determine
which objects are visible and which are hidden
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Clipping
Point Clipping Line Clipping Polygon Clipping
Hidden Surface Removal
Basic algorithms for HSR
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Get rid of objects that are surely not visible Frustum culling Occlusion culling Back-face culling
Optimizing visibility
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6 planes
Inside = visible volume
Is a point is inside? Object
bounding box
Speed up
Frustum culling
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Some objects are fully occluded by others Spatial relations between objects Portals, occlusion culling Realtime rendering
Occlusion culling
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Which object faces are visible? Remember normal vector (face orientation)
Back-face culling
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Some parts of the scene
are not visible from some
- ther parts of the scene
Portal culling
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Optimizing visibility
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Back-face culling Depth sort Z-Buffer
Basic algorithms for HSR
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How do we test back-facing polygons ? Dot product the normal and view direction
Back-face culling
𝑂•V > 0
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Normal
Cross product of surface tangent vectors Length normalized to 1
Surface Normals
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Dot product the normal and view direction Fragment normals can be interpolated from vertex normals
Vertex / Fragment Normals
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3D rendering pipeline
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3D polygons Modeling Transformation Lighting Viewing Transformation Projection Transformation Clipping Scan Conversion 2D Image
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Back-face culling Remove all polygons that are back-facing
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“Painter’s algorithm” Sort surfaces by maximum depth Draw surfaces in back to front order
Depth sort
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Sort faces in a back-to-front order, render New pixels over-write
- ld pixels
Painter’s algorithm
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Intersecting faces Cyclically overlapping faces Redundant rendering
Painter’s algorithm problems
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3D rendering pipeline
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3D polygons Modeling Transformation Lighting Viewing Transformation Projection Transformation Clipping Scan Conversion 2D Image
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Sorting is often O(n log n) Usually software only Mostly using BSP-trees
Depth sort
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Warnock algorithm
subdivide screen into a quadtree until
whole cell empty or whole cell inside polygons
Reversed painter’s algorithm
paint front-to-back and paint only empty areas
Z-buffer
remember z-value for each pixel and only paint when new z is
higher
Other algorithms
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Also known as depth buffering Stores closest depth of objects for every pixel
Draw only pixels with less depth Depths are interpolated between vertices
Z-Buffer
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works in screen space z-buffer w×h
for each 0≤x≤w,0≤y≤h: z-buffer[x,y] ←
zmin for each face: rasterize it into pixels {x,y,z} for each face’s pixel (x,y,z): if z > z-buffer[x,y] then : z-buffer[x,y] ← z and screen[x,y] ← face color
Z-Buffer
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GPU support precision issues might occur z-buffer test before per-pixel-lighting or pixel shading
saves a lot of redundant work
memory demands (width×height×precision)
can be reduced by scanline (width×1×precision)
Z-buffer pros and cons
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Z-Buffer
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3D rendering pipeline
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3D polygons Modeling Transformation Lighting Viewing Transformation Projection Transformation Clipping Scan Conversion 2D Image
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Sorting not needed Excellent for hardware Requires additional memory to store
the depth values
Subject to aliasing Z-Buffer
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Can be solved in different ways
Painter’s algorithm / Depth sort
Binary space partitioning (BSP) Warnock algorithm (Quadtree)
Z-buffering Raycasting / Raytracing
Visibility
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Viewing-frustum culling Back-face culling Contribution culling (LoD) Occlusion culling
Potentially visible set (PVS) Portal rendering
Culling
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T extures and Mappings
Next Week
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Acknowledgements
Thanks to all the people, whose work is shown here and whose
slides were used as a material for creation of these slides:
Matej Novotný, GSVM lectures at FMFI UK Peter Drahoš, PPGSO lectures at FIIT STU
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