Visibility and Hidden Surface Removal

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<strong>Visibility</strong> is expensive • Image space – brute-force – O( #pixels * #objects) – 1286 x 1024 resolution <strong>and</strong> 1 million polygons – Complexity: O(1.3 x 10 12 ) • Object space – brute-force – Worst-case: each object compared with the others – Complexity: O(n 2 ), e.g., 1 million polygons → O(10 12 ) © Machiraju/Zhang/Möller 18
How to improve efficiency • Pay attention to order in which primitives are processed, e.g., if back to front then just “paint” • Be as lazy as possible! – Costly operations are to be avoided as much as possible, e.g., use of bounding boxes – Try to make use of previous computations, e.g., utilize coherence • Specifically … © Machiraju/Zhang/Möller 19
Page 1 and 2: Visibility and Hidden Surface Remov
Page 3 and 4: Reading • Angel - Chapter 6.10-6.
Page 5 and 6: Visibility (2) • Connecting dots
Page 7 and 8: Visibility (4) • Include shading
Page 9 and 10: Visibility (6) • wireframe © Mac
Page 11 and 12: Visibility (8) • Inter-object vis
Page 13 and 14: Why compute visibility? • Realism
Page 15 and 16: Classification of algorithms • Hi
Page 17: Object Space for each object in wor
Page 21 and 22: 1. Coherence • Why? — Object pr
Page 23 and 24: 1. Edge and face coherence • Edge
Page 25 and 26: 2. Use of projection normalization
Page 27 and 28: 2. Perspective Transform • Can br
Page 29 and 30: 3. Bounding Objects (2) • For ren
Page 31 and 32: 3. Bounding Objects (4) • rectang
Page 33 and 34: 4. Back-face culling • Assumption
Page 35 and 36: 5. Spatial Partitioning • break a
Page 37 and 38: 6. Hierarchy • Use (e.g., semanti
Page 39 and 40: z-buffer algorithm revisited • On
Page 41 and 42: z-buffer: exploiting depth coherenc
Page 43 and 44: z-buffer: bilinear interpolation
Page 45 and 46: List Priority (2) • Depth compari
Page 47 and 48: List Priority (4) • Do extents in
Page 49 and 50: List Priority (6) • Do polygons c
Page 51 and 52: List Priority (8) • If these test
Page 53 and 54: List Priority (10) • More example
Page 55 and 56: Scanline: data structure • Recall
Page 57 and 58: Scanline Example • Another repres
Page 59 and 60: Scanline: scan example 2 • At sca
Page 61 and 62: Scanline: scan example 4 • Mainta
Page 63 and 64: Scanline problems • Beware of lar
Page 65 and 66: Building the BSP trees • Object s
Page 67 and 68: BSP traversal example • Rendering
Page 69 and 70:
Warnock’s subdivision • Divide
Page 71 and 72:
Warnocks Algorithm (3) - Single sur
Page 73 and 74:
Warnock’s Algorithm • If none o
Page 75:
Final issues on area subdivision
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Visibility and Hidden Surface Removal

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