Visibility and Hidden Surface Removal

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z-buffer: exploiting depth coherence • From one scanline (y) to the next (y + 1): left polygon edge point: from (x, y) to (x + 1/m, y+1), where m is the slope of the polygon edge • So the new z A z x =z C z y =z A/m + B C © Machiraju/Zhang/Möller Pre-computed <strong>and</strong> stored 42
z-buffer: bilinear interpolation • If the polygon is non-planar, or not analytically defined, it is possible to approximate using bilinear interpolation Depth values known at vertices Interpolate between them then on scanline • Not just for depth, can do it for color (Gouraud shading), surface normals, or texture coordinates • Subdivision or refinement may be necessary is error is too great © Machiraju/Zhang/Möller 43
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 and 18: Object Space for each object in wor
Page 19 and 20: How to improve efficiency • Pay a
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: z-buffer: exploiting depth coherenc
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

Visibility and Hidden Surface Removal

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