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Point-based Graphics for Estimated Surfaces Tyler Johnson Department of Computer Science University of North Carolina at Chapel Hill COMP 236 Final Project Presentation – Spring, 2006

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2 Point-based Graphics for Estimated Surfaces Project Motivation Multi-projector display system Required for image correction: projector calibration display surface representation viewing location Surface estimation produces points

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3 Point-based Graphics for Estimated Surfaces Outline Surface Splats Sub-sampling point-clouds Real-time surface splat rendering Application to projective displays

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4 Point-based Graphics for Estimated Surfaces Surface Splats Point-based No connectivity Circular center – c ={x,y,z} normal – n = {x,y,z} radius - r Elliptical replace r with major, minor axes a and b

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5 Point-based Graphics for Estimated Surfaces Sub-sampling Point-clouds Produce a set of circular surface splats from a set of points Based on [Wu J., Kobbelt L., Optimized Sub- sampling of Point Sets for Surface Splatting]

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6 Point-based Graphics for Estimated Surfaces Sub-sampling Point-clouds Create initial set of splats At each point p i Create new splat s i with center p i Find G = {k nearest neighbors of p i } Fit least squares plane to find normal of s i Determine r by growing s i to include points in G until global error tolerance is reached

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7 Point-based Graphics for Estimated Surfaces Sub-sampling Point-clouds Greedy selection of splats until model is closed. Splat selection based on surface area Model closed when all points covered by a splat

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8 Point-based Graphics for Estimated Surfaces Examples 93,000 points sampled from triangle mesh 41,000 circular surface splats

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9 Point-based Graphics for Estimated Surfaces Examples 94,000 points sampled from triangle mesh 34,000 circular surface splats

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10 Point-based Graphics for Estimated Surfaces Examples Radii decreased to illustrate underlying splat representation.

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11 Point-based Graphics for Estimated Surfaces Rendering Surface Splats Three-pass algorithm on the GPU Visibility Pass – Fill depth buffer Attribute Pass – Splat material properties Lighting Pass – Normalization and lighting [Botsch M., Hornung A., Zwicker M., Kobbelt L., High-Quality Surface Splatting on Todays GPUs]

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12 Point-based Graphics for Estimated Surfaces Visibility Pass Send all splats down the pipeline as points Fill depth buffer vertex program calc splat size in screen-space, generate fragments fp invert viewport transform point on near plane p n use p n to reconstruct 3D point on splat surface in eye space p e if p e is within radius of splat, output transformed depth of p e

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13 Point-based Graphics for Estimated Surfaces Attribute Pass Send all splats down the pipeline again Splat material properties vp calc splat size in screen-space, generate fragments fp reconstruct p e on the surface of the splat as in visibility pass weight normal and color of splat with kernel at splat center add weighted normal and color to separate accumulation textures output transformed depth of p e minus depth offset

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14 Point-based Graphics for Estimated Surfaces Lighting Pass Render full-screen quad to generate fragments Normalization and lighting vp nothing fp divide accumulated color and normal by total weight use depth texture to reconstruct 3D point calc per-pixel lighting

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15 Point-based Graphics for Estimated Surfaces Application to Projective Display Display surface Estimation

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16 Point-based Graphics for Estimated Surfaces Application to Projective Display Rendering Projective texturing perform in attribute pass to determine color must also invert viewing transform Video

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17 Point-based Graphics for Estimated Surfaces Conclusions Surface splat representations suffer from many of the same problems as polygon meshes holes, insufficient sampling etc. Local least-squares fitting may reduce noise in estimating planar surfaces Lack of connectivity may be advantageous in continuous surface estimation

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