CSL 859: Advanced Computer Graphics. Dept of Computer Sc. & Engg. IIT Delhi

Transcription

1 CSL 859: Advanced Computer Graphics Dept of Computer Sc. & Engg. IIT Delhi

2 Point Based Representation Point sampling of Surface Mesh construction, or Mesh-less Often come from laser scanning Or even natural light How do you render How do you peform other processing Visibility, Collision etc. Related concepts: image based representation, particle systems

3 Laser Range Scanning Michaelangelo Project Laser scanners sample points on a 3D shape Often on a grid Large number of samples Most surfaces have a high frequency

4 Point-Based Rendering

5 Surfels [Pfister et al., SIGGRAPH 2000]

6 Sampling Known Objects 3D Rasterization Layered Depth Images Cast rays through the object along each axis Advance ray by regular increments Store pre-filtered texture colors at the points Project the surfel into texture space and filter to get a single color Disk radius >= maximum inter sample distance rk = r0 2 k

7 Filter shape (e.g., Gaussian) is usually circular/spherical We want that shape on screen => ellipse in space EWA Filter = low-pass filter warped reconstruction filter Elliptical Weighted Average Low-Pass Filter Volume

8 Filter shape (e.g., Gaussian) is usually circular/spherical We want that shape on screen => ellipse in space EWA Filter = low-pass filter warped reconstruction filter Elliptical Weighted Average Low-Pass Filter W Volume

9 Filter shape (e.g., Gaussian) is usually circular/spherical We want that shape on screen => ellipse in space EWA Filter = low-pass filter warped reconstruction filter Elliptical Weighted Average Projection Low-Pass Filter W Volume

10 Filter shape (e.g., Gaussian) is usually circular/spherical We want that shape on screen => ellipse in space EWA Filter = low-pass filter warped reconstruction filter Elliptical Weighted Average Projection Low-Pass Filter W Convolution Volume

11 Filter shape (e.g., Gaussian) is usually circular/spherical We want that shape on screen => ellipse in space EWA Filter = low-pass filter warped reconstruction filter Elliptical Weighted Average Projection Low-Pass Filter W Convolution Volume

12 Storing surfels 3 Layered depth images (LDI), one per axis LDI = Images with multiple <depth,color> per pixel Makes a Layered Depth Cube (LDC) Pixel spacing h0 related to expected screen resolution Octree with node = bxb block of pixels Bottom-up construction Make pixel spacing = h0 2 i Filter down each block a) b)

13 Projection View frustum culling Traverse blocks to find the right resolution One surfel per pixel, or n for supersampling i n max = Length of projected block diagonals/b If i n max > filter footprint, traverse children Warp blocks to screen space Fast incremental algorithms [GrossMan & Daly] Only a few operations per surfel fewer than matrix multiplication due to regularity of samples

14 Filling Use Z buffer Each surfel covers an area Project this area orthographically and scan convert Approximate ellipse with a bounding parallelogram Depth varies linearly: surfel normal May have holes (magnification or surfel orientation) Shading: Per-surfel Phong illumination Also incorporates environment/normal maps Reconstruct image by filling holes between projected surfels Apply a filter in screen space Super-sample to improve quality

15 Splatting and Reconstruction

16 QSplat Primary goal is interactive rendering of very large point-data sets Built for the Digital Michelangelo Project [Rusinkiewicz and Levoy, SIGGRAPH 2000]

17 Sphere Trees A hierarchy of spheres, with leaves containing single vertices Each sphere stores center, radius, normal, normal cone width, and color (optional) Tree built the same way one would build a KDtree Median cut method Rendered really large models for the day Focus on memory layout and data quantization

18 Rendering Sphere Trees Start at root Do a visibility test View frustum Also back-face cull based on normal cone Recurse or Draw Recurse based on projected area of sphere with an adapted threshold To draw, use normals for lighting and z-buffer to resolve occlusion

19 Splat Shape Several options Square (OpenGL point ) Circle (triangle fan or texture mapped square) Gaussian (have to do two-pass) Can squash splats depending on viewing angle Sometimes causes holes at silhouettes, can be fixed by bounding squash factor

20 Splat Shape

21 Splat Silhouettes

22 Few Splats

23 Many Splats

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25 Surface Reconstruction: Cocone p Voronoi cell of p p + pole of p = point in the Voronoi cell farthest from p ε < 0.1 the vector from p to p + is within π/8 of the true surface normal The surface is nearly flat within the cell

26 Surface Reconstruction: Cocone p + p Voronoi cell of p p + pole of p = point in the Voronoi cell farthest from p ε < 0.1 the vector from p to p + is within π/8 of the true surface normal The surface is nearly flat within the cell

27 Surface Reconstruction: Cocone p + p Voronoi cell of p p + pole of p = point in the Voronoi cell farthest from p ε < 0.1 the vector from p to p + is within π/8 of the true surface normal The surface is nearly flat within the cell

28 Surface Reconstruction: Cocone p + p Voronoi cell of p p + pole of p = point in the Voronoi cell farthest from p ε < 0.1 the vector from p to p + is within π/8 of the true surface normal The surface is nearly flat within the cell

29 Surface Reconstruction: Cocone p + p Voronoi cell of p p + pole of p = point in the Voronoi cell farthest from p ε < 0.1 the vector from p to p + is within π/8 of the true surface normal The surface is nearly flat within the cell

30 Sample Reconstructed Surfaces courtesy Tamal Dey, OSU

31 Moving Least Squares For point set P, MLS(P) is a projection operator which maps each point to itself: MLS(P) = {x: ψ(p, x) = x} ψ(p, x): Find a local reference plane at x: p(u,v) Compute local polynomial approximation to surface on the plane: p(u,v)

32 MLS courtesy Luiz Velho

33 Reference domain The local plane: is computed so as to minimize a local weighted sum of squared distances of the points pi to the plane

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35 Light Field Uniformly sample two planes plane of cameras Many plane-pairs needed Need compression Quantization

36 Light Field Uniformly sample two planes plane of cameras Many plane-pairs needed Need compression Quantization

37 Light Field Uniformly sample two planes plane of cameras Many plane-pairs needed Need compression Quantization

38 Light Field Uniformly sample two planes plane of cameras Many plane-pairs needed Need compression Quantization

39 Rendering For each desired ray: Compute intersection with (u,v) and (s,t) planes Take closest ray Filter from the closest

40 Compression Vector quantization Build a codebook of 4D tiles Each tile an index into the codebook Example: 2x2x2x2 tiles, 16 bit index = 24:1 compression