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Sebastian Enrique Columbia University senrique@cs.columbia

CS6998 - Topics on Computational Vision and Graphics Apr 20 th , 2004. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials. Sebastian Enrique Columbia University senrique@cs.columbia.edu. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials. CS6998.

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Sebastian Enrique Columbia University senrique@cs.columbia

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  1. CS6998 - Topics on Computational Vision and Graphics Apr 20th, 2004 Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials Sebastian Enrique Columbia University senrique@cs.columbia.edu

  2. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Problem • As far as I know, real-time rendering of objects using its BRDF was not achieved yet. • I decided to deal with this problem, with the goal to create a system with the following initial requirements: • Allow rendering of any kind of mesh. • Allow real-time viewpoint changes. • Allow real-time lighting changes. • Allow selection of material from a set of BRDF samples. • Compute final colors per pixel. Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 2

  3. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Decisions and Simplifications • Meshes should be made of triangles. Topology information of the mesh (vertices positions and indices of each triangle) should be completed with vertex normals. • Viewpoint can be rotated and zoomed in and out, but not translated. Change of camera target –the origin of the coordinate system- is also not allowed. Perspective projection will be used. • Illumination will be limited to a white distant point light source. This means that every point in the surface will be receiving light from the same direction. The user should be able to change this direction. • CUReT public BRDF materials databse will be used. It contains 61 material samples. • Final colors should be computed in the GPU using fragment shaders. • We will not deal with shadows and interreflections. Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 3

  4. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 CUReT • 205 measurements of 61 materials under different light and view directions. • A representation or interpolation should be used to get the BRDF of each material under novel light and view directions: Zernike polynomials (mapping of points on a hemisphere over the unit disk). • It is a good representation for smooth BRDFs and scattered data. It is not so good for materials with high specular lobes. • 55 coefficients for polynomials of order 8. • 5 coefficients for polynomials of order 2, which is good for most of the materials in the database. Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 4

  5. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Per Vertex Implementation • Colors are computed for each vertex in software and then passed to the graphics hardware using OpenGL. • Pixel values in between vertices are interpolated using Gouraud shading. • Zernike polynomials are evaluated with corresponding material coefficients to get the correct color depending on light and viewing directions every frame. • Some costly operations on angles are precomputed and stored in a table to speed up real-time processing. • Extra features of the application such as to show surface normals and N dot L type of rendering are done using pixel and vertex shaders. Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 5

  6. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Per Pixel Implementation • Same operations done per vertex could be done per pixel using a fragment shader. • Precomputed values can be passed as textures. • Current implementation involves two 2D-textures (Zernike coefficients and precomputed operations on angles) and one 3D-texture (OpenGL 1.2 extensions required). • Color computation for Zernike polynomials of order 2 (5 coefficients) requires only 1 rendering pass (1 pixel shader). • To compute order 5 (55 coefficients) 8 passes are required with current Cg implementation (quite slow) in current graphics hardware. • I haven’t finished software part + debugging of per pixel implementation. Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 6

  7. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Results • Happy Buddha model: 32,328 vertices; 69,451 triangles – Per Vertex – 5 coefficients. • Materials: Plant, Orange Peel, and Insulation, using same light direction / pose. Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 7

  8. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Results (cont.) • Dragon model: 22,998 vertices; 47,794 triangles – Per Vertex – 5 coefficients. • Material Rabbit Fur changing light direction (top) and view direction (bottom). Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 8

  9. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Results (cont.) • Stanford Bunny model: 35,947 vertices; 69,451 triangles – Per Vertex – 5 coefficients. • Material Sponge changing light direction and view direction in every image. Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 9

  10. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Results (cont.) • Stanford Bunny model: 35,947 vertices; 69,451 triangles – Per Vertex – 5 coefficients. • Left: rendered with Rug B material. • Middle: showing surface normals. • Right: wireframe using N dot L. Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 10

  11. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 Conclusions • Real-time rendering of BRDF materials using any mesh was implemented and possible. • Images shown before were rendered per vertex with Zernike polynomials of order 2; for order 8, vertices and triangles should be reduced 4 times for real-time rendering in test machine (Pentium 4 3Gz 1Gb RAM nVidia GeForce FX5900). • Other BRDF representations should be analyzed to render in real-time more specular BRDFs materials. • Next step is to finish per pixel implementation. • Natural extension for this is to use environment lighting. • Shadows could be added using traditional techniques like shadow mapping. • First, I must correct some problems like artifacts in grazing angles and not matching final colors with original CUReT rendered spheres (coefficients are not in good shape?). Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 11

  12. Real-Time Rendering Using CUReT BRDF Materials with Zernike Polynomials CS6998 Apr 20th, 2004 The End • Aknowledgments • Ravi Ramamoorthi for CUReT materials Zernike coefficients and some Zernike polynomials code. • The Stanford 3D Scanning Repository for models used. • Georgia Institute of Technology for tools to manipulate PLY files. • Questions? • Thanks for listening... Sebastian Enrique - Columbia University - senrique@cs.columbia.edu 12

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