Illumination for Computer Generated Pictures Classical Rendering Paper Summaries Bui Tuong Phong University of Utah Communications of the ACM, Vol. 18, No 6, 1975 Warnock Shading Newell, Newell, and Sancha • Flat shading • Flat shading of polygons • Decrease intensity with distance from • Transparency & light and object highlights due to reflected light • Highlights Gouraud Shading Gouraud Shading • Interpolation • Compute shading at – A to B each vertex – A to D • Interpolate – P to Q shading • = Bilinear Interpolation 1
Problem with Phong Shading Gouraud Shading • Highlights across polygons Phong Shading Phong Shading • Interpolate Normals –N t = tN 1 + (1 - t)N 0 • Evaluate Shading for each pixel Lambert’s law Diffuse Shading I diffuse = k d I light cos θ n n L L θ e θ 2
Specular Shading Phong Shading Add specular by looking at lights reflection, r I total = k a I ambient + Σ I i ( k d (N . L) + k s (V . R) n shiney ) Shiny surfaces, such as a i = 1 mirror n n L L r r θ θ e θ θ e σ σ Hand-tuned Phong shading Phong Shaded Spheres The Aliasing Problem in Computer Generated Shaded Images Frank Crow University of Texas at Austin Communications of the ACM, Vol. 20, No. 11, 1977 3
Problems with rendering pixels: Problems with rendering pixels: Jaggies Loss of Detail Problems with rendering pixels: Problems with just rendering Disintegrating Texture pixels • 1) along edge of silhouette of object or crease in a surface – Jaggies • 2) very small objects – Can disappear between dots • 3) areas of complex detail Possible Solutions Solution • Increase Resolution • Super-sampling (more samples than pixels) – Sometimes impractical • Low-pass prefiltering (averaging of super- samples) • Blurring – Removes detail • Sample represents finite area, not infinitesimal spot 4
Solution: Convolution Filter Nyquist Limit • Signal can be reproduced if the highest frequencey in the signal does not exceed one half the sampling frequency – called the Nyquist Limit – N sample >= 2* N analog • Failing to do so produces Aliasing Prefiltering Prefiltering Filtering Results 5
Mip-Mapping Pyramidal Parametrics • MIP from Latin phrase – Multum in parvo – “many things in a small place” Lance Williams NYIT SIGGRAPH 1983 Mipmapping MipMapping Memory Requirements • Image pyramid • Half height and width • Compute d – Gives 2 images • Bilinear Interpolate in each image From Tomas Akenine-Moller 6
Mipmapping Mipmapping • Interpolate between those bilinear values • Compute d – Trilinear interpolation • Over blur, approximating quad with square From Tomas Akenine-Moller From Tomas Akenine-Moller Results: The Rendering Equation James T. Kajiya CalTech SIGGRAPH 1986 7
Ray Tracing Jell-O Brand Gelatin Paul S. Heckbert Pixar SIGGRAPH 1987 Credits • http://escience.anu.edu.au/lecture/cg/Revisal/AntiAliasing/alias2b.en.html#39 • Pixar shutterbug images: http://www.siggraph.org/education/materials/HyperGraph/shutbug.htm 8
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