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To Do Outline Phong Illumination Model Idea of Phong Illumination Phong Formula To Do Foundations of Computer Graphics (Spring 2010) . Work on HW4 milestone CS 184, Lecture 18: Shading & Texture Mapping . Prepare for final push on HW 4, HW 5 http://inst.eecs.berkeley.edu/~cs184 Many slides from Greg Humphreys, UVA and Rosalee Wolfe, DePaul tutorial teaching texture mapping visually Chapter 11 in text book covers some portions Outline Phong Illumination Model . Brief discussion on Phong illumination model . Specular or glossy materials: highlights and Gouraud, Phong shading . Polished floors, glossy paint, whiteboards . For plastics highlight is color of light source (not object) . Texture Mapping (bulk of lecture) . For metals, highlight depends on surface color . Really, (blurred) reflections of light source These are key components of shading Roughness Idea of Phong Illumination Phong Formula . Find a simple way to create highlights that are view- I ()RE p dependent and happen at about the right place R . Not physically based -L . Use dot product (cosine) of eye and reflection of E light direction about surface normal . Alternatively, dot product of half angle and normal . Raise cosine lobe to some power to control sharpness or roughness R ? R LLNN 2( ) 1 Alternative: Half-Angle (Blinn-Phong) Flat vs. Gouraud Shading I ()NH p N H glShadeModel(GL_FLAT) glShadeModel(GL_SMOOTH) Flat - Determine that each face has a single normal, and color the entire face a single value, based on that normal. In practice, both diffuse and specular Gouraud – Determine the color at each vertex, using the normal at components for most materials that vertex, and interpolate linearly for pixels between vertex locations. Gouraud Shading – Details Gouraud and Errors I1221()()yys Iyy s Ia yy12 . I1 = 0 because (N dot E) is negative. I ()()yy Iyy 1331s s . I = 0 because (N dot L) is negative. Ib 2 I1 yy13 y1 Iab()()xx p Ixx b p a . Any interpolation of I1 and I2 will be 0. I p xxba Ia I p Ib Scan line ys y2 I2 y3 I3 I1 = 0 I2 = 0 area of Actual implementation efficient: difference desired equations while scan converting highlight 2 Phongs make a Highlight Problems with Interpolated Shading . Besides the Phong Reflectance model (cosn), there is a . Silhouettes are still polygonal Phong Shading model. Interpolation in screen, not object space: perspective distortion . Phong Shading: Instead of interpolating the intensities . Not rotation or orientation-independent between vertices, interpolate the normals. How to compute vertex normals for sharply curving surfaces? . The entire lighting calculation is performed for each pixel, based on the interpolated normal. (OpenGL doesn’t do this, but you can with current programmable shaders) . But at end of day, polygons is mostly preferred to explicitly representing curved objects like spline patches for rendering I1 = 0 I2 = 0 2 Outline Texture Mapping . Brief discussion on Phong illumination model . Important topic: nearly all objects textured and Gouraud, Phong shading . Wood grain, faces, bricks and so on . Adds visual detail to scenes . Texture Mapping (bulk of lecture) . Meant as a fun and practically useful lecture These are key components of shading Polygonal model With surface texture Adding Visual Detail Parameterization . Basic idea: use images instead of more polygons to represent fine scale color variation ++ = geometry image texture map • Q: How do we decide where on the geometry each color from the image should go? Option: Varieties of projections Option: unfold the surface [Piponi2000] [Paul Bourke] 3 Option: make an atlas Option: it’s the artist’s problem charts atlas surface [Sander2001] Outline How to map object to texture? . Types of projections . To each vertex (x,y,z in object coordinates), must associate 2D texture coordinates (s,t) . Interpolating texture coordinates . So texture fits “nicely” over object . Broader use of textures Idea: Use Map Shape Planar mapping . Map shapes correspond to various projections . Like projections, drop z coord (s,t) = (x,y) . Planar, Cylindrical, Spherical . Problems: what happens near z = 0? . First, map (square) texture to basic map shape . Then, map basic map shape to object . Or vice versa: Object to map shape, map shape to square . Usually, this is straightforward . Maps from square to cylinder, plane, sphere well defined . Maps from object to these are simply spherical, cylindrical, cartesian coordinate systems 4 Cylindrical Mapping Spherical Mapping . Cylinder: r, θ, z with (s,t) = (θ/(2π),z) . Convert to spherical coordinates: use latitude/long. Note seams when wrapping around (θ = 0 or 2π) . Singularities at north and south poles Cube Mapping Cube Mapping Outline 1st idea: Gouraud interp. of texcoords I1221()()yys Iyy s Ia . Types of projections yy12 I ()()yy Iyy . Interpolating texture coordinates 1331s s Ia I1 yy13 y1 . Broader use of textures Iab()()xx p Ixx b p a Ia xxba Ia I p Ib Scan line ys y2 I2 y3 I3 Actual implementation efficient: difference equations while scan converting 5 Artifacts Interpolating Parameters . McMillan’s demo of this is at . The problem turns out to be fundamental to http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture21/Slide05.html interpolating parameters in screen-space . Another example . Uniform steps in screen space uniform steps in world space http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture21/Slide06.html . What artifacts do you see? . Why? . Why not in standard Gouraud shading? . Hint: problem is in interpolating parameters Texture Mapping Interpolating Parameters . Perspective foreshortening is not getting applied to our interpolated parameters . Parameters should be compressed with distance . Linearly interpolating them in screen-space doesn’t do this Linear interpolation Correct interpolation of texture coordinates with perspective divide Hill Figure 8.42 Perspective-Correct Interpolation Texture Map Filtering . Skipping a bit of math to make a long story short… . Naive texture mapping aliases badly . Rather than interpolating u and v directly, interpolate u/z and v/z . Look familiar? int uval = (int) (u * denom + 0.5f); . These do interpolate correctly in screen space int vval = (int) (v * denom + 0.5f); . Also need to interpolate z and multiply per-pixel int pix = texture.getPixel(uval, vval); . Problem: we don’t know z anymore . Actually, each pixel maps to a region in texture . Solution: we do know w 1/z . |PIX| < |TEX| . So…interpolate uw and vw and w, and compute . Easy: interpolate (bilinear) between texel values u = uw/w and v = vw/w for each pixel . |PIX| > |TEX| . This unfortunately involves a divide per pixel . Hard: average the contribution from multiple texels . http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture21/Slide14.html . |PIX| ~ |TEX| . Still need interpolation! 6 Mip Maps MIP-map Example . Keep textures prefiltered at multiple resolutions . For each pixel, linearly interpolate between two closest levels (e.g., trilinear filtering) . No filtering: . Fast, easy for hardware AAAAAAAGH MY EYES ARE BURNING . MIP-map texturing: . Why “Mip” maps? Where are my glasses? Outline Texture Mapping Applications . Types of projections . Modulation, light maps . Interpolating texture coordinates . Bump mapping . Broader use of textures . Displacement mapping . Illumination or Environment Mapping . Procedural texturing . And many more Modulation textures Bump Mapping Map texture values to scale factor . Texture = change in surface normal! Wood texture Texture value Sphere w/ diffuse texture Sphere w/ diffuse texture Swirly bump map and swirly bump map I T(s,t)(I K I (K (N L) K (V R)n )S I K I K I ) E A A L D S L L T T S S 7 Displacement Mapping Illumination Maps . Quake introduced illumination maps or light maps to capture lighting effects in video games Texture map: Light map Texture map + light map: Environment Maps Solid textures Texture values indexed by 3D location (x,y,z) • Expensive storage, or • Compute on the fly, e.g. Perlin noise Images from Illumination and Reflection Maps: Simulated Objects in Simulated and Real Environments Gene Miller and C. Robert Hoffman SIGGRAPH 1984 “Advanced Computer Graphics Animation” Course Notes Procedural Texture Gallery 8 9.
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