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MIT 6 837 - Texture Mapping

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1MIT EECS 6.837, Durand and CutlerTexture Mapping & Other Fun StuffMIT EECS 6.837, Durand and CutlerLast Time?• Distribution Ray Tracing• Bounding Boxes• Spatial Acceleration Data Structures– Regular Grid– Adaptive Grids– Hierarchical Bounding Volumes• Flattening the Transformation HierarchyMIT EECS 6.837, Durand and CutlerRegular Grid Discussion• Advantages?– easy to construct– easy to traverse• Disadvantages?– may be only sparsely filled– geometry may still be clumpedMIT EECS 6.837, Durand and CutlerAdaptive GridsNested Grids Octree/(Quadtree)• Subdivide until each cell contains no more than n elements, or maximum depth d is reachedMIT EECS 6.837, Durand and CutlerPrimitives in an Adaptive Grid• Can live at intermediate levels, orbe pushed to lowest level of gridOctree/(Quadtree)MIT EECS 6.837, Durand and CutlerAdaptive Grid Discussion• Advantages?– grid complexity matches geometric density• Disadvantages?– more expensive to traverse (especially octree)2MIT EECS 6.837, Durand and CutlerBounding Volume Hierarchy• Find bounding box of objects• Split objects into two groups•RecurseMIT EECS 6.837, Durand and CutlerBounding Volume Hierarchy• Find bounding box of objects• Split objects into two groups•RecurseMIT EECS 6.837, Durand and CutlerBounding Volume Hierarchy• Find bounding box of objects• Split objects into two groups•RecurseMIT EECS 6.837, Durand and CutlerBounding Volume Hierarchy• Find bounding box of objects• Split objects into two groups•RecurseMIT EECS 6.837, Durand and CutlerBounding Volume Hierarchy• Find bounding box of objects• Split objects into two groups•RecurseMIT EECS 6.837, Durand and CutlerWhere to split objects?• At midpoint OR• Sort, and put half of the objects on each side OR• Use modeling hierarchy3MIT EECS 6.837, Durand and CutlerIntersection with BVH• Check sub-volume with closer intersection firstMIT EECS 6.837, Durand and CutlerIntersection with BVH• Don't return intersection immediately if the other subvolume may have a closer intersectionMIT EECS 6.837, Durand and CutlerBounding Volume Hierarchy Discussion• Advantages– easy to construct– easy to traverse–binary• Disadvantages– may be difficult to choose a good split for a node– poor split may result in minimal spatial pruning MIT EECS 6.837, Durand and CutlerQuestions?MIT EECS 6.837, Durand and CutlerToday• 2D Texture Mapping– Perspective Correct Interpolation– Specifying Texture Coordinates– Illumination & Reflectance• Procedural Solid Textures • Other Mapping Techniques• Texture AliasingMIT EECS 6.837, Durand and CutlerThe Problem:• We don't want to represent all this detail with geometry4MIT EECS 6.837, Durand and CutlerThe Quest for Visual RealismMIT EECS 6.837, Durand and CutlerTexture Mapping• Increase the apparent complexity of simple geometry• Like wallpapering or gift-wrapping with stretchy paper• Curved surfaces require extrastretching or even cutting MIT EECS 6.837, Durand and CutlerPhoto-texturesMIT EECS 6.837, Durand and CutlerTexture Tiling• Specify a texture coordinate (u,v) at each vertex• Canonical texture coordinates (0,0) → (1,1)seamless tiling (repeating)tiles with visible seams(0,0) (3,0)(0,3)(0,0) (3,0)(0,3)(0,0)(1,1)(0,0)(1,1)MIT EECS 6.837, Durand and CutlerTexture Interpolation• Specify a texture coordinate (u,v) at each vertex• Can we just linearly interpolate the values in screen space?(0,0) (1,0)(0,1)MIT EECS 6.837, Durand and CutlerInterpolation - What Goes Wrong?texture source what we get what we want• Linear interpolation in screen space:5MIT EECS 6.837, Durand and CutlerSpecify More Coordinates?• We can reduce the perceived artifacts by subdividing the model into smaller triangles. • However, sometimes the errors become obvious– At "T" joints – Between levels-of-detail(mipmapping... in a few weeks)MIT EECS 6.837, Durand and CutlerSubdivisionMIT EECS 6.837, Durand and CutlerSubdivisiontexture source what we get what we wantMIT EECS 6.837, Durand and CutlerVisualizing the Problem• Notice that uniform steps on the image plane do not correspond to uniform steps along the edge.MIT EECS 6.837, Durand and CutlerLinear Interpolation in Screen Space linear interpolation in screen spaceinterpolation in 3-spaceMIT EECS 6.837, Durand and CutlerPerspective Correct Interpolation We need a mapping from t values to s values:Solve for s in terms of t:Unfortunately, at this point in the pipeline (after projection) we no longer have z. However, we do have w1= 1/z1and w2= 1/z2, so:6MIT EECS 6.837, Durand and CutlerToday• 2D Texture Mapping– Perspective Correct Interpolation– Specifying Texture Coordinates– Illumination & Reflectance• Procedural Solid Textures • Other Mapping Techniques• Texture AliasingMIT EECS 6.837, Durand and CutlerTexture Mapping Difficulties• Tedious to specify texture coordinates • Acquiring textures is surprisingly difficult– Photographs have projective distortions – Variations in reflectance and illumination– Tiling problemsMIT EECS 6.837, Durand and CutlerCommon Texture Coordinate Mappings• Orthogonal• Cylindrical• Spherical • Perspective Projection•Texture ChartMIT EECS 6.837, Durand and CutlerProjective Textures• Use the texture like a slide projector• No need to specify texture coordinates explicitly• A good model for shading variations due to illumination• A fair model for reflectance (can use pictures)MIT EECS 6.837, Durand and CutlerProjective Texture Example• Modeling from photographs• Using input photos as texturesFigure from Debevec, Taylor & Malikhttp://www.debevec.org/ResearchMIT EECS 6.837, Durand and CutlerTexture Mapping & Illumination• Texture mapping can be used to alter some or all of the constants in the illumination equation: – pixel color, diffuse color, alter the normal, ….Phong's Illumination ModelConstant Diffuse Color Diffuse Texture ColorTexture used as Label Texture used as Diffuse Color7MIT EECS 6.837, Durand and CutlerTexture Chart• Pack triangles intoa single imageMIT EECS 6.837, Durand and CutlerQuestions?MIT EECS 6.837, Durand and CutlerToday• 2D Texture Mapping• Procedural Solid Textures• Other Mapping Techniques• Texture AliasingMIT EECS 6.837, Durand and CutlerProcedural TexturesImage by Turner Whittedf (x,y,z) → colorMIT EECS 6.837, Durand and Cutler• Advantages:– easy to implement in ray tracer – more compact


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MIT 6 837 - Texture Mapping

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