texture mapping computer graphics • texture mapping © 2006 fabio pellacini • 1 why texture mapping? • objects have spatially varying details • represent as geometry: correct, but very expensive computer graphics • texture mapping © 2006 fabio pellacini • 2 why texture mapping? • use simple geometry • store varying properties in images • map to objects [Wolfe / SG97 Slide set] [Wolfe / SG97 computer graphics • texture mapping © 2006 fabio pellacini • 3 why texture mapping? • produces compelling results [Jeremy Birn] computer graphics • texture mapping © 2006 fabio pellacini • 4 why texture mapping? • easily change object appearance [Praun et al., 2001] computer graphics • texture mapping © 2006 fabio pellacini • 5 mapping function • surfaces are 2d domains • determine a function that maps them to images Mapping Function Surface Image computer graphics • texture mapping © 2006 fabio pellacini • 6 mapping functions – projections • maps 3d surface points to 2d image coordinates f ℜ3 → ]1,0[: 2 • different types of projections – often corresponding to simple shapes – useful for simple object [Wolfe / SG97 Slide set] [Wolfe / SG97 computer graphics • texture mapping © 2006 fabio pellacini • 7 projections – planar computer graphics • texture mapping © 2006 fabio pellacini • 8 projections – cubical computer graphics • texture mapping © 2006 fabio pellacini • 9 projections – cylindrical computer graphics • texture mapping © 2006 fabio pellacini • 10 projections – spherical computer graphics • texture mapping © 2006 fabio pellacini • 11 projections • planar projection along xy plane of size (w,h) – use affine transform to orient the plane differently ()(/,/)f p p= x w p y h • spherical projection of unit sphere – consider point in spherical coordinates ()(,)f p = φ θ • cylindrical projection of unit cylinder of height h – consider point in cylindrical coordinates – treat caps separately ()(,/)f p = φpy h computer graphics • texture mapping © 2006 fabio pellacini • 12 looking up texture values • normal: do not repeat texture – clamp image coordinates to [0,1] then lookup • tiled: repeat texture multiple times – take mod of image coordinates then lookup normal tiled computer graphics • texture mapping © 2006 fabio pellacini • 13 texture mapping artifacts • tiling textures might introduce seems – discontinuities in the mapping function – change texture to be “tileable” when possible computer graphics • texture mapping © 2006 fabio pellacini • 14 texture mapping artifacts • mapping textures will introduce distortions – unavoidable artifacts • local scale and rotation differences distorted undistorted computer graphics • texture mapping © 2006 fabio pellacini • 15 mapping function – explicit coordinates • store texture coordinates on control points • interpolate as any other parameter – follow interpolation rule defined by surface type • parametric surfaces: can use parameters directly • known as UV mapping computer graphics • texture mapping © 2006 fabio pellacini • 16 uv mapping subdivision surfaces level 0 level 1 level 2 computer graphics • texture mapping © 2006 fabio pellacini • 17 uv mapping vs. projection parameterization projection computer graphics • texture mapping © 2006 fabio pellacini • 18 uv mapping parametric surfaces [Wolfe / SG97 Slide set] [Wolfe / SG97 computer graphics • texture mapping © 2006 fabio pellacini • 19 uv mapping polygon meshes computer graphics • texture mapping © 2006 fabio pellacini • 20 uv mapping polygon meshes [Piponi et al., 2000] computer graphics • texture mapping © 2006 fabio pellacini • 21 uv mapping polygon meshes • break up model intro single texture [© Discreet] computer graphics • texture mapping © 2006 fabio pellacini • 22 interpolating uv coordinates on meshes • pay attention when rasterizing triangles – for raytracing just use baricentric coordinates texture linear interp. perspective interp. [MIT OpenCourseware] used also for colors computer graphics • texture mapping © 2006 fabio pellacini • 23 painting textures on models • if painting is required, paint directly on surfaces – system determines inverse mapping to update image – seems/distortions present, but user does not know computer graphics • texture mapping © 2006 fabio pellacini • 24 texture magnification • linearly interpolate closest pixels in texture [MIT OpenCourseware] texture rendered image computer graphics • texture mapping © 2006 fabio pellacini • 25 texture minification • compute average of texture pixels projected onto each view pixels [MIT OpenCourseware] texture rendered image computer graphics • texture mapping © 2006 fabio pellacini • 26 texture minification • remember point-sampling introduces artifacts – need average of texture below a pixel [MIT OpenCourseware] computer graphics • texture mapping © 2006 fabio pellacini • 27 mip-mapping • approximate algorithm for computing filters • store texture at different resolution • look up the appropriate image based on its projected size [MIT OpenCourseware] computer graphics • texture mapping © 2006 fabio pellacini • 28 3d solid texturing • define a 3D field of values, indexed using P – in-memory array: too much memory – procedurally: hard to define • often add noisy-like details on 2d images [Wolfe / SG97 Slide set] [Wolfe / SG97 computer graphics • texture mapping © 2006 fabio pellacini • 29 types of mapping computer graphics • texture mapping © 2006 fabio pellacini • 30 texture mapping material parameters • diffuse coefficient computer graphics • texture mapping © 2006 fabio pellacini • 31 texture mapping material parameters • specular coefficient computer graphics • texture mapping © 2006 fabio pellacini • 32 displacement mapping • variations of surface positions, thus normals – requires fine tessellation of object geometry computer graphics • texture mapping © 2006 fabio pellacini • 33 displacement mapping • update position by displacing points along normal PPNd = + h • recompute normals by evaluating derivatives – no closed form solution: do it numerically PPPP∂ ∂ Δ Δ N ∝ d× d ≈ d× d d u∂ ∂ vΔ uΔ v computer graphics • texture mapping © 2006 fabio pellacini • 34 bump mapping • variation of surface normals – apply normal perturbation without updating positions computer graphics • texture mapping © 2006 fabio pellacini • 35 bump mapping • simple example: bump mapping xy plane u(,)(,)(,)PP vd = u v+ hN u= v u=x v + y(,) h + u z v PP∂ ∂ ⎛ ∂h ⎞ ⎛ ∂h ⎞ N ∝ d× = dx⎜ + z×⎟ ⎜ y + ⎟ = z d ∂u∂ v ⎝ ∂u ⎠ ⎝ ∂v ⎠ ∂h ∂h =z − x− y ∂u ∂v computer graphics • texture mapping © 2006 fabio pellacini • 36 bump vs. displacement mapping bump map displacement map computer graphics • texture mapping © 2006 fabio pellacini • 37 bump vs. displacement mapping bump map displacement map computer graphics • texture mapping © 2006 fabio pellacini • 38 combining maps types • combine multiple maps to achieve realistic effects computer graphics • texture mapping © 2006 fabio pellacini • 39 lighting effects using texture mapping computer graphics • texture mapping © 2006 fabio pellacini • 40 shadow mapping • graphics pipeline does not allow shadow queries • we can use texturing and a multipass algorithm [NVIDIA/Everitt al.] et project a color texture “project” a depth texture computer graphics • texture mapping © 2006 fabio pellacini • 41 shadow mapping algorithm • pass 1: render scene from light view • pass 1: copy depth buffer in a new texture • pass 2: render scene from camera view • pass 2: transform each pixel to light space • pass 2: compare value to depth buffer • pass 2: if current < buffer depth then shadow computer graphics • texture mapping © 2006 fabio pellacini • 42 shadow mapping algorithm [NVIDIA/Everitt al.] et camera view light view shadow buffer computer graphics • texture mapping © 2006 fabio pellacini • 43 shadow mapping algorithm [NVIDIA/Everitt al.] et camera view light distance projected shadow buffer computer graphics • texture mapping © 2006 fabio pellacini • 44 shadow mapping limitations • not enough resolution: blocky shadows – pixels in shadow buffer too large when projected [Fernando et al., 2002] • biasing: surfaces shadow themselves – remember the epsilon in raytracing – made much worst by resolution limitation computer graphics • texture mapping © 2006 fabio pellacini • 45 environment mapping • graphics pipeline does not allow reflections • we can use texturing and a multipass algorithm [Wolfe / SG97 Slide set] [Wolfe / SG97 computer graphics • texture mapping © 2006 fabio pellacini • 46 environment mapping algorithm • pass 1: render scene 6 times from object center • pass 1: store images onto a cube • pass 2: render scene from the camera view • pass 2: use cube projection to look up values • variation of this works also for refraction computer graphics • texture mapping © 2006 fabio pellacini • 47 environment map limitations • incorrect reflections – objects in incorrect positions: better for distant objs – “rays” go through objects • inefficient: need one map for each object computer graphics • texture mapping © 2006 fabio pellacini • 48 light effects take home message • pipeline not suitable for lighting computations – algorithms are complex to implement and not robust • lots of tricks and special cases – but fast • interactive graphics: use pipeline algorithms • high-quality graphics: use pipeline for view, raytracing for lighting computer graphics • texture mapping © 2006 fabio pellacini • 49 texturing demos OpenGL tutor: texture.exe NVidia samples: bumpy_shiny_patch.exe hw_shadowmap_simple.exe simple_soft_shadows.exe computer graphics • texture mapping © 2006 fabio pellacini • 50.