Texture Mapping

Home , Planar projection, UV mapping

texture mapping

• objects have spatially varying details • represent as geometry: correct, but very expensive

• use simple geometry • store varying properties in images • map to objects [Wolfe / SG97 Slide set] [Wolfe / SG97

• produces compelling results [Jeremy Birn]

• easily change object appearance [Praun et al., 2001]

• surfaces are 2d domains • determine a function that maps them to images

Mapping Function

Surface Image

• 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

• planar projection along xy plane of size (w,h) – use affine transform to orient the plane differently

f p = yx hpwp )/,/()( • 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 = φ y hp )/,()(

• 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

• tiling textures might introduce seems – discontinuities in the mapping function – change texture to be “tileable” when possible

• mapping textures will introduce distortions – unavoidable artifacts • local scale and rotation differences

• 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

level 0 level 1 level 2

parameterization projection

• break up model intro single texture [© Discreet]

• pay attention when rasterizing triangles – for raytracing just use baricentric coordinates

texture linear interp. perspective interp. [MIT OpenCourseware]

• if painting is required, paint directly on surfaces – system determines inverse mapping to update image – seems/distortions present, but user does not know

• linearly interpolate closest pixels in texture [MIT OpenCourseware]

• compute average of texture pixels projected onto each view pixels [MIT OpenCourseware]

• remember point-sampling introduces artifacts – need average of texture below a pixel [MIT OpenCourseware]

• approximate algorithm for computing filters • store texture at different resolution • look up the appropriate image based on its projected size [MIT OpenCourseware]

• 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

• diffuse coefficient

• specular coefficient

• variations of surface positions, thus normals – requires fine tessellation of object geometry

• update position by displacing points along normal

d = + hNPP • recompute normals by evaluating derivatives – no closed form solution: do it numerically ∂ ∂ Δ ΔPPPP N ∝ × dd ≈ × dd d ∂ ∂ Δ Δvuvu

• variation of surface normals – apply normal perturbation without updating positions

• simple example: bump mapping xy plane

d = PP + vuhvuvu ),(),(),( N = ++= vuhvu ),( zyx

∂ ∂PP ⎛ ∂h ⎞ ⎛ ∂h ⎞ N ∝ × dd ⎜ += ⎟ ⎜ +× zyzx ⎟ = d ∂ ∂vu ⎝ ∂u ⎠ ⎝ ∂v ⎠ ∂h ∂h −= − yxz ∂u ∂v

bump map displacement map

• combine multiple maps to achieve realistic effects

• 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

• 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

camera view light view shadow buffer

camera view light distance projected shadow buffer

• 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

• 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

• incorrect reflections – objects in incorrect positions: better for distant objs – “rays” go through objects • inefficient: need one map for each object

• 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