7. Texture Mapping. Idea. Examples Image Textures. Motivation. Textures can be images or procedures. Textures can be 2D or 3D

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1 3 4 Idea Add srface detail withot raising geometric complexity Textres can be images or procedres Textres can be D or 3D Motiation Wireframe Model + Lighting & Shading + Textre Mapping towards more realism Examples Image Textres + Flytastic II (

2 5 7 8 Examples Image Textres Examples Bmp Map in Hardware Examples Bmp Map 6 Examples Displacement Map

3 Examples Enironment Map 9 Concept of Textre Mapping Find mappings between different coordinate systems Inert transformation from textre coordinates to image pixel Pixel coordinates Textre coordinates srface coordinates w(,) = (x,y,z) Isses Definition of textre coordinates Srface parametrization Anti aliasing Textre filtering Leel-of-Detail Hardware acceleration 0 Analytical 3D Sfraces. Key to textre mapping: Parametrization x ( s, t ) s y ( s, t ) sphere: t z ( s, t ) sin θ sin φ θ cos φ φ cos θ sin φ. Map parameters to textre coordinates s ( s, t ) s (, ) inerse: t ( s, t ) t (, )

4 Mapping a textre onto a sphere Use linear map θ A + B = φ C + D θ π / = φ π / 4 + π / 3 Parametrization of Triangle Meshes Find textre coordinates for ertices Take normal or ray from center of graity Spherical coordinates (θ,φ ) Triangle ertex Center of Graity Problems: Mltiple Intersections 5 Oerlaps Tiny and large triangles optimize coordinates by moing ertices on sphere cost fnction (area, angles, oerlap) find minimm iteratiely Topologically not a sphere ct mesh optimize patches separately Example 4 Problems Craig Gotsman et. al. 6

5 Textre Map Textre map corresponds to parametrization stretched at nose tip compressed at nose tip Tim Weyrich et. al. 7 Rasterization From textre coordinates of ertices to textre coordinates of pixels Linear interpolation in screen-space (as in Gorad shading): Images by Fredo Drand textre sorce what we get what we want 9 Parametrized Triangle Mesh OBJ Files: t t t n n n f /09/ 0/0/0 // f /3/ 9/4/9 0/0/9 f 53/03/53 9/4/9 /3/ Vertex positions Textre coordinates Normals Faces (triangles) coordnr/texnr/normalnr 8 Perspectie Interpolation Linear ariation in world coordinates yields non-linear ariation in screen coordinates: (0, 0 ) projection plane (, ) Perspectie interpolation implemented in today s graphics cards 0

6 t t t t t t Textre Filtering (,) are real pixel coordinates, e.g. (6.4, 3.7): nearest bi-linear color = map[6,4] color = s + s map [6,3] + s map [6,4] + s 6 s s 7 map [7,3] map [7,4] Enironment Map Method to render reflectie objects Compte intersection of reflected ray with srronding sphere Take parameter ales of intersection as textre coordinates n (θ,φ) 3 Textre Mapping in OpenGL loadimage(&textre_data); glgentextres(, &texid); glbindtextre(gl_texture_d, texid); glteximaged(gl_texture_d, 0, GL_RGB, w, h, 0, GL_RGB, GL_UNSIGNED_BYTE, textre_data); w = n, h = m glbindtextre(gl_texture_d, texid); glbegin(gl_triangles); gltexcoordf( 0, 0 ); glvertex(x 0,y 0,z 0 ); gltexcoordf(, ); glvertex(x,y,z ); gltexcoordf(, ); glvertex(x,y,z ); glend();, [0 K ] Ttor Examples Reflection mapping sing OpenGL 4

7 Cbe Mapping Sphere can be replaced by cbe Simplify comptations 5 An Example Mapping of distances from laser range data 7 Linear Mapping Uses object or eye coordinates (In)dependent of transforms Can be sed to compte distance from objects y -x z -z 6 x Projectie Textres Generalize textre coordinates to a 4D homogeneos ector (,, r, q) Textre matrix comptes fll 4x4 transform to ( p, p ) sed for textre lookp Textre image can be projected independent of iewing projection Applications: Slide projector Spotlight simlation 8

8 Projection Polygon Screen Textre Eye 9 Mip-Mapping Minimized textres prodce aliasing effects Store textre at mltiple leels-of-detail Use smaller ersions when far from camera MIP comes from the Latin mltm in paro, meaning a mltitde in a small space. withot mipmap with mipmap mipmap 3 Examples 30 Textre Interpolation Compte textre ale (R,G,B) as fnction of (,,z) Tri-linear interpolation z z 3

9 ' Comptation of the Mip Map Color = weighted aerage of nearby pixels (filter) See glbilddmipmaps() 33 Bmp Mapping Gien a srface p(,) and a pertrbation ale b (Jim Blinn) p p n = = p p Point p on the bmpy srface b p ' = p + n n p b p Bmp pattern Compte normal at Point p n = p ' p ' 35 Bmp Mapping Adding srface detail withot adding geometry Pertrbation of srface normal Details interact with light Bmps are small compared to geometry Bmp pattern is taken from a (textre-) map Can also be procedral (fractals) 34 Bmp Mapping Partial deriaties at point p p ' p (b n ) = + n Pertrbed normal approximated by (see Blinn) n ' = n + b ( n p ) + b ( n p ) 36

10 Bmp Mapping Discretization sing Finite Differences b(, ) b = b(, ) b = b(, b(, ) + b(, ) b(, ) ) + b(, ) b(, ) b(, ) b(, ) b(, ) b(, ) 37 Frther Topics Textre Paging Textre Blending and compositing (RGBA) Mltiple Textres Dynamic Textres Bill boarding 39 Alpha Textres Example: Mltipass Bmp 38 Examples Billoards: Xaier Décoret et al. 40