Einführung in Visual Computing

Transcription

1 Einführung in Visual Computing Textures Werner Purgathofer

2 Surface-Rendering Methods polygon rendering methods ray tracing global illumination environment mapping texture mapping bump mapping Werner Purgathofer 2

3 Textures in the Rendering Pipeline scene objects in object space transformed vertices in clip space scene in normalized device coordinates raster image in pixel coordinates3 object capture/creation modeling viewing projection vertex stage ( vertex shader ) clipping + homogenization viewport transformation rasterization shading pixel stage ( fragment shader )

4 Environment Mapping Principle reflection mapping defined over surface of an enclosing universe (sphere, cube, cylinder) spherical environment map leighmachin.com objects in scene Werner Purgathofer 4

5 Environment Mapping Examples Jim Blinn Werner Purgathofer 5 Haeberli/Segal

6 Environment Mapping Calculation information in the environment map intensity values for light sources sky background objects environment map pixel projected onto surface reflected onto environment map Werner Purgathofer 6 pixel projection onto environment map projection reference point surface pixel

7 Environment Mapping Calculation information in the environment map intensity values for light sources sky background objects pixel area projected onto surface reflected onto environment map Werner Purgathofer 7 environment map pixel area projection onto environment map projection reference point surface pixel area

8 Environment Mapping Example Werner Purgathofer 8

9 Environment Mapping Filtering environment maps may be filtered for not so reflective surfaces Werner Purgathofer 9

10 Environment Mapping with Cube-Map (1) z y x r (1/1) define textures on 6 sides of a cube, each parameterized in (u,v) v (0/0) u direction vector r starts at (0,0,0) Werner Purgathofer 10

11 Environment Mapping with Cube-Map (2) v v (0/0) z u Werner Purgathofer 11 y x r (1/1) find (u,v) from the direction vector r(x r,y r,z r ): if x r > y r and x r > z r then front face u = (y r + x r )/2x r v = (z r + x r )/2x r top view analogous formulas for the other 5 faces ( x> y x> z, y> x y> z, y> x y> z, z> x z> y, z> x z> y ) x r x r y r y 0 u 1

12 Environment Mapping with Cube-Map (3) z y x r (1/1) calculation of the direction vector r: r n v r n v v v (0/0) u at a pixel: viewing direction v and normal vector n r + v = (2n v)n r = (2n v)n v Werner Purgathofer 12

13 Environment Mapping Example Werner Purgathofer 13

14 Adding Surface Detail most objects do not have smooth surfaces brick walls gravel roads carpets surface texture required D.Molyneaux Werner Purgathofer / Computergraphik 1 14 Artificial Studios Stanford

15 Adding Surface Detail modeling surface detail with polygons small polygon facets (e.g., checkerboard squares) facets overlaid on surface polygon (parent) parent surface used for visibility calculations facets used for illumination calculations impractical for complicated surface structure Werner Purgathofer 15

16 Texture Mapping: Principle texture patterns mapped onto surfaces texture pattern: raster image or procedure (modifies surface intensities) Jim Blinn texture space: (u,v) array coordinates texture-surface transformation object space: (u*,v*) surface parameters viewing & projection transformation image space: (x,y) pixel coordinates Werner Purgathofer 16

17 Texture Mapping: Transformation texture mapping texture scanning (u,v) (x,y) inverse scanning (x,y) (u,v) texture space: (u,v) array coordinates texture-surface transformation M T object space: (u*,v*) surface parameters viewing & projection transformation M VP image space: (x,y) pixel coordinates texture-surface transformation u* = u*(u,v) = a u* u + b u* v + c u* v* = v*(u,v) = a v* u + b v* v + c v* Werner Purgathofer 17

18 Texture Mapping: Inverse Transformation projecting pixel areas to texture space = = inverse scanning (x,y) (u,v) v 1 projected pixel area M 1 T M 1 VP 0 0 calculation of anti-aliasing with filter operations M 1 VP M 1 T Werner Purgathofer 18 1 u surface pixel area

19 Texture-Mapping: Cylindrical Surface M VP u* = θ, with 0 θ π/2 v* = z with 0 z h x = r cos u* y = r sin u* z = v* M 1 VP pixel surface point (x,y,z) (x,y,z) (u*,v*): u* = cos 1 (x/r), v* = z Werner Purgathofer 19 x² + y² = r² x, y 0 0 z h h x z θ r (u*,v*) y

20 Texture-Mapping: Cylindrical Surface M T u* = u π/2, v* = v h 1 v h z r (u*,v*) M 1 T u = 2u*/π, v = v*/h (u* = cos 1 (x/r), v* = z) u x θ u = cos 1 (x/r)/π, y v = z/h Werner Purgathofer 20

21 Texture Mapping: Anti-aliasing anti-aliasing with filter operations project pixel area into texture space and take average texture value speed ups: mip-mapping summed-area table method backprojected pixel texture space Werner Purgathofer 21

22 Perspective Correct Textures on Triangles mapping a texture on a triangle with barycentric coordinates: p(α,β,γ) = α a + β b + γ c color(x,y) = α t 0 + β t 1 + γ t 2 fails after perspective transform! correct: Werner Purgathofer 22

23 Perspective Correct Textures on Triangles solution: keep homogeneous weights h 0,h 1,h 2 of a, b, c and correct the barycentric values d = h 1 h 2 + h 2 β(h 0 h 1 ) + h 1 γ(h 0 h 2 ) β w = h 0 h 2 β/d γ w = h 0 h 1 γ/d α w = 1 β w γ w u = α w u 0 + β w u 1 + γ w u 2 v = α w v 0 + β w v 1 + γ w v 2 color(x,y) = t(u,v) instead of u=αu 0 +βu 1 +γu 2 v=αv 0 +βv 1 +γv 2 color(x,y) = t(u,v) Werner Purgathofer 23

24 Solid Texturing texture defined in 3D every position in space has a color coherent textures across corners Werner Purgathofer 24

25 Solid Texturing Examples examples for application of 3D textures on a scull and a face Univ.Swansea Univ.Swansea Werner Purgathofer 25

26 Procedural Texturing procedural texture definition texture-function t(x,y,z) returns intensity avoid M T 2D (surface texturing) or 3D (solid texturing) stochastic variations (noise function) examples wood grains marble foam Alias Wavefront Werner Purgathofer 26

27 Bump Mapping Principle bumps are visible because of shading modeling of bumps is very costly. trick: insert a detail structure b: + = bt Werner Purgathofer 27 v u

28 Bump Mapping Examples Jim Blinn Dave Pape Gamestar Werner Purgathofer 28 Stanford

29 Reminder: Derivation of a Function f(x) x derivation of a function in one variable is the slope of the function f'(x) x f'(x) = df(x)/dx = df/dx Werner Purgathofer 29

30 Reminder: Partial Derivation of a Function f(x,y) y f(x,y)/ y = f/ y f(x,y)/ x = f/ x x partial derivations of a function in two variables are the slopes of the functions when you keep one of the variables fixed, they are slopes of tangents Werner Purgathofer 30

31 Bump Mapping Calculation surface roughness simulated perturbation function varies surface normal locally bump map b(u,v) p(u,v) surface point n * = p u p v n = n * / n * p'(u,v) = p(u,v) + b(u,v) n = modified surface point Werner Purgathofer 31 surface normal b(u,v) n + p(u,v) n p (u,v) v u Perlin

32 Bump Mapping Calculation p'(u,v) = p(u,v) + b(u,v) n n' = (p u ' p v ') p u ' = (p+bn)/ u = p u +b u n+bn u because p u ' p u +b u n p v ' p v +b v n n' = (p u +b u n) (p v +b v n) b is very small Alias Wavefront n' = p u p v +b v (p u n)+b u (n p v )+b u b v (n n) n n=0 n' = n * +b v (p u n)+b u (n p v ) Werner Purgathofer 32

33 Bump Mapping Representation bump map b(u,v) defined as raster image b u, b v : approximated with finite differences Alias Wavefront Werner Purgathofer 33

34 Bump Mapping Problems sources of error distortions at grazing angles wrong silhouette (geometry is not changed!) wrong shadows missing bump shadows light effects on back side Werner Purgathofer 34 Copyright Alias Wavefront

35 Bump Mapping: Grazing Angles red buttons appear too flat, although they are shaded in 3D Werner Purgathofer 35

36 Bump Mapping Problems sources of error distortions at grazing angles wrong silhouette (geometry is not changed!) wrong shadows missing bump shadows light effects on back side Werner Purgathofer 36 Copyright Alias Wavefront

37 Bump Mapping: Wrong Silhouette bump mapping correct geometry Lifeng Wang Lifeng Wang Werner Purgathofer 37 Copyright Alias Wavefront

38 Bump Mapping Problems sources of error distortions at grazing angles wrong silhouette (geometry is not changed!) wrong shadows missing bump shadows light effects on back side Werner Purgathofer 38 Copyright Alias Wavefront

39 Bump Mapping: Missing Bump Shadows bump mapping correct shadows Lifeng Wang Lifeng Wang Werner Purgathofer 39 Copyright Alias Wavefront

40 Bump Mapping Problems sources of error distortions at grazing angles wrong silhouette (geometry is not changed!) wrong shadows missing bump shadows light effects on back side Werner Purgathofer 40 Copyright Alias Wavefront

41 Bump Mapping: Back Side Light Effects Werner Purgathofer 41 Copyright Alias Wavefront

42 Bump Mapping Problems sources of error distortions at grazing angles wrong silhouette (geometry is not changed!) wrong shadows missing bump shadows light effects on back side there exist special algorithms to repair each error Werner Purgathofer 42 Copyright Alias Wavefront

43 Displacement Mapping correct version of bump mapping surface points are moved from their original position outline of object changes much harder to implement than bump mapping rare in practice latest hardware partially supports it blender.org Werner Purgathofer 43 Stefan Jeschke

44 Multitexturing: Combination of Mappings 2 or more textures applied to a surface examples: texture + dirt texture + light map texture + bump map photo + annotations + = Werner Purgathofer 44

45 Multitexturing: Combination of Mappings bump mapping & environment mapping & texture mapping Werner Purgathofer 45 Marek Mizanin