Surface Rendering. Surface Rendering

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1 Surface Rendering Surface Rendering Introduce Mapping Methods - Texture Mapping - Environmental Mapping - Bump Mapping Go over strategies for - Forward vs backward mapping 2 1

2 The Limits of Geometric Modeling Although graphics cards can render over 10 million polygons per second, that number is insufficient for many phenomena - Clouds - Grass - Terrain - Hair 3 Consider the problem of modeling an orange (that is a SunKist, not the color) Start with an orange-colored sphere - Too simple Motivation: Modeling an Orange Replace sphere with a more complex shape - To capture surface characteristics (small dimples) - Takes SO many polygons to model all the dimples 4 2

3 Motivation: Modeling an Orange (2) Take a picture of a real orange, scan it, and paste onto simple geometric model - This process is texture mapping Still might not be sufficient because resulting surface will be smooth - Need to change local shape - Bump mapping 5 Motivation: Modeling an Orange (3) Detail surface variation Noisy Surface Patterned surface Complex structure Bumpy surface 6 3

4 Three Types of Mapping Texture Mapping - Uses images to fill inside of polygons Environmental (reflection mapping) - Uses a picture of the environment for texture maps - Allows simulation of highly specular surfaces Bump mapping - Emulates altering normal vectors during the rendering process 7 Texture Mapping geometric model texture mapped 8 4

5 Environment Mapping 9 Bump Mapping 10 5

6 Texture Mapping Geometry and lighting alone do not provide sufficient visible detail Paste 2D image onto 3D surface Surface appears much more complex than reality 11 Texture Mapping 12 6

7 Texture Mapping 13 Texture Mapping 14 7

8 Mapping textures to models Although the idea is simple---map an image to a surface---there are several tricky steps involved 2D image 3D surface 15 Mapping textures to models parametric coordinates texture coordinates world coordinates screen coordinates 16 8

9 Mapping textures to models How do we find mapping? Consider going from texture coordinates to a point a surface Must define mapping x = x(s,t) y = y(s,t) z = z(s,t) t s (x,y,z) 17 Texture "Painting" 3D Paint packages establishes an arbitrary mapping (model to map) Then records the texture as the user "paints" on the model 18 9

10 Rendering Textures In rendering, we perform backward mapping - Given a pixel, we want to know which point on an object it corresponds to and - Given a point on an object, we want to know which point in the texture it corresponds or: Map of the form s = s(x,y,z) t = t(x,y,z)? These functions are difficult to find in general 19 Simple Backward mapping A direct solution to the simple mapping problem can be found analytically Example: mapping a cube 20 10

11 Simple Backward mapping Example: map to cylinder 21 Simple Backward mapping Parametric cylinder x = r cos 2p u y = r sin 2p u z = v/h Maps rectangle in u,v space to cylinder of radius r and height h in world coordinates Thus, s = u t = v maps from the texture space u v 22 11

12 Two-part (Backward) mapping One solution to the general mapping problem is a two-part mapping: first map the texture to a simple intermediate surface (like the cylinder) Then map to the object of interest 23 Two-Part Mapping Second, map from the intermediate object to the actual object by: - Normals from intermediate to actual - Normals from actual to intermediate 24 12

13 Two-Part Mapping In General, no direct method exists Best choice of secondary mapping depends on the model being mapped Sampling Assume texture parameterized by s,t

14 Sampling the texture Associate texture coordinates with each vertex on the surface Sampling the texture During drawing, look up color from texture using continuous texture coordinates 29 14

15 Sampling the texture u, v 30 Sampling the texture Nearest neighbor - Blocky results u, v 31 15

16 Nearest Sampling Example 32 Sampling Nearest neighbor - Blocky results Linear blending - Smooth appearance u, v 33 16

17 Sampling Nearest neighbor - Blocky results Linear blending - Smooth appearance 1 u, v 1 34 Nearest Sampling Example 35 17

18 Linear Sampling Example 36 Other Problems with Texture Mapping Textures often composed of separate pieces called charts Boundaries don t match Sampling issues Not bad for color Huge problem for displacement mapping 37 18

19 Other Uses of Texture Mapping Environment Mapping Bump/Normal Mapping Displacement Mapping. Any attribute of the surface position, normal, color, etc can be placed in a texture 38 Environment Mapping Cheap attempt at modeling reflections Makes surfaces look metallic Use six textures to model faces of a cube Assume cube faces infinitely far away The normal (or reflected eye vector) is used to find which of the textures to use and what texture coordinate 39 19

20 Environment Mapping 40 Environment Mapping 41 20

21 Environment Mapping Reflected ray: r 2( n v) n v viewer v n r reflective surface environment texture image Texture is transferred in the direction of the reflected ray r from the environment map onto the object 42 How to represent the map viewer 43 21

22 How to represent the map viewer 44 How to represent the map viewer 45 22

23 How to represent the map viewer Store colors of every possible direction in texture maps 46 How to represent the map viewer c c c c c v Store colors of every possible direction in texture maps 47 23

24 How to represent the map viewer c c c c c v Store colors of every possible direction in texture maps Look up texture maps based on reflected vector 48 Environment Mapping 49 24

25 Environment Mapping 50 Environment Mapping Easy to use with simple projection for a box but can cause distortions 51 25

26 Bump/Normal Mapping Replace colors R,G,B with coordinates X,Y,Z Interpret pixels as adjusted normals Makes the shading look more complicated than geometry really is After bump mapping 52 Bump Mapping (2D Example) Surface with normals Bump texture New surface with texture 53 26

27 Bump Mapping 54 Bump/Normal Mapping Example 55 27

28 Bump/Normal Mapping Example 56 Bump/Normal Mapping Example 57 28

29 Bump Mapping combined with Texture 58 Bump Mapping combined with Texture 59 29

30 Displacement Mapping Offset geometry in direction of normal Encode offset inside texture Used to actually change the geometry and provide more detail (especially silhouette) 60 Bump/Normal Mapping Example 61 30

31 Displacement Mapping Example 62 Displacement Mapping Example 63 31

32 More Examples 64 More Examples 65 32

33 Problems with Displacement Maps Actually move geometry based on texture map how is still open question in general Expensive and difficult to implement in many rendering pipelines 66 33

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