Fall 2011 CS 480/680 Computer Graphics Texture Mapping Dr. Frederick C Harris, Jr. Objectives Introduce Mapping Methods Texture Mapping
Environment Mapping Bump Mapping Consider basic strategies Forward vs backward mapping Point sampling vs area averaging 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 Skin 3 Modeling an Orange
Consider the problem of modeling an orange (the fruit) Start with an orange-colored sphere Too simple Replace sphere with a more complex shape Does not capture surface characteristics (small dimples) Takes too many polygons to model all the dimples
4 Modeling an Orange (2) Take a picture of a real orange, scan it, and paste onto simple geometric model This process is known as texture mapping Still might not be sufficient because resulting surface will be smooth Need to change local shape
Bump mapping 5 Three Types of Mapping Texture Mapping Uses images to fill inside of polygons Environment (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 6 Texture Mapping geometric model
Where does mapping take place? Mapping techniques are implemented at the end of the rendering pipeline Very efficient because few polygons make it past the clipper 10 Is it simple?
Although the idea is simple---map an image to a surface---there are 3 or 4 coordinate systems involved 2D image 3D surface 11 Coordinate Systems Parametric coordinates May be used to model curves and surfaces
Texture coordinates Used to identify points in the image to be mapped Object or World Coordinates Conceptually, where the mapping takes place Window Coordinates Where the final image is really produced 12
Basic problem is how to find the maps Consider mapping from texture coordinates to a point a surface Appear to need three functions x = x(s,t) y = y(s,t) z = z(s,t) (x,y,z) t
But we really want to go the other way s 14 Backward Mapping We really want to go backwards Given a pixel, we want to know to which
point on an object it corresponds Given a point on an object, we want to know to which point in the texture it corresponds Need a map of the form s = s(x,y,z) t = t(x,y,z) Such functions are difficult to find in general 15
Two-part mapping One solution to the mapping problem is to first map the texture to a simple intermediate surface Example: map to cylinder 16 Cylindrical Mapping parametric cylinder x = r cos 2p u
y = r sin 2pu z = v/h maps rectangle in u,v space to cylinder of radius r and height h in world coordinates s=u t=v maps from texture space 17
Spherical Map We can use a parametric sphere x = r cos 2pu y = r sin 2pu cos 2pv z = r sin 2pu sin 2pv in a similar manner to the cylinder but have to decide where to put the distortion Spheres are used in environmental maps 18
Box Mapping Easy to use with simple orthographic projection Also used in environment maps 19 Second Mapping Map from intermediate object to actual object Normals from intermediate to actual
Normals from actual to intermediate Vectors from center of intermediate actual intermediate 20 Aliasing Point sampling of the texture can lead to aliasing errors
point samples in u,v miss blue stripes (or x,y,z) space point samples in texture space 21 Area Averaging A better but slower option is to use area averaging
preimage pixel Note that preimage of pixel is curved 22
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