texture mapping. 2 the limits of geometric modeling although graphics cards can render over 10...
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Texture Mapping
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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
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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
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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
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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
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Texture Mapping
geometric model texture mapped
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More Than Wallpaper
• Color or image textures are the simplest form of texture.
• Real-world surface textures often: change with light change with viewpoint
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Bump Mapping
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Bump Map and Displacement Map
• Examples: Golf ball
• Bump Map vs. Displacement Map: Bump Map: only the looks change
Displ. Map: the actual surface points change.
See the next two slides from Crysis 2 DX11 (http://www.mycrysis.com/gallery/screenshot)
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Figure 8.10 of “3D Computer Graphics, 3rd Ed.” by Alan Watt
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Environment Mapping
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Environment Map
Figure 18.9 of “3D Computer Graphics, 3rd Ed.” by Alan Watt
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Procedural Texture
• Do we really need to store the image of a checkerboard?
• Solid texture. Example: wood carving.• More advacned: Perlin noise.
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Where does mapping take place?
• Mapping techniques are implemented at the end of the rendering pipeline
Very efficient because few polygons pass down the geometric pipeline
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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
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Coordinate Systems
• Parametric coordinates May be used to model curved surfaces
• Texture coordinates Used to identify points in the image to be mapped
• World Coordinates Conceptually, where the mapping takes place
• Screen Coordinates Where the final image is really produced
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Texture Mapping
parametric coordinates
texture coordinates
world coordinatesscreen coordinates
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Mapping Functions
• Basic problem is how to find the maps• Consider mapping from texture coordinates to a point a surface
• Appear to need three functionsx = x(s,t)y = y(s,t)z = z(s,t)
• But we really want to go the other way
s
t
(x,y,z)
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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
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Aliasing
• Point sampling of the texture can lead to aliasing errors
point samples in u,v (or x,y,z) space
point samples in texture space
miss blue stripes
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Area Averaging
A better but slower option is to use area averaging
Note that preimage of pixel is curved
pixelpreimage