CS 4600 Fall 2015 1
Texture Mapping
From: Ed Angel
University of New Mexico
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Objectives
• Introduce Mapping Methods- Texture Mapping
- Environment Mapping
- Bump Mapping
•Consider basic strategies- Forward vs backward mapping
- Point sampling vs area averaging
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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 known as 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
• 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
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Texture mapping
• Texture mapping: adding surface detail by mapping texture patterns to the surface
• Developed by Catmull (1974), Blinn and Newell (1976), and others
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Texture Mapping
• Maps a pattern (texture) onto a surface• Texels fill each pixel• Texels selected from sample pattern
(texture map)• Pattern is repeated
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Texture Maps
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Texture Maps
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Wallpaper, Analogue Texture Map
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Flooring, Tiling, etc
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Examples of Mapped Texture
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Examples
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Texture Mapping
geometric model texture mapped
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Environment Mapping
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Bump Mapping
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Bump Mapping
Look at smooth
silhouettes
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Displacement Mapping
Look at silhouette
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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 make it past the clipper
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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 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
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Texture Mapping
parametric coordinates
texture coordinates
world coordinateswindow 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 texel, 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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Basic Concept
• Relate a 2D image to a 3D model
• Texture coordinates- Texture coordinate is a 2D
coordinate (s,t) which maps to a location on a texture map
• Texture coordinates are over the interval [0,1], typically
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Elements of Texture Mapping
• Texture source function (can be 3D)
• Inverse map: Texture (s,t) ← Surface (x(s,t), y(s,t), z(s,t))
• Typical texture sources- Procedure
- Tabular data (texture map)
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Texture Mapping Techniques
• 2D texture mapping: paint 2D pattern onto the surface
• Environmental (reflection) mapping
• Bump mapping: perturb surface normals to fool shading algorithms
• Procedural texture mapping, 3D texture
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Make a nice can of soup?
30
Make a nice can of soup?
+
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Cylindrical Mapping
parametric cylinder explicit cylinder
x = r cos 2 uy = r sin 2uz = hv
maps rectangle in u,v space to cylinderof radius ө and height h in world coordinates
s = ut = v
maps from texture space
h
(ө,h)
ө
x = r cos 2y = r sin 2z = h
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Cylindrical Mapping
parametric cylinder explicit cylinder
x = r cos 2 uy = r sin 2uz = hv
maps rectangle in u,v space to cylinderof radius ө and height h in world coordinates
s = ut = v
maps from texture space
h(0, 0)
(ө,h)
ө
x = r cos 2y = r sin 2z = h
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Cylindrical Mapping
parametric cylinder explicit cylinder
x = r cos 2 uy = r sin 2uz = hv
maps rectangle in u,v space to cylinderof radius ө and height h in world coordinates
s = ut = v
maps from texture space
h(0, 0)
(0, 0.5)
(ө,h)
ө
x = r cos 2y = r sin 2z = h
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Cylindrical Mapping
parametric cylinder explicit cylinder
x = r cos 2 uy = r sin 2uz = hv
maps rectangle in u,v space to cylinderof radius ө and height h in world coordinates
s = ut = v
maps from texture space
h(0, 0)
(0, 0.5)
(0, 1)
(ө,h)
ө
x = r cos 2y = r sin 2z = h
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Cylindrical Mapping
parametric cylinder explicit cylinder
x = r cos 2 uy = r sin 2uz = hv
maps rectangle in u,v space to cylinderof radius ө and height h in world coordinates
s = ut = v
maps from texture space
h(0, 0)
(0, 0.5)
(0.5,0)
(0, 1)
(ө,h)
ө
x = r cos 2y = r sin 2z = h
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Cylindrical Mapping
parametric cylinder explicit cylinder
x = r cos 2 uy = r sin 2uz = hv
maps rectangle in u,v space to cylinderof radius ө and height h in world coordinates
s = ut = v
maps from texture space
h(0, 0)
(0, 0.5)
(0.5,0)
(0, 1)(0.5,1)
(ө,h)
ө
x = r cos 2y = r sin 2z = h
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Cylindrical Mapping
parametric cylinder explicit cylinder
x = r cos 2 uy = r sin 2uz = hv
maps rectangle in u,v space to cylinderof radius ө and height h in world coordinates
s = ut = v
maps from texture space
h(0, 0)
(0, 0.5)
(0.5,0)(1, 0)
(0, 1)(0.5,1)
(ө,h)
ө
x = r cos 2y = r sin 2z = h
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Cylindrical Mapping
parametric cylinder explicit cylinder
x = r cos 2 uy = r sin 2uz = hv
maps rectangle in u,v space to cylinderof radius ө and height h in world coordinates
s = ut = v
maps from texture space
h(0, 0)
(0, 0.5)
(0.5,0)
(1, 1)
(1, 0)
(0, 1)(0.5,1)
(ө,h)
ө
x = r cos 2y = r sin 2z = h
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Spherical Map
We can use a parametric sphere
x = r cos 2uy = r sin 2u cos 2vz = r sin 2u sin 2v
in a similar manner to the cylinderbut have to decide where to putthe distortion
Spheres are used in environmental maps
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Spherical Map
ө
ø
(0.5,1)
(0,0.5)
(ө, 1)
(ө,0)
(ө,ø)
(1,0.5)
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Box Mapping
•Easy to use with simple orthographic projection
•Also used in environment maps
Gerri’s Game
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Texture Mapping
What if we don’t have a cylinder or sphere?
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Two-part mapping
•One solution to the mapping problem is to first map the texture to a simple intermediate surface
•Example: map to cylinder
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Two-part mapping
•One solution to the mapping problem is to first map the texture to a simple intermediate surface
•Example: map to cylinder
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Second Mapping
• Map from intermediate object to actual object
- Normals from intermediate to actual
- Normals from actual to intermediate
- Vectors from center of intermediate
intermediateactual
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More Examples
http://astronomy.swin.edu.au/~pbourke/texture/texturemapping
Texture Mapping, Paul Bourke (1987)
Planar Cubic Cylindrical
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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
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