Texturing - CS Course Webpages

Texturing

Texture Mapping
• Geometry and lighting alone do not provide
sufficient visible detail
• Going from 3‐D to 2‐D
“Paste” 2D image onto 3D surface
• Surface appears much more complex than
reality
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Texture Mapping

Texture Mapping
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Texture Mapping
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Texture Mapping
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Texture Mapping
• Assume texture parameterized by u, v
v
1
0
0
u
1
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Texture Mapping
• Any u, v coordinate maps to a point on the
image
v
1
0
0
u
1
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Texture Mapping
• Associate texture coordinates with each
vertex on the surface
v
1
0
0
u
1
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Texture Mapping
• During polygon drawing, lookup color from
texture using interpolated texture coordinates
v
1
0
0
u
1
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Texturing: Geometry
1. Compute object space location (x, y, z) from screen
space location (i, j)
2. Use projector function to obtain object surface coordinates
(s, t ) from (x,y,z)
(Usually we don’t care about the interior of the object)
3. Corresponder function to find texel
coordinates (u, v)
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Cylindrical Projector
• Convert rectangular coordinates (x, y, z) to
cylindrical (r, theta, phi), use only
(theta, phi) to index texture image

Spherical projector
• Convert rectangular coordinates (x, y, z) to
spherical (theta, phi)
Spherical projector

Sampling Textures
1. Nearest neighbor
Blocky results
2.Bilinear Interpolation
Smooth
u,v

Nearest neighbor
• Assume we can compose the previous steps
(projector, corresponder, etc.) to define a
transformation function M from integer screen
coordinates (i, j) to real‐valued texture coordinates
(s, t) such that M (i, j) = (s, t)
• Now we just copy the texel at (round(s),
round(t)) to the pixel at (i, j) and we’re done,
right?

• Problem is that it can cause aliasing effects
• Why? Because the round() function causes
discontinuous switches in which texel is
nearest and hence is the color drawn

Nearest Neighbor
Blocky results

Bilinear Interpolation (BLI)
Idea: Blend four texel values surrounding
source, weighted by nearness
Vertical blend
Horizontal blend

Deal with Range
• repeat: Start entire texture over
• mirror: Flip copy of texture in each direction
– Get continuity of pattern
• clamp to border: Surround with border color

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
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Environment Mapping
• Problem: To render pixel on mirrored surface
correctly, we need to follow reflection of eye
vector back to first intersection with another
surface and get its color(especially for glass
surface, metal surface...)
• This is an expensive procedure with ray
tracing
• Idea: Approximate with texture mapping

Environment Mapping
• Key idea: Render 360 degree view of
environment from center of object with
sphere or box as intermediate surface
• Intersection of eye reflection vector with
intermediate surface provides texture
coordinates for reflection/environment
mapping
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Environment Mapping
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Environment Mapping(Cube mapping)
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Environment Mapping
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Environment Mapping
N
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Environment Mapping
N
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Bump/Normal Mapping
• Specify perturbation of normals by texture
• Height map: store scalar “altitude”
• Normal map: store nomals in RGB
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Bump/Normal Mapping Example
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Bump/Normal Mapping Example
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Displacement Mapping
• Offset geometry in direction of normal
• Encode offset inside texture
• Used to actually change the geometry and
provide more detail
• Difficult/expensive to perform with current
hardware
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Displacement Mapping Example
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Problems with Texture Mapping
• Textures composed of separate pieces called
“charts”
• Boundaries don’t match
• Sampling issues
• ……
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