mit eecs 6.837, durand and cutler texture mapping & other fun stuff
TRANSCRIPT
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MIT EECS 6.837, Durand and Cutler
Texture Mapping & Other Fun Stuff
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MIT EECS 6.837, Durand and Cutler
Last Time?
• Distribution Ray Tracing• Bounding Boxes• Spatial Acceleration
Data Structures– Regular Grid– Adaptive Grids– Hierarchical Bounding Volumes
• Flattening the Transformation Hierarchy
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MIT EECS 6.837, Durand and Cutler
Regular Grid Discussion
• Advantages?– easy to construct– easy to traverse
• Disadvantages?– may be only sparsely filled– geometry may still be clumped
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MIT EECS 6.837, Durand and Cutler
Adaptive Grids
Nested Grids Octree/(Quadtree)
• Subdivide until each cell contains no more than n elements, or maximum depth d is reached
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MIT EECS 6.837, Durand and Cutler
Primitives in an Adaptive Grid• Can live at intermediate levels, or
be pushed to lowest level of grid
Octree/(Quadtree)
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MIT EECS 6.837, Durand and Cutler
Adaptive Grid Discussion
• Advantages?– grid complexity matches geometric density
• Disadvantages?– more expensive to traverse (especially octree)
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MIT EECS 6.837, Durand and Cutler
Bounding Volume Hierarchy
• Find bounding box of objects
• Split objects into two groups
• Recurse
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MIT EECS 6.837, Durand and Cutler
Bounding Volume Hierarchy
• Find bounding box of objects
• Split objects into two groups
• Recurse
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MIT EECS 6.837, Durand and Cutler
Bounding Volume Hierarchy
• Find bounding box of objects
• Split objects into two groups
• Recurse
![Page 10: MIT EECS 6.837, Durand and Cutler Texture Mapping & Other Fun Stuff](https://reader035.vdocuments.site/reader035/viewer/2022062805/5697bff21a28abf838cbbf6d/html5/thumbnails/10.jpg)
MIT EECS 6.837, Durand and Cutler
Bounding Volume Hierarchy
• Find bounding box of objects
• Split objects into two groups
• Recurse
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MIT EECS 6.837, Durand and Cutler
Bounding Volume Hierarchy
• Find bounding box of objects
• Split objects into two groups
• Recurse
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MIT EECS 6.837, Durand and Cutler
Where to split objects?• At midpoint OR• Sort, and put half of the objects on each side OR• Use modeling hierarchy
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MIT EECS 6.837, Durand and Cutler
Intersection with BVH
• Check sub-volume with closer intersection first
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MIT EECS 6.837, Durand and Cutler
Intersection with BVH
• Don't return intersection immediately if the other subvolume may have a closer intersection
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MIT EECS 6.837, Durand and Cutler
Bounding Volume Hierarchy Discussion
• Advantages– easy to construct– easy to traverse– binary
• Disadvantages– may be difficult to choose a good split for a node– poor split may result in minimal spatial pruning
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MIT EECS 6.837, Durand and Cutler
Questions?
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MIT EECS 6.837, Durand and Cutler
Today
• 2D Texture Mapping– Perspective Correct Interpolation– Specifying Texture Coordinates– Illumination & Reflectance
• Procedural Solid Textures • Other Mapping Techniques• Texture Aliasing
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MIT EECS 6.837, Durand and Cutler
The Problem:
• We don't want to represent all this detail with geometry
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MIT EECS 6.837, Durand and Cutler
The Quest for Visual Realism
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MIT EECS 6.837, Durand and Cutler
Texture Mapping• Increase the apparent
complexity of simple geometry
• Like wallpapering or gift-wrapping with stretchy paper
• Curved surfaces require extrastretching or even cutting
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MIT EECS 6.837, Durand and Cutler
Photo-textures
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MIT EECS 6.837, Durand and Cutler
Texture Tiling
• Specify a texture coordinate (u,v) at each vertex• Canonical texture coordinates (0,0) → (1,1)
seamless tiling (repeating)tiles with visible seams(0,0) (3,0
)
(0,3)
(0,0) (3,0)
(0,3)
(0,0)
(1,1)
(0,0)
(1,1)
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MIT EECS 6.837, Durand and Cutler
Texture Interpolation
• Specify a texture coordinate (u,v) at each vertex• Can we just linearly interpolate the values in
screen space?
(0,0) (1,0)
(0,1)
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MIT EECS 6.837, Durand and Cutler
Interpolation - What Goes Wrong?
texture source what we get what we want
• Linear interpolation in screen space:
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MIT EECS 6.837, Durand and Cutler
Specify More Coordinates?
• We can reduce the perceived artifacts by subdividing the model into smaller triangles.
• However, sometimes the errors become obvious– At "T" joints – Between levels-of-detail
(mipmapping... in a few weeks)
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MIT EECS 6.837, Durand and Cutler
Subdivision
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MIT EECS 6.837, Durand and Cutler
Subdivision
texture source what we get what we want
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MIT EECS 6.837, Durand and Cutler
Visualizing the Problem
• Notice that uniform steps on the image plane do not correspond to uniform steps along the edge.
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MIT EECS 6.837, Durand and Cutler
Linear Interpolation in Screen Space
linear interpolation in screen space
interpolation in 3-space
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MIT EECS 6.837, Durand and Cutler
Perspective Correct Interpolation We need a mapping from t values to s values:
Solve for s in terms of t:
Unfortunately, at this point in the pipeline (after projection) we no longer have z. However, we do have w1= 1/z1 and w2 = 1/z2, so:
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MIT EECS 6.837, Durand and Cutler
Today
• 2D Texture Mapping– Perspective Correct Interpolation– Specifying Texture Coordinates– Illumination & Reflectance
• Procedural Solid Textures • Other Mapping Techniques• Texture Aliasing
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MIT EECS 6.837, Durand and Cutler
Texture Mapping Difficulties
• Tedious to specify texture coordinates
• Acquiring textures is surprisingly difficult – Photographs have
projective distortions – Variations in
reflectance and illumination
– Tiling problems
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MIT EECS 6.837, Durand and Cutler
Common Texture Coordinate Mappings
• Orthogonal• Cylindrical• Spherical • Perspective
Projection• Texture
Chart
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MIT EECS 6.837, Durand and Cutler
Projective Textures• Use the texture
like a slide projector
• No need to specify texture coordinates explicitly
• A good model for shading variations due to illumination
• A fair model for reflectance (can use pictures)
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MIT EECS 6.837, Durand and Cutler
Projective Texture Example
• Modeling from photographs• Using input photos as textures
Figure from Debevec, Taylor & Malikhttp://www.debevec.org/Research
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MIT EECS 6.837, Durand and Cutler
Texture Mapping & Illumination• Texture mapping can be used to alter some or all of the
constants in the illumination equation: – pixel color, diffuse color, alter the normal, ….
Phong's Illumination Model
Constant Diffuse Color Diffuse Texture Color Texture used as Label Texture used as Diffuse Color
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MIT EECS 6.837, Durand and Cutler
Texture Chart
• Pack triangles intoa single image
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MIT EECS 6.837, Durand and Cutler
Questions?
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MIT EECS 6.837, Durand and Cutler
Today
• 2D Texture Mapping• Procedural Solid Textures• Other Mapping Techniques• Texture Aliasing
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MIT EECS 6.837, Durand and Cutler
Procedural Textures
Image by Turner Whitted
f (x,y,z) → color
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MIT EECS 6.837, Durand and Cutler
• Advantages:– easy to implement in ray tracer – more compact than texture maps
(especially for solid textures) – infinite resolution
• Disadvantages– non-intuitive – difficult to match existing texture
Procedural Textures
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MIT EECS 6.837, Durand and Cutler
Questions?
Ken Perlin
Justin Legakis
Justin Legakis
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MIT EECS 6.837, Durand and Cutler
Today
• 2D Texture Mapping• Procedural Solid Textures• Other Mapping Techniques:
– Bump Mapping– Displacement Mapping– Environment Mapping (for Reflections)– Light Maps (for Illumination)
• Texture Aliasing
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MIT EECS 6.837, Durand and Cutler
What's Missing?• What's the difference between a real
brick wall and a photograph of the wall texture-mapped onto a plane?
• What happens if we change the lighting or the camera position?
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MIT EECS 6.837, Durand and Cutler
Remember Gouraud Shading?
• Instead of shading with the normal of the triangle, shade the vertices with the average normal and interpolate the color across each face
Illusion of a smooth surface with smoothly
varying normals
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MIT EECS 6.837, Durand and Cutler
Phong Normal Interpolation
• Interpolate the average vertex normals across the face and compute per-pixel shading
(Not Phong Shading)
Must be renormalized
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MIT EECS 6.837, Durand and Cutler
Bump Mapping
• Use textures to alter the surface normal– Does not change the actual shape of the surface– Just shaded as if it were a different shape
Sphere w/Diffuse Texture Swirly Bump Map Sphere w/Diffuse Texture & Bump Map
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MIT EECS 6.837, Durand and Cutler
Bump Mapping• Treat the texture as a single-valued height function
• Compute the normal from the partial derivatives in the texture
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MIT EECS 6.837, Durand and Cutler
Another Bump Map Example
Cylinder w/Diffuse Texture Map
Bump Map
Cylinder w/Texture Map & Bump Map
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MIT EECS 6.837, Durand and Cutler
What's Missing?
• There are no bumps on the silhouette of a bump-mapped object
• Bump maps don’t allow self-occlusion or self-shadowing
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MIT EECS 6.837, Durand and Cutler
Displacement Mapping• Use the texture map to actually move the surface point
• The geometry must be displaced before visibility is determined
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MIT EECS 6.837, Durand and Cutler
Displacement Mapping
Image from:
Geometry Caching for Ray-Tracing Displacement Maps
by Matt Pharr and Pat Hanrahan.
note the detailed shadows cast by the stones
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MIT EECS 6.837, Durand and CutlerKen Musgrave
Displacement Mapping
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MIT EECS 6.837, Durand and Cutler
Today
• 2D Texture Mapping• Procedural Solid Textures• Other Mapping Techniques:
– Projective Shadows and Shadow Maps– Bump Mapping– Displacement Mapping– Environment Mapping (for Reflections)– Light Maps (for Illumination)
• Texture Aliasing
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MIT EECS 6.837, Durand and Cutler
Environment Maps• We can simulate reflections by using the direction of the reflected
ray to index a spherical texture map at "infinity".
• Assumes that all reflected rays begin from the same point.
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MIT EECS 6.837, Durand and Cutler
What's the Best Chart?
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MIT EECS 6.837, Durand and Cutler
Environment Mapping Example
Terminator II
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MIT EECS 6.837, Durand and Cutler
Texture Maps for Illumination
Quake
• Also called "Light Maps"
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MIT EECS 6.837, Durand and Cutler
Questions?
Image by Henrik Wann JensenEnvironment map by Paul Debevec
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MIT EECS 6.837, Durand and Cutler
Today
• 2D Texture Mapping• Procedural Solid Textures• Other Mapping Techniques:• Texture Aliasing
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MIT EECS 6.837, Durand and Cutler
Textures can Alias
• Aliasing is the under-sampling of a signal, and it's especially noticeable during animation
nearest neighbor
mipmaps & linear interpolation
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MIT EECS 6.837, Durand and Cutler
Textures can Alias
• Small details may "pop" in and out of view
nearest neighbor mipmaps & linear interpolation
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MIT EECS 6.837, Durand and Cutler
Next Time:
Real-TimeShadows