Texturing

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Instructor: Christopher Rasmussen (cer@cis.udel.edu)

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March 15, 2022 ❖ Lecture 11

Outline

• Bump maps
• Texturing pipeline
• More applications
• Light maps
• Environment maps
• Shadow maps

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Bump Mapping

• So far we’ve been thinking of textures modulating color and transparency only
• Billboards, decals, lightmaps, etc.
• But any other per-pixel properties are fair game...
• Pixel normals usually smoothly varying
• Computed at vertices for Gouraud shading; color interpolated
• Interpolated from vertices for Phong shading
• Textures allow setting per-pixel normal with a bump map

Bump map: Example

from wikipedia.org

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Sphere WITH bumps

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Sphere

animated GLSL example

Bump mapping: Why?

• Can get a lot more surface detail without expense of more object vertices to light, transform

courtesy of Nvidia

Bump + color map: Example

Courtesy of http://www.alejandrosegovia.net

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Bump mapping: Example

from MIT CG lecture notes

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Bump mapping: Example

courtesy of A. Awadallah

Height map

Bump texture applied to teapot

Bump mapping: How?

• Idea: Perturb pixel normals n(u, v) derived from object geometry to get additional detail for shading
• Compute lighting per pixel (like Phong)

from Hill

Bump mapping: Representations

• 3-D vector m(u, v) added directly to normal n
• Or: 2-D vector of coefficients (b_u, b_v) that scale u, v vectors tangent to surface

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from Akenine-Moller & Haines

Bump representation: Height map f(u, v)

• Store just scalar “altitude” at each pixel
• Get b_u, b_v from partial derivatives:

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• Approximate with finite differencing

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from Akenine-Moller

& Haines

Example: Converting height maps to normal displacements (aka normal maps)

Z coordinate set to some constant scale factor; (X, Y) normalized to [0, 1] range.

Right image is mostly blue because “straight up” vector is (0.5, 0.5, 1)

courtesy of Nvidia

Bump mapping: Issues

• Bumps don’t cast shadows
• Geometry doesn’t change, so silhouette of object is unaffected
• Textures can be used to modify underlying geometry with displacement maps
• Generally in direction of surface normal

courtesy of Nvidia

from https://en.wikipedia.org/wiki/Normal_mapping

Displacement Mapping

courtesy of spot3d.com

Bump mapping

Displacement mapping

Displacement Mapping the Sphere

courtesy of geeks3d.com

Displacement Mapping – Height Maps

courtesy of artofillusion.org -- Julian MacDonald

Texture mapping: Steps

• Creation: Where does the texture image come from?
• Geometry: Transformation from 3-D shape locations to 2-D texture image coordinates
• Rasterization: What to draw at each pixel (since texture coords. are floats)
• E.g., bilinear interpolation vs. nearest-neighbor

Texturing: Creation

• Reproductions
• Photographs
• Handpainted
• Directly-computed functions
• E.g., lightmaps, visibility maps
• Procedurally-built
• Synthesize with randomness, pattern-generating rules, etc.
• More about this after midterm

courtesy of H. Elias

courtesy of Nvidia

Procedural bump mapping

Texture mapping applications: Lightmaps

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courtesy of K. Miller

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Idea: Precompute expensive static lighting effects (such as ambient occlusion or diffuse reflectance) and “bake” them into color texture. Then scene looks more realistic as camera moves without expense of recomputing effects

Texture mapping application: Lightmaps

Tenebrae Quake screenshot

Lightmap example: Diffuse lighting only

Lightmap example: Light configuration

Lightmap example: Diffuse + lightmap

Texturing Pipeline (Geometry + Rasterization)

1. Compute object space location (x, y, z) from screen space location (i, j)

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list adapted from Akenine-Moller & Haines

courtesy of R. Wolfe

Texturing Pipeline (Geometry + Rasterization)

• Compute object space location (x, y, z) from screen space location (i, j)
• Use projector function to obtain object surface coordinates (u, v) (3-D -> 2-D projection)

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list adapted from Akenine-Moller & Haines

courtesy of R. Wolfe

Texturing Pipeline (Geometry + Rasterization)

• Compute object space location (x, y, z) from screen space location (i, j)
• Use projector function to obtain object surface coordinates (u, v) (3-D -> 2-D projection)
• Use corresponder function to find texel coordinates (s, t) (2-D -> 2-D transformation)
• Scale, shift, wrap like viewport transform in geometry pipeline

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list adapted from Akenine-Moller & Haines

courtesy of R. Wolfe

Texturing Pipeline (Geometry + Rasterization)

• Compute object space location (x, y, z) from screen space location (i, j)
• Use projector function to obtain object surface coordinates (u, v) (3-D -> 2-D projection)
• Use corresponder function to find texel coordinates (s, t) (2-D -> 2-D transformation)
• Scale, shift, wrap like viewport transform in geometry pipeline
• Filter texel at (s, t)

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list adapted from Akenine-Moller & Haines

courtesy of R. Wolfe

Texturing Pipeline (Geometry + Rasterization)

• Compute object space location (x, y, z) from screen space location (i, j)
• Use projector function to obtain object surface coordinates (u, v) (3-D -> 2-D projection)
• Use corresponder function to find texel coordinates (s, t) (2-D -> 2-D transformation)
• Scale, shift, wrap like viewport transform in geometry pipeline
• Filter texel at (s, t)
• Modify pixel (i, j)

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list adapted from Akenine-Moller & Haines

courtesy of R. Wolfe

Texture coordinates at vertices

• Polygons can be treated as parametric patches by assigning texture coordinates to vertices
• The standard OpenGL way

courtesy of

R. Wolfe

Parametric Surfaces

• If we have a surface patch already parametrized by some natural (u, v) such that x = f(u, v), y = g(u, v), z = h(u, v), we can use parametric coordinates u, v without a projector

courtesy of R. Wolfe

Projector Functions

• Want way to get from 3-D point to 2-D surface coordinates as an intermediate step
• Idea: Project complex object onto simple object’s surface with parallel or perspective projection (focal point inside object)
• Mesh: piecewise planar (default option

with texture coords)

• Plane
• Cylinder
• Sphere
• Cube

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Planar projector

courtesy of R. Wolfe

Planar projector

Orthographic projection onto XY plane: u = x, v = y

...onto YZ plane

...onto XZ plane

courtesy of

R. Wolfe

Cylindrical projector

• Convert rectangular coordinates (x, y, z) to cylindrical (r, h, θ), use only (h, θ) to index texture image

courtesy of

R. Wolfe

Spherical projector

• Convert rectangular coordinates (x, y, z) to spherical (r, θ, Φ), use only (θ, Φ)

courtesy of R. Wolfe

Projecting in non-standard directions

• Texture projector function doesn’t have to project ray from object center through position (x, y, z)—you can use any attribute of that position. For example:
• Ray comes from another location
• Ray is surface normal n at (x, y, z)
• Ray is reflection-from-eye vector r at (x, y, z)
• Etc.

Projecting in non-standard directions

• This can lead to interesting or informative effects

courtesy of R. Wolfe

Different ray directions for a spherical projector

Environment/Reflection 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
• This is an expensive procedure with ray tracing
• Idea: Approximate with texture mapping

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from Angel

Environment mapping: Details

• 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

courtesy of R. Wolfe

Making environment textures: Cube

• Cube map straightforward to make: Render/ photograph six rotated views of environment
• 4 side views at compass points
• 1 straight-up view, 1 straight-down view

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Skybox demo

Making environment textures: Sphere

• Or construct from several photographs of mirrored sphere

courtesy of P. Debevec

Environment mapping: Example

courtesy of G. Miller

~1982

Environment mapping: Example

From “Terminator II” (1991)

YouTube link

Environment mapping example: Same scene, different lighting

courtesy of P. Debevec

Reflection map demo

Environment Bump Mapping

• Idea: Bump map perturbs eye reflection vector

from Akenine-Moller

& Haines

Environment mapping: Issues

• Only physically correct under assumptions that object shape is convex and radiance comes from infinite distance
• Object concavities mean self-reflections, which won’t show up
• Other objects won’t be reflected
• Parallel reflection vectors access same environment texel, which is only a good approximation when environment objects are very far from object

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v

from Angel

Shadow Maps

• Idea: If we render scene from point of view of light source, all visible surfaces are lit and hidden surfaces are in shadow
• “Camera” parameters here = spotlight characteristics

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View from light

View from camera

Z-buffering

• A per-pixel hidden surface elimination technique
• Maintain an image-sized buffer of the nearest depth drawn at each pixel so far
• Only draw a pixel if it’s closer than what’s been rendered already

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from Hill

Z-buffer: Example

courtesy of DAM Entertainment

Color buffer

Depth buffer

Z-buffering

• A per-pixel hidden surface elimination technique
• Maintain an image-sized buffer of the nearest depth drawn at each pixel so far
• Only draw a pixel if it’s closer than what’s been rendered already

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from Hill

Shadow Maps

• Idea: If we render scene from point of view of light source, all visible surfaces are lit and hidden surfaces are in shadow
• “Camera” parameters here = spotlight characteristics
• When rasterizing scene from eye view, transform each pixel to get 3-D position with respect to the light
• Project pixel to (i, j, depth) with respect to light
• Compare depth to value in shadow buffer (aka light’s z-buffer*) at (i, j) to see if it is visible to light = not shadowed

View from light

View from camera

Shadow Maps

• Shadow edges have aliasing depending on shadow map resolution and scene geometry
• Shadow edges are “hard” by default

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from GPU Gems

Shadow Maps

• Shadow edges have aliasing depending on shadow map resolution and scene geometry
• Shadow edges are “hard” by default
• Solutions to both problems typically involve multiple offset shadow buffer lookups

WebGL shadowmap example (airplane)

WebGL shadowmap example (interactive)

WebGL shadowmap example (animals)