BRDF f ( , , , ) r i i r r camera Computer 3D - - PDF document

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Texture Mapping

Paper Summaries

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Computer Graphics as Virtual Photography

camera (captures light) synthetic image camera model (focuses simulated lighting)

processing

photo processing tone reproduction real scene 3D models Photography: Computer Graphics: Photographic print

Remember this?

• Bi-directional Reflectance Function

) , , , (

r r i i r

f BRDF θ φ θ φ =

At a given point, gives relative reflected illumination in any direction with respect to incoming illumination coming from any direction

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Illumination Models

• Illumination model - function or algorithm used

to describe the reflective characteristics of a given surface.

• More accurately, function or algorithm used to

approximate the BRDF.

Phong Model

specular diffuse ambient

V) R ( N) S ( ) (

∑ ∑

• +
• +

=

i k i i s i i i d a a

e

L k L k L k V L

Question

• What if Phong (or other) Illumination

models aren’t good enough?

– Texture Mapping – use an image – Procedural Shading – program your own

Texture Mapping

• Developed in 1974 by Ed Catmull, currently

president of Pixar

• Goal: Make Phong shading less plastic looking

Texture Mapping

• A means to define surface characteristics of

an object using an image

• Mapping a 2D image onto a 3D surface
• Coordinate spaces in texture mapping

– Texture space (u, v) – Object space (xo,yo,zo) – Screen space (x, y)

Texture Mapping - Uses

• Surface color - most common
• Normal vector perturbations (bump mapping)
• Reflection

– illumination

• specular
• diffuse
• transparency

– environment mapping

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Texture Mapping

Watt

Texture Mapping

• Key to texture mapping is parameterization

– 3D geometry must be expressed as a function

• f 2 variables, u and v.

– Examples:

• Planar
• Spherical
• Bi-cubic patch
• Cylindrical

Texture Mapping

texture space (u,v)

• bject space (xo,yo, zo)

screen space (x,y)

parameterization projection

Texture Mapping

• Spherical Mapping

Texture Mapping

• Bi-cubic surfaces

What is a texture?

• Two Types:

– Image file – Mathematically/procedurally generated

• Contents:

– Made up of texels – Photos shot straight on – E.g., wood grain, marble, patterns

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Texture mapping

Photographic Textures

Direct Mapping

• Simplest form of mapping
• Texture coordinates equal polygon
• coordinates. (u = x and v = y )
• How to fill? Polygon filling

– Same scanline algorithm as CGI – color data pulled from texture array

Texture Mapping - Direct Mapping

Texture mapping

Photographic Textures

Texture Mapping - Direct Mapping

• Problems:

– Causes texture to be clipped, or entire polygon not filled.

• Solution:

– Need an algorithm that stretches & shrinks texture over a polygon. Affine mapping comes to the rescue.

Texture Mapping - Affine Mapping

• Stretching and shrinking of the texture is

based on the premise of sampling.

• Texture coordinates become necessary

– Arbitrary mapping of texture coordinates to polygon coordinates

• Additional calculations required

– dxdy, dudy, dvdy all need to be calculated for each edge. dudx, dvdx for each scanline.

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Texture Mapping – Affine Mapping

Texture is like a rubber sheet stretched to fit model

Texture Mapping

Watt

Texture Mapping – Affine Mapping (Warping)

⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ 1 Matrix n Translatio Matrix Rotation Matrix Projection 1 n v u z y x

Foley/VanDam(745)

Texture Mapping - Affine Mapping

• But this can have different problems due to sampling:

– Small textures on large models/polygons tend to become blocky. – Large textures on small models/polygons tend to become grainy.

Texture Mapping

• There are other mappings as well

– e.g., cylindrical – Any mapping from 3D -> 2D will do

Projective Texture

Texture Mapping

• Texture Mapping Applets

http://www.cs.brown.edu/exploratories/free Software/catalogs/texture_mapping.html

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Texture mapping – Bump Mapping Texture Mapping- Bump Mapping

Adds roughness to surfaces Quick way to add detail to an

• bject

Polygon remains physically flat, but appears bumpy

Jim Blinn

Bump Mapping Theory

• If your eyes see light and dark bumps
• Flat surfaces reflect more light
• Bumpy surfaces reflect less

Bump Mapping Theory

• Surfaces angled upward tend to be

brightly lit

• Downward inclined surfaces tend to be

darker

Bump Mapping-Theory

Texture Mapping- Bump Mapping

• Perturbing surface normal
• Texture map represents displacements from the

normal

• Use perturbed normal in illumination model

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Bump Mapping

• Perlin Dnoise example

Normal += Dnoise (point)

[Perlin85]

Texture Mapping

• Bump Mapping

Bump Mapping

• Applet

http://users.interfriends.net/maurid/Bump Mapping.htm Texture Mapping- Environment mapping

• Create an image, representing the reflection of the

world onto an object

• Use surrounding sphere or box, image is texture map

indexed by direction of reflection ray

• Poor-man’s ray tracing - cheaper
• Can also be used to do illumination (image-based

lighting)

Texture Mapping- Illumination mapping

• Not associated with a particular object but with

an imaginary surface surrounding the scene

– Specular Reflection – indexed by reflected ray – Diffuse - by surface normal – Transparency – refracted ray direction

Environment Mapping

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Texture Mapping

• Environment mapping

Texture mapping

Reflection mapping

Texture Mapping

• Advantages of texture mapping

– Easy way to add complexity to a scene – Hardware support

• Issues:

– Aliasing - because of holes or overlaps – Limited resolution (zoom in DOOM effect) – Static image

Texture mapping

• Aliasing

– Sampling – images are discrete, not continuous. – Resolution of sampled space (in this case texture map) is not fine enough

Texture mapping

• Aliasing- point sampling in middle of pixel - need

more!

Texture Mapping – Aliasing

Watt

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Texture Mapping

• Aliasing -because of interpolation and perspective

projection

aliased image anti-aliased image

Texture Mapping - Anti-aliasing

• Point sample at higher resolution (sometimes very

difficult)

– Nearest

• Pick the closest texel

– Linear

• Take an average of surrounding texels

– Mip-Mapping

• Multiple textures of the same image
• Use low pass filter before sampling
• Can sometimes use stochastic sampling to improve

results

Texture mapping

• Texture Map Aliasing Applet

http://www.nbb.cornell.edu/neurobio/land/ OldStudentProjects/cs490- 96to97/anson/TextureMappingApplet/

Texture Mapping

• Mipmaps

– Pre-calculate your texture map at many resolutions (or layers) – Store all “texture layers” in a single image. – Use “appropriate” layer when performing rendering, interpolating between levels as required:

Texture Mapping

• Mipmaps

Texture Mapping

• Mipmaps - dimensions

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Texture Mapping

• Static

– Texture map image is taken under a single lighting condition – What happens when lighting conditions of the scene doesn’t match that of your texture?

Texture Mapping – Radiance Maps

• Provides approximated radiance values, not

simply color info, as a texture.

• Radiance map not only for the distant scene,

but in reflections from objects.

• Radiance in map used in global illumination

solution

• Technique used in Fiat Lux

Recent Texture Research

• 2001 Proceedings

– Illumination & Texture Photorealism: Texture Mapping Progressive Meshes – Procedural Modeling: Feature Based Cellular Texturing – Point-Based: Surface Splatting

Recent Texture Research

• 2003 Proceedings

– GraphCut Textures – Wang Tiles – Synthesis of Progressively Variant Textures on Arbitrary Surfaces – View Dependent Displacement Mapping