2D Texture Mapping - Drexel CCIdavid/Classes/CS432/... · Lecture 15 Slide 25 6.837 Fall 2002...

2D Texture Mapping

CS 432 Interactive Computer GraphicsProf. David E. Breen

Department of Computer Science

1E. Angel and D. Shreiner: Interactive Computer Graphics 6E © Addison-Wesley 2012

Slide Creditsn Jonathan Cohen - Johns Hopkins

Universityn Shayan Sarkar - Carnegie Mellon

Universityn Leonard McMillan, Jovan Popovic, Fredo

Durand - MITn Steve Marschner - Cornell Universityn David Luebke - University of Virginian Pat Hanrahan - Stanford University

The Quest for Visual Realism

Photo-textures

The concept isvery simple!

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Lecture 15 Slide 25 6.837 Fall 2002

Adding Texture Mapping to IlluminationTexture mapping can be used to alter some or all of the constants in theillumination equation. We can simply use the texture as the final color for the pixel,or we can just use it as diffuse color, or we can use the texture to alter the normal,or... the possibilities are endless!

Phong's Illumination Model

Constant Diffuse Color Diffuse Texture Color Texture used as Label Texture used as Diffuse Color

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03/14/2002 15-462 Graphics I 15

Difficulties with texture mappingDifficulties with texture mapping

• Another difficulty is how to map a 2D image onto an arbitrary 3D model– Ex: If you wanted to map onto a sphere, you can’t do it without

distorting the texture

jpg (JPEG Image, 640x480 pixels) http://www.cs.cornell.edu/Courses/cs417/2003sp/Lectures/Lecture25/Slide13.jpg

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David Luebke 1/19/99

Antialiasing andAntialiasing andTexture MappingTexture Mapping

ll Texture mapping is uniquely harderTexture mapping is uniquely harder–– Coherent textures present pathologicalCoherent textures present pathological

artifactsartifacts–– Correct filter shape changesCorrect filter shape changes

ll Texture mapping is uniquely easierTexture mapping is uniquely easier–– Textures are known ahead of timeTextures are known ahead of time–– They can thus be They can thus be prefilteredprefiltered

ll More on texture problemsMore on texture problems–– Coherent texture frequencies becomeCoherent texture frequencies become

infinitely high with increasing distanceinfinitely high with increasing distancenn Ex: checkerboard receding to horizonEx: checkerboard receding to horizon

–– Unfiltered textures lead to Unfiltered textures lead to compressioncompressionnn Ex: pixel covers entire checkerboardEx: pixel covers entire checkerboardnn Unfiltered mapping: pixel is black or whiteUnfiltered mapping: pixel is black or whitenn Moving checkerboard Moving checkerboard ŸŸ flashing pixels flashing pixels

ll Problem: a square pixel on screenProblem: a square pixel on screenbecomes a curvilinear quadrilateralbecomes a curvilinear quadrilateralin texture map (see W&W, p 140)in texture map (see W&W, p 140)

ll The coverage and area of this shapeThe coverage and area of this shapechange as a function of the mappingchange as a function of the mapping

ll Most texture antialiasing algorithmsMost texture antialiasing algorithmsapproximate this shape somehowapproximate this shape somehow

ll Mip-mappingMip-mapping–– MIP = MIP = Multim Multim in in Parvo Parvo (many things in(many things in

a small place)a small place)–– Ignores shape change of inverse pixelIgnores shape change of inverse pixel–– But allows But allows sizesize to vary to vary

ll Idea: store texture as a pyramid ofIdea: store texture as a pyramid ofprogressively lower-resolutionprogressively lower-resolutionimages, filtered down from originalimages, filtered down from original

AntialiasingAntialiasing: Mip-Mapping: Mip-Mapping

Depth of Mip-Map

Antialiasing: Mip MappingAntialiasing: Mip Mapping

ll Distant textures use higher levels ofDistant textures use higher levels ofthe the mipmapmipmap

ll Thus, the texture map is Thus, the texture map is prefilteredprefilteredll Thus, reduced aliasing!Thus, reduced aliasing!

ll WhichWhich level of mip-map to use? level of mip-map to use?–– Think of mip-map as 3-D pyramidThink of mip-map as 3-D pyramid–– Index into mip-map with 3 coordinates:Index into mip-map with 3 coordinates:

u, v, du, v, d (depth) (depth)ll Q:Q: What does d correspond to in the What does d correspond to in the

mip-map?mip-map?ll A: size of the filterA: size of the filter

ll The size of the filter (i.e., The size of the filter (i.e., dd in the in themip-map) depends on the pixelmip-map) depends on the pixelcoverage area in the texture mapcoverage area in the texture map–– In general, treat d as a continuousIn general, treat d as a continuous

valuevalue–– Blend between nearest mip-map levelBlend between nearest mip-map level

using using tri-lineartri-linear interpolationinterpolation

ll Q: WhatQ: What’’s wrong with the mip-maps wrong with the mip-mapapproach to approach to prefiltering prefiltering texture?texture?

ll A: Assumes pixel maps to square inA: Assumes pixel maps to square intexture spacetexture space

ll More sophisticated inverse pixelMore sophisticated inverse pixelfilters (see F&vD p 828):filters (see F&vD p 828):–– Summed area tablesSummed area tables–– Elliptical weighted average filteringElliptical weighted average filtering

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Texture and Materials http://graphics.stanford.edu/courses/cs348b-02/lectures/lecture12/walk003.html

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03/14/2002 15-462 Graphics I 32

Environment MappingEnvironment Mapping

• Allows for world to be reflected on an object without modeling the physics

• Map the world surrounding an object onto a cube

• Project that cube onto the object• During the shading calculation:

– Bounce a ray from the viewer off the object (at point P)– Intersect the ray with the environment map (the cube), at point E– Get the environment map’s color at E and illuminate P as if there

were a virtual light source at position E– You see an image of the environment reflected on shiny surfaces

Environment Maps If, instead of using the ray from the surface point to the projectedtexture's center, we used the direction of the reflected ray to index atexture map. We can simulate reflections. This approach is not completelyaccurate. It assumes that all reflected rays begin from the same point.

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What's the Best Chart?

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Reflection Mapping

03/14/2002 15-462 Graphics I 30

Bump MappingBump Mapping

• How do you make a surface look rough?– Option 1: model the surface with many small polygons– Option 2: perturb the normal vectors before the shading

calculation• the surface doesn’t actually change, but shading makes it look that

way• bump map fakes small displacements above or below the true

surface• can use texture-mapping for this• For the math behind it all look at Angel 9.4

Bump MappingTextures can be used to alter the surface normal of an object. This does not change the actualshape of the surface -- we are only shading it as if it were a different shape! This technique iscalled bump mapping. The texture map is treated as a single-valued height function. Thevalue of the function is not actually used, just its partial derivatives. The partial derivatives tellhow to alter the true surface normal at each point on the surface to make the object appearas if it were deformed by the height function.

Since the actual shape of the object does not change, the silhouette edge of the object willnot change. Bump Mapping also assumes that the Illumination model is applied at every pixel(as in Phong Shading or ray tracing).

Sphere w/Diffuse Texture

Swirly Bump Map

Sphere w/Diffuse Texture & Bump Map

Bump mapping

TvuzvuyvuxP )],(),,(),,([=v

vu PPNvvv

NvuBPPvvv

),(+=¢

D+-D-=

2),(),( tsBtsB

D+-D-=

2),(),( tsBtsB

Compute bump map partialsby numerical differentiation

Initial point

Normal

Simulated elevated point after bump

Variation of normal in u direction

Variation of normal in v direction

vvuu PBPBNN ++ª¢

If Pu and Pv are orthogonal and N is normalized: Nv

More Bump Map Examples

Cylinder w/Diffuse Texture Map

Bump Map

Cylinder w/Texture Map & Bump Map

One More Bump Map Example

Notice that the shadow boundaries remain unchanged.

03/14/2002 15-462 Graphics I 31

Bump MappingBump Mapping

• In CG, we can perturb the normal vector without having to make any actual change to the shape.

• What would be the problems with bump mapping?

Original model (5M) Simplified (500) Simple model with bump map

Displacement MappingWe use the texture map to actually move the surface point. This is calleddisplacement mapping. How is this fundamentally different than bumpmapping?

The geometry must be displaced before visibility is determined. Is thiseasily done in the graphics pipeline? In a ray-tracer?

Stochastic Microgeometry forDisplacement Mappingn Reconstruct a stochastic distribution

over a mesh

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The Best of All WorldsAll these texture mapping modes are great!

The problem is, no one of them does everything well.

Suppose we allowed several textures to be applied to each primitiveduring rasterization.

2D Texture Mapping - Drexel CCIdavid/Classes/CS432/... · Lecture 15 Slide 25 6.837 Fall 2002...

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