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Mesostructure Rendering Techniques

Presented by Keith Yerex

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Mesostructure

Mesostructure is used to refer to details that are too large to be modeled by reflectance functions, and too small to be modeled efficiently by polygons

Commonly rendered with bump-mapping, horizon mapping, and/or displacement mapping.

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Bump-mapping

Store the normals of the true surface in a texture map, and use these normals in lighting equations. (dot3)

Normals can be stored in object space, or tangent space. In either case, the light must be transformed into that coordinate system.

[Blinn 78]

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Tangent space

Repeating bump/horizon/displacement maps must be represented in tangent space

Tangent space is a coordinate system made of the normal N, the tangent T, and the binormal B

Where T is in the direction of increasing texture coordinate u and B=NxT

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Horizon mapping

The horizon angle is precomputed for a discrete number of directions

An incoming light angle must be above the horizon in order to illuminate the surface

[Max 88]

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Displacement Mapping

A displacement map specifies displacement in the direction of the surface normal, for each point on a surface

from Klautz & Seidel

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Displacement Mapping

Generally expressed as a function of u,v texture coordinates (or parametric surface parameters)

Stored as a 2d texture, and/or computed procedurally

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The Problem

How can we render a model given as a set of polygons, and a displacement map?

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Current solutions

GeometricSubdivide and displace

Volume slice rendering

Ray tracing

Image SpaceParallax mapping

Relief textures

View dependent texturing / BDTF

View dependent displacement mapping

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Subdivide and Displace

Subdivide each polygon into many tiny polygons, and displace the new vertices along their normals using the displacement map

Produces many new vertices and triangles, which all need to be transformed and rendered.

Improvements include adaptive subdivision, and hardware implementation.

[Cook 84]

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Volume Slicing

Generate polygons that slice through the displacement volume

Render each slice, but draw only pixels where the displacement map value is greater than height of the slice at that position

Slices alignment varies(bump-out shells, orthogonal, screen aligned)

[Kautz & Seidel]

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Volume Slicing

Alpha test can be used for efficient hardware implementationStill generates a lot of geometry and high overdraw/fill-rate

from Klautz & Seidel

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Ray tracing

In ray tracing, rays are simply intersected with the displacement map, rather than the polygon

[Smits et al]

Reference Plane

Max Displacement

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Image Space MethodsFor a given viewing direction and texture coordinates P find the displacement in texture space l

from Wang et al

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Parallax mapping

Makes the approximation that l=V*H(P)*scale+bias

Where H(P) is the height at the point of incidence.

Very efficient, and pretty convincing, but not accurate

Movie

[Kaneko et al]

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Parallax mapping

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Relief Textures

Instead of inverse mapping, use a forward mapping (from texture to image)

Warping is implemented efficiently by a 1d pre-warp, followed by standard texture mapping.

[Oliveira, Bishop, McAllistor]

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View Dependent Texturing

Store textures from all possible views, and then just pick the best one from a list when rendering a new view (or blend the best few)

BDTF also stores different lighting conditions for all views

Very large memory requirements

[Debevec]

[Dana et al]

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View Dependent Displacement Mapping

Store the depth maps along all possible viewing angles.

Computing the texture coordinate offset then becomes as simple as

[Wang et al]

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VDM - curvatureFor curved surfaces, the situation is slightly more complicated

So depths are pre-computed for variations in curvature as well as viewing direction

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VDM – function

The vdm function dVDM(x,y,,,c), represents the depth to the surface along any ray to a surface with any curvature.

Note that if texture coordinates are unique, the curvature dimension doesn’t need to be stored.

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VDM - shadows

Self shadowing is easily computed given the vdm function

This is used for curved surfaces also, even though it isn’t correct.

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VDM - silhouette

A maximum view polar angle function MVM(x,y,,c) is used to store silhouette information

Any rays where < MVM(x,y,,c) are not rendered

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VDM - compression

The 5D vdm function is sampled in this paper at 128x128 x 32x8 x 16

Plus another 4MB for the mvm function.

Taking 68MB of memory!

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VDM - compression

First, flatten dVDM and MVM into one 2d matrix A=[AVDM,AMVM]Rows of A are indexed by x,y, and columns are indexed by ,c (or just c for ,AMVM)

SVD is applied to A: A=UET=WET

Where E= [EVDM,EMVM]

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VDM – compression

The two functions can now be reconstructed as:

Only a the first few eigenfunctions Ei need to be used since the eigenvalues (and Wi) decrease rapidly with i

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VDM – compression

Using 8 eigenfunctions EVDM and 4 eigenfunctions EMVM reduces the data size to 4MB

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VDM – results

Movie

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References James F. Blinn, Simulation of wrinkled surfaces, Proceedings of the 5th annual conference on Computer graphics and interactive techniques, p.286-292, August 23-25, 1978

Robert L. Cook, Shade trees, Proceedings of the 11th annual conference on Computer graphics and interactive techniques, p.223-231, January 1984

Kristin J. Dana , Bram van Ginneken , Shree K. Nayar , Jan J. Koenderink, Reflectance and texture of real-world surfaces, ACM Transactions on Graphics (TOG), v.18 n.1, p.1-34, Jan. 1999

Jan Kautz , Hans-Peter Seidel, Hardware accelerated displacement mapping for image based rendering, No description on Graphics interface 2001, p.61-70, June 07-09, 2001, Ottawa, Ontario, Canada

Max, N. 1988. Horizon mapping: shadows for bump-mapped surfaces. The Visual Computer 4, 2, 109--117.

Manuel M. Oliveira , Gary Bishop , David McAllister, Relief texture mapping, Proceedings of the 27th annual conference on Computer graphics and interactive techniques, p.359-368, July 2000

Brian E. Smits , Peter Shirley , Michael M. Stark, Direct Ray Tracing of Displacement Mapped Triangles, Proceedings of the Eurographics Workshop on Rendering Techniques 2000, p.307-318, June 26-28, 2000

Lifeng Wang, Xi Wang, Xin Tong, Stephen Lin, Shimin Hu, Baining Guoand Heung-Yeung Shum, View-dependent displacement mapping, ACM Trans. Graph.22 (3), 2002

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Questions?