Mesh ColorCem Yuksel John Keyser Donald H. House

Texas A&M University

SIGGRAPH 2010

2010/12/06 Xiang

Outline

1. Introduction2. Mesh Color Structure3. Mesh Color Properties4. Filtering5. Experimental Result6. Disscusion7. Conclusion8. Reference

1. Introduction

2D texture

3D texture

TextureMapping

Some problem & Some challenge

Texture Mapping Challenge

• 2D texture− Seams− No local texture detail adjustment− Very sensitive to model topology

• 3D texture− Challenge to One-to-one mapping− Sharp and thin edge requires high textue resolution to

avoid color bleeding− Slightest change in the textured 3D model may require to

regenerate map− Big memory requirement

Color bleeding

Mesh Color Structure

Number of color samples per vertex = 1Number of color samples per edge =

Number of color samples per face =

With different resolution, Add color samples on triangle.

Mesh Color Properties No mapping No discontinuities (no seams) Guaranteed one-to-one correspondence Correct MIP-map filtering Local resolution adjustment Permits model editing and subdivision Compatible with current graphics pipeline

Mesh Color Structure

The 3D surface position of any color sample can be computed using barycentric coordinates based on the index of the color sample.

[1,0,0]

[0,1,0] [0,0,1]

The barycentric coordinate of Color Sample Cij

Like standard map, mesh colors can be usable in the current graphics pipeline.

Mesh Color Structure

• Colors are shared along edges - Guaranteed continuity

Mesh Color Structure

• Color sample density can be concentrated on areas with hight detail - achieving maximum texture detail with minimal memory consumption

Non-uniform Face Resolution

Mesh Color Structure

• Color sample density can be concentrated on areas with hight detail - achieving maximum texture detail with minimal memory consumption

Non-uniform Face Resolution Shared Edge

Editting Mesh Color Geometry

• Mesh colors can easily support most other mesh editing operations without the need for resampling.

Other Mesh

• Quad Mesh can use bilinear coordinates.

triangulate the polygonposition sample use bilinear interpolation

How to project to screen pixel?

Nearest Filtering

Find the nearest triangle, and use the barycentric coordinates to interpolate the color of the red point.

Nearest Filtering

Interpolation with weight from the points of the triangle

Nearest Filtering

Linear Filtering

• Staircase artifacts of nearest-filtering can be hidden by linear filtering.

Nearest filtering Linear filtering

blending

Mip-map FilteringMIP-map filtering

R=8 R=4 R=2 R=1

Face & Edge Vertex

FilteringStaircase artifact

Under sampling artifact

blurring

Filtering

• Correct Filtering - Mesh Colors result is the same as 2D Texture

Experiment Result

Experiment Result

Experiment Result

Memory Efficient

Experiment Result

Performance

Fast

under Hardware support

Discussion

• Periodic texture tiling is not supported.• If discontinuities is desired, mesh color can’t

support.• Non-equal edge – result isn’t good

Use polygon meshUse subdivide Non-equal edge

Conclusion

1. Easy to use2. Easy to implement3. High quality4. High performance5. Mesh Colors are ideally suited for

– 3D painting– Storing precomputed data

• Ambient occlusion

6. Mesh Colors provide a solution to the fundamental problems of texture mapping.

Reference

• [1] L´E VY, B., AND MALLET, J.-L. 1998. Non-distorted texture mapping for sheared triangulated meshes. In Proceedings of SIGGRAPH’98, 343–352.

• [2] BENNIS, C., V´EZIEN, J.-M., AND IGL´ESIAS, G. 1991. Piecewise surface flattening for non-distorted texture mapping. Proc. SIGGRAPH ’91, ACM SIGGRAPH Comp. Graph. 25, 4, 237–246.