1 / 25

Smooth Geometry Images

Smooth Geometry Images. Frank Losasso, Hugues Hoppe, Scott Schaefer, Joe Warren. Overview. Provide a simple representation using a single uniform bi-cubic B-spline. Multiple Patches. Single Patch. Geometry Images. [Gu et al 2002]. Sample arbitrary surface using a regular 2D grid

madeleinej
Download Presentation

Smooth Geometry Images

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Smooth Geometry Images Frank Losasso, Hugues Hoppe, Scott Schaefer, Joe Warren

  2. Overview • Provide a simple representation using a single uniform bi-cubic B-spline Multiple Patches Single Patch

  3. Geometry Images [Gu et al 2002] • Sample arbitrary surface using a regular 2D grid • Connectivity is implicit

  4. [Gu et al 2002] cut parametrize

  5. [Gu et al 2002] cut sample

  6. [Gu et al 2002] cut store render [r,g,b] = [x,y,z]

  7. General cut [Gu et al 2002] • Supports surfaces of arbitrary genus • But, boundary has complicated topology – requires sideband a a’ a’ a

  8. Our Approach: X-Cut • Special type of cut curve • Make a X-cut centered at x • Unfold domain into a square image • Creates simple boundary symmetries

  9. The X-Cut

  10. Spherical Remeshing mesh M sphere S domain D image I [Praun and Hoppe 2003] demo

  11. How To Obtain Control Points • B-spline is approximating should not directly sample surface • Instead, use least-squares fitting: 

  12. How To Obtain Smoothness • Application of boundary rules • Pad image to recreate 1-ring around all vertices

  13. Add a simple linear constraint C1 How To Obtain Smoothness • All vertices regular, except boundary midpoints generally not C1

  14. Bi-cubic Subdivision on GPU 4 operators, stored as fragment programs limit bilinearsubdivision meshaveraging tangent repeat

  15. 4 operators, stored as fragment programs Bi-cubic Subdivision on GPU limit bilinearsubdivision meshaveraging tangent repeat

  16. Rendering • “Interpret as vertex array” (OpenGL extension) • Render using triangles

  17. … … … Subsampled Subdivided Discrete Subdivision Levels • Both sub-sampling and subdivision are easily implemented (2k+1) x (2k+1) Original Image

  18. Continuous Subdivision Levels • Prevent ‘popping’ when changing subdivision levels gk gk+1

  19. Continuous Subdivision Levels • Prevent ‘popping’ when changing subdivision levels linearsubdivision 1- +  gk+ bilinearsubdivision meshaveraging gk gk+1

  20. Real-Time Demo

  21. Displacement Mapping simulation CPU GPU 33x33 GPU scalardisplacementmap 257x257

  22. Performance Results

  23. Drawbacks and Limitations • Genus cannot be >0 • Surface rippling

  24. Summary • Closed smooth surface using single patch • Stored as geometry image • Simple and efficient GPU evaluation • Continuous level-of-detail • Displacement mapping 5x5 9x9

  25. Eye candy 65x65 65x65 33x33

More Related