Recent progress in acquiring shape from range data permits the acquisition of seamless million-polygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product B-spline surface patches with accompanying displacement maps. This choice of representation yields a coarse but efficient model suitable for animation and a fine but more expensive model suitable for rendering.
The first step in our process consists of interactively painting patch boundaries over a rendering of the mesh. In many applications, interactive placement of patch boundaries is considered part of the creative process and is not amenable to automation. The next step is gridded resampling of each bounded section of the mesh. Our resampling algorithm lays a grid of springs across the polygon mesh, then iterates between relaxing this grid and subdividing it. This grid provides a parameterization for the mesh section, which is initially unparameterized. Finally, we fit a tensor product B-spline surface to the grid. We also output a displacement map for each mesh section, which represents the error between our fitted surface and the spring grid. These displacement maps are images; hence this representation facilitates the use of image processing operators for manipulating the geometric detail of an object. They are also compatible with modern photo-realistic rendering systems.
Our resampling and fitting steps are fast enough to surface a million polygon mesh in under 10 minutes - important for an interactive system.
Paper in postscript with low resolution color figures
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Paper in postscript with medium resolution color figures
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Figures from the paper:
JPEG image of figure 5
JPEG image of figure 8
JPEG image of figure 11
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JPEG image of figure 13
The captions for these figures can be found in the paper. You can also read the captions here.
And finally, a more distinct image corresponding to Figure 11d.
After leaving Stanford, Venkat Krishnamurthy co-founded Paraform Technologies with Brian Kissel to commercial the ideas in his dissertation. In 2001, Paraform was awarded a Technical Achievement Award by the Academy of Motion Picture Arts and Sciences for developement of the "Paraform Digital Form Development Software". By then, his software had been used on a number of movies, including "Lake Placid", "The Haunting", "HollowMan", "End of Days", and "Minority Report". As of this writing (2003), Paraform has been bought by Metris International, and his software continues to be sold and used in the entertainment and manufacturing industries.
(This historical note written by Marc Levoy.)