Abstract
We introduce new techniques for modelling with interpolating implicit surfaces. This form of implicit surface was first used for problems of surface reconstruction and shape transformation, but the emphasis of our work is on model creation. These implicit surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is created from these constraints using a variational scattered data interpolation approach, and the iso-surface of this function describes a surface. Like other implicit surface descriptions, these surfaces can be used for CSG and interference detection, may be interactively manipulated, are readily approximated by polygonal tilings, and are easy to ray trace. A key strength for model creation is that interpolating implicit surfaces allow the direct specification of both the location of points on the surface and the surface normals. These are two important manipulation techniques that are difficult to achieve using other implicit surface representations such as sums of spherical or ellipsoidal Gaussian functions ("blobbies"). We show that these properties make this form of implicit surface particularly attractive for interactive sculpting using the particle sampling technique introduced by Witkin and Heckbert. Our formulation also yields a simple method for converting a polygonal model to a smooth implicit model, as well as a new way to form blends between objects.
- Bittar, E., Tsingos, N., and Gascuel, M.-P. 1995. Automatic reconstruction of unstructured 3D data: Combining a medial axis and implicit surfaces. Computer Graphics Forum (Proceedings of Eurographics '95) 14, 3, 457--468.Google Scholar
- Blinn, J. F. 1982. A generalization of algebraic surface drawing. ACM Trans. Graph. 1, 3, 235--256. Google Scholar
- Bloomenthal, J. 1988. Polygonization of implicit surfaces. Computer-Aided Geometric Design 5, 4, 341--355. Google Scholar
- Bloomenthal, J. 1994. An implicit surface polygonizer. In Graphics Gems IV, P. S. Heckbert, Ed. Academic Press, Cambridge, 324--349. Google Scholar
- Bloomenthal, J. 1997. Introduction to Implicit Surfaces. Morgan Kaufmann Publishers, Inc., San Francisco, CA. Google Scholar
- Carr, J. C., Mitchell, T. J., Beatson, R. K., Cherrie, J. B., Fright, W. R., McCallum, B. C., and Evans, T. R. 2001. Reconstruction and representation of 3d objects with radial basis functions. Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 2001), 67--76. Google Scholar
- Celniker, G. and Gossard, D. 1991. Deformable curve and surface finite-elements for free-form shape design. Computer Graphics (SIGGRAPH 91) 25, 4 (July), 257--266. Google Scholar
- Duchon, J. 1977. Spline minimizing rotation-invariant semi-norms in Sobolev spaces. In Constructive Theory of Functions on Several Variables, Lecture Notes in Mathematics 571, W. Schempp and K. Zeller, Eds. Springer-Verlag, Berlin.Google Scholar
- Duff, T. 1992. Interval arithmetic and recursive subdivision for implicit functions and constructive solid geometry. Computer Graphics (SIGGRAPH 92) 26, 2 (July), 154--168. Google Scholar
- Dyn, N. 1987. Interpolation of scattered data by radial basis functions. In Topics in Multivariate Approximation, L. L. S. C. K. Chui and F. I. Utreras, Eds. Academic Press, Cambridge, 47--61.Google Scholar
- Girosi, F., Jones, M., and Poggio, T. 1993. Priors, stabilizers and basis functions: from regularization to radial, tensor and additive splines. Tech. rep., MIT Artificial Intelligence Laboratory. June. A.I. Memo No. 1430. Google Scholar
- Grimson, W. E. L. 1983. Surface consistancy constraints in vision. Computer Vision, Graphics, and Image Processing 24, 1 (Oct.), 28--51.Google Scholar
- Hart, J. 1993. Ray tracing implicit surfaces. Siggraph 93 Course Notes: Design, Visualization and Animation of Implicit Surfaces, 1--16.Google Scholar
- Hart, J. 1997. Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer 12, 10, 527--545.Google Scholar
- Kalra, D. and Barr, A. 1989. Guarenteed ray intersection with implicit surfaces. Computer Graphics (SIGGRAPH 89) 23, 4, 297--306. Google Scholar
- Keren, D. and Gotsman, C. 1998. Tight fitting of convex polyhedral shapes. Int. J. Shape Modeling, 111--126.Google Scholar
- Lorensen, W. and Cline, H. E. 1987. Marching cubes: A high resolution 3-D surface construction algorithm. Computer Graphics (SIGGRAPH 87) 21, 4 (July), 163--169. Google Scholar
- Miraki, S. 1991. Volumetric shape description of range data using 'blobby model'. Computer Graphics (SIGGRAPH 91) 25, 4 (July), 227--235. Google Scholar
- Morse, B., Yoo, T. S., Rheingans, P., Chen, D. T., and Subramanian, K. 2001. Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. Shape Modelling International, 89--98. Google Scholar
- Nishimura, H., Hirai, M., Kawai, T., Kawata, T., Shirkawa, I., and Omura, K. 1985. Object modeling by distribution function and a method of image generation. Trans. Inst. Elect. Commun. Eng. Japan J68-D, 4, 718--725.Google Scholar
- Pedersen, H. 1995. Decorating implicit surfaces. Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 95), 291--300. Google Scholar
- Pedersen, H. 1996. A framework for interactive texturing on curved surfaces. Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 96), 295--302. Google Scholar
- Roth, S. 1982. Ray casting as a method for solid modeling. Computer Graphics and Image Processing 18, 2, 109--144.Google Scholar
- Savchenko, V. V., Pasko, A. A., Okunev, O. G., and Kunni, T. L. 1995. Function representation of solids reconstructed from scattered surface points and contours. Computer Graphics Forum 14, 4 (Oct.), 181--188.Google Scholar
- Snyder, J. 1992. Interval analysis for computer graphics. Computer Graphics (SIGGRAPH 92) 26, 2 (July), 121--130. Google Scholar
- Stander, B. T. and Hart, J. C. 1997. Guaranteeing the topology of an implicit surface polygonization for interactive modeling. Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 97), 279--286. Google Scholar
- Szeliski, R. 1990. Fast surface interpolation using hierarchical basis functions. IEEE Trans. Pattern Anal. Mach. Intell. 12, 6 (June), 513--528. Google Scholar
- Taubin, G. 1993. An improved algorithm for algebraic curve and surface fitting. In Fourth International Conference on Computer Vision (ICCV '93). IEEE, Berlin, Germany, 658--665.Google Scholar
- Terzopoulos, D. 1988. The computation of visible-surface representations. IEEE Trans. Pattern Anal. Mach. Intell. 10, 4 (July), 417--438. Google Scholar
- Turk, G. and O'Brien, J. 1999. Shape transformation using variational implicit functions. Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 1999), 335--342. Google Scholar
- Welch, W. and Witkin, A. 1994. Free-form shape design using triangulated surfaces. Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 94), 247--256. Google Scholar
- Witkin, A. P. and Heckbert, P. S. 1994. Using particles to sample and control implicit surfaces. Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 94), 269--278. Google Scholar
- Wyvill, G., McPheeters, C., and Wyvill, B. 1986. Data structures for soft objects. The Visual Computer 2, 4, 227--234.Google Scholar
Index Terms
- Modelling with implicit surfaces that interpolate
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