ABSTRACT
This paper describes a framework for introducing visually smooth surfaces into sketch-based freeform modeling systems. An existing sketch-based freeform modeling system generates rough polygonal meshes with uneven triangulations after each operation. Our approach generates a dense, visually smooth polygonal mesh by beautifying and refining the original rough mesh. A beautification process generates near-equilateral triangles with a near-uniform distribution of vertices to mask the noise and bad sampling of the uneven mesh. The vertices are distributed on a smoothed surface that approximately interpolates the original mesh. Refinement generates a smooth, dense mesh by subdividing the beautified mesh and moving the vertices to the interpolative surface. The smooth interpolative surface is computed via implicit quadratic surfaces that best fit the mesh locally in a least-squares sense.
- M. Desbrun, M. Mayer, P Schröder, and A. H. Barr. Implicit fairing of irregular meshes using diffusion and curvature flow. SIGGRAPH 99 Conference Proceedings, pages 317--324, 1999. Google ScholarDigital Library
- P. Dombrowski. Krümmungsgrößen Gleichungsdefinierter Untermannigfaltigkeiten Riemannscher Mannigfaltigkeiten. Mathematische Nachrichten, vol. 38, pages 133--190. Berlin: Akademie Verlag, 1968.Google Scholar
- H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer, and W. Stuetzle. Piecewise smooth surface reconstruction. SIGGRAPH 1994 Conference Proceedings, pages 295--302, 1994. Google ScholarDigital Library
- J. Hughes, Differential Geometry of Implicit Surfaces in 3-Space--a Primer. Technical Report CS-03-05, Computer Science Dept., Brown University, 2003.Google Scholar
- T. Igarashi, S. Matsuoka, and H. Tanaka. Teddy: a sketching interface for 3D freeform design. SIGGRAPH 99 Conference Proceedings, pages 409--416, 1999. Google ScholarDigital Library
- L. Kobbelt. Discrete fairing and variational subdivision for freeform surface design. The Visual Computer, Vol. 16, Issue 3/4, pages 142--158, 2000.Google Scholar
- L. Kobbelt, T. Bareuther, H. P. Seidel. Multiresolution shape deformations for meshes with dynamic vertex connectivity, Computer Graphics Forum, Vol. 19, No 3, pages 249--260, 2000.Google ScholarCross Ref
- D. Levin. Mesh-independent surface interpolation. To appear in Advances in Comp. Math.Google Scholar
- J. Maillot and J. Stam. A unified subdivision scheme for polygonal modeling. Eurographics '01 proceedings, 2001.Google ScholarCross Ref
- S. Mann, C. Loop, M. Lounsbery, D. Meyers, J. Painter, T. DeRose, and K. Sloan. A survey of parametric scattered data fitting using triangular interpolants. In Hans Hagen, editor, Curve and Surface Design, pages 145--172. SIAM, 1992.Google ScholarCross Ref
- L. Markosian, J. M. Cohen, T. Crulli, and J. F. Hughes. Skin: a constructive approach to modeling free-form shapes. SIGGRAPH 99 Conference Proceedings, pages 393--400, 1999. Google ScholarDigital Library
- H. P. Moreton and C. H. Sequin. Functional optimization for fair surface design. SIGGRAPH 92 Conference Proceedings, pages 167--176, 1992. Google ScholarDigital Library
- R. Schneider and L. Kobbelt. Geometric fairing of irregular meshes for free-form surface design. To appear in Computer Aided Geometric Design. Google ScholarDigital Library
- G. Taubin. A signal processing approach to fair surface design. SIGGRAPH 95 Conference Proceedings, pages 351--358, 1995. Google ScholarDigital Library
- G. Taubin. Estimating the tensor of curvature of a surface from a polyhedral approximation. Fifth International Conference on Computer Vision, pages 902--907, 1995. Google ScholarDigital Library
- G. Turk. Re-tiling polygonal surfaces. Computer Graphics, Vol. 26, No. 2, (SIGGRAPH 92), pages 55--64, 1992. Google ScholarDigital Library
- G. Turk and J. F. O'Brien. Variational implicit surfaces. Technical Report GITGVU 9915, Georgia Institute of Technology, May 1999.Google Scholar
- A. Vlachos, J. Peters, C. Boyd, and J. L. Mitchell. Curved PN triangles. Proc. of Interactive 3D Graphics, pages 159--166, 2001. Google ScholarDigital Library
- J. Vorsatz, C. Rossl, L. Kobbelt, and H. Seidel. Feature sensitive remeshing. Eurographics '01 proceedings, pages 393--401, 2001.Google ScholarCross Ref
- D. Zorin, W. Sweldens, and P. Schröder. Interpolating subdivision for meshes of arbitrary topology. SIGGRAPH 96 Conference Proceedings, pages 189--192, 1996. Google ScholarDigital Library
- Smooth meshes for sketch-based freeform modeling
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