Algorithm 783: Pcp2Nurb -- smooth free-form surfacing with linearly trimmed bicubic B-splines Unrestricted control polyhedra facilitate modeling free-form surfaces of arbitrary topology and local patch-layout by allowing n-sided, possibly nonplanar, facets and m-valent vertices. By cutting off edges and corners, the smoothing of an unrestricted control polyhedron can be reduced to the smoothing of a planar-cut polyhedron. A planar-cut polyhedron is a generalization of the well-known tensor-product control structure. The routine Pcp2Nurb in turn translates planar-cut polyhedra to a collection of four-sided linearly trimmed bicubic B-splines and untrimmed biquadratic B-splines. The routine can thus serve as central building block for overcoming topological constraints in the mathematical modeling of smooth surfaces that are stored, transmitted, and rendered using only the standard representation in industry. Specifically, on input of a nine-point subnet of a planar-cut polyhedron, the routine outputs a trimmed bicubic NURBS patch. If the subnet does not have geometrically redundant edges, this patch joins smoothly with patches from adjacent subnets as a four-sided piece of a regular C 1 surface. The patch integrates smoothly with untrimmed biquadratic tensor-product surfaces derived from subnets with tensor-product structure. Sharp features can be retained in this representation by using geometrically redundant edges in the planar-cut polyhedron. The resulting surface follows the outlines of the planar-cut polyhedron in the manner traditional tensor-product splines follow the outline of their rectilinear control polyhedron. In particular, it stays in the local convex hull of the planar-cut polyhedron. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Duczek, Sascha; Gabbert, Ulrich: Efficient integration method for fictitious domain approaches (2015)
  2. Chen, Wenyu; Zheng, Jianmin; Cai, Yiyu: Monge mapping using hierarchical NURBS (2010)
  3. Sauvage, Basile; Hahmann, Stefanie; Bonneau, Georges-Pierre; Elber, Gershon: Detail preserving deformation of B-spline surfaces with volume constraint (2008)
  4. Cheutet, Vincent; Daniel, Marc; Hahmann, Stefanie; La Greca, Raphael; Leon, Jean-Claude; Maculet, Robert; Menegaux, David; Sauvage, Basile: Constraint modeling for curves and surfaces in CAGD: a survey (2007)
  5. Tonon, Fulvio: Analytical formulas for the geometric and inertia quantities of the largest removable blocks around tunnels (2007)
  6. Kim, Jinwook; Kim, Soojae; Ko, Heedong; Terzopoulos, Demetri: Fast GPU computation of the mass properties of a general shape and its application to buoyancy simulation (2006)
  7. Stefanus, L.Yohanes: Shape representations with blossoms and buds (2006)
  8. Elber, Gershon: Global curve analysis via a dimensionality lifting scheme (2005)
  9. Janardan, Ravi (ed.); Smid, Michiel (ed.); Dutta, Debasish (ed.): Geometric and algorithmic aspects of computer-aided design and manufacturing. DIMACS workshop computer aided design and manufacturing, October 7--9, 2003, Piscataway, New Jersey. (2005)
  10. Li, Xueqing; Wang, Wenping; Martin, Ralph R.; Bowyer, Adrian: Using low-discrepancy sequences and the Crofton formula to compute surface areas of geometric models (2003)
  11. Biermann, Henning; Martin, Ioana M.; Zorin, Denis; Bernardini, Fausto: Sharp features on multiresolution subdivision surfaces. (2002)
  12. Soldea, Octavian; Elber, Gershon; Rivlin, Ehud: Exact and efficient computation of moments of free-form surface and trivariate based geometry (2002)
  13. Hirota, G.; Maheshwari, R.; Lin, M.C.: Fast volume-preserving free-form deformation using multi-level optimization (2000)
  14. Peters, Jörg: Algorithm 783: Pcp2Nurb -- smooth free-form surfacing with linearly trimmed bicubic B-splines (1998)