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## Modeling with Cubic A-Patches (1995)

Citations: | 68 - 37 self |

### Citations

1142 |
Curves and surfaces for computer aided geometric design
- Farin
- 2002
(Show Context)
Citation Context ...four dimensional vectors with nonnegative integer components. The following basic facts about the BB form will be used in this paper. The first is derived from the directional derivative formulas(see =-=[Far90]-=-). Lemma 2.1. If f(p) = P jj=n bsB ns(ff), then b (n\Gamma1)e i +e j = b ne i + 1 n (p j \Gamma p i ) T rf(p i ); j = 1; 2; 3; 4; j 6= i (2.2) where rf(p) = [ @f(p) @x @f(p) @y @f(p) @z ] T : Formula ... |

72 |
Finite Element Stiffness Matrices for Analysis of Plate Bending,"
- Clough, Tocher
- 1967
(Show Context)
Citation Context ...m. We too use the simplicial hull approach in this paper but enumerate the exceptional situations and provide some heuristic strategies for rectifying them. In [Guo91b], Guo uses a Clough-Tocher split=-=[CT65] and subdi-=-vides each face tetrahedron of the simplicial hull, hence utilizing three patches per face of T . In this paper, we consider the computed "normals" at the given data points, and distinguish ... |

27 |
Smooth piecewise quadratic surfaces
- Dahmen
- 1989
(Show Context)
Citation Context ...es to form a C 1 smooth surface interpolating scattered data points and respecting the topology of a given surface triangulationsT of the points. For this problem, prior approaches have been given by =-=[Dah89]-=- using quadric patches, [DTS93, Guo91a, Guo91b] using cubic patches and [BI92] using quintic for convex triangulations and degree seven patches for arbitrary surface triangulations T . All these paper... |

23 |
Cubicoids: modeling and visualization
- Dahmen, Thamm-Schaar
- 1993
(Show Context)
Citation Context ...eted and singularity problems of implicit patches. In this paper our cubic A-patches are guaranteed to be nonsingular and single sheeted within each tetrahedron. 2 While the details of the methods of =-=[DTS93]-=- and [Guo91b] differ somewhat, they both use the scheme of [Dah89] of building a surrounding simplicial hull (consisting of a series of tetrahedra) of the given triangulation T . Such a simplicial hul... |

22 | Surface Fitting with Implicit Algebraic Surface Patches" Tories in Surface Modeling, edited by H - Bajaj - 1992 |

22 | The Emergence of Algebraic Curves and Surfaces in Geometric Design. In - Bajaj - 1993 |

21 |
Ci Smoothing of Polyhedra with Implicit Algebraic Splines", Compuler Graphics(Siggraph92),26,79-88
- Bajaj, Ihm
(Show Context)
Citation Context ...ing the topology of a given surface triangulationsT of the points. For this problem, prior approaches have been given by [Dah89] using quadric patches, [DTS93, Guo91a, Guo91b] using cubic patches and =-=[BI92]-=- using quintic for convex triangulations and degree seven patches for arbitrary surface triangulations T . All these papers provide heuristics to overcome the multiple sheeted and singularity problems... |

16 | Surface generation using implicit cubics - Guo - 1991 |

1 | C’ smoothing of polyhedra with implicit algebraic splines - J, ANDIHM - 1992 |

1 | Smooth low degree approximations of arbitrary polyhedra - BAJAJ, CHEN, et al. - 1994 |

1 | 1995. with Cubic A-Patches - IIM |

1 | Approximation of dense scattered data using algebraic surfaces - thesis - 1991 |

1 | Minimum curvature veriation curves networks and surface for fair free form shape design - x - 1993 |

1 | Local smooth surface interpolation: A classification - Ptirtttw - 1990 |

1 | Interpolation on surfaces using minimum norm networks - RYITMAXN - 1992 |

1 | Piecewise algebraic surface patches - SIFR - 1985 |

1 | Algebraic Curtw.s - JWR - 1978 |