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Toric surface patches
, 2002
"... We define a toric surface patch associated with a convex polygon, which has vertices with integer coordinates. This rational surface patch naturally generalizes classical Bézier surfaces. Several features of toric patches are considered: affine invariance, convex hull property, boundary curves, impl ..."
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Cited by 11 (2 self)
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We define a toric surface patch associated with a convex polygon, which has vertices with integer coordinates. This rational surface patch naturally generalizes classical Bézier surfaces. Several features of toric patches are considered: affine invariance, convex hull property, boundary curves
Implicit Surface Patches
, 1997
"... Contents 1 Introduction 2 2 Mathematical Preliminaries 2 3 Curvlinear Mesh Scheme 5 4 Simplex and Box Based Schemes 7 4.1 Smooth Interpolation of a Polyhedron with C 1 Apatches : : : : : : : : : : : : : : : : : 7 4.2 Smooth Interpolation with C 2 Apatches : : : : : : : : : : : : : : : : : : ..."
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Cited by 8 (5 self)
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: : : : : : : : : : : : : : : : : : : : : : : : : : : 12 4.3 Smooth Reconstruction of Surfaces and FunctionsonSurfaces from Scattered Data : : : 12 5 Subdivision Based Schemes 15 6 Conclusion 20 B1: APatches 2 1 Introduction While it is possible to model a general closed surface of arbitrary genus as a single implicit surface patch, the geometry
On Degenerate Surface Patches
, 1992
"... A local construction of a GC 1 interpolating surface to given scattered data in R 3 can give rise to degenerate BernsteinB'ezier patches. That means the parametrization at vertices is not regular in the sense that the length of the tangent vector to any curve passing through a vertex is z ..."
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Cited by 1 (1 self)
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A local construction of a GC 1 interpolating surface to given scattered data in R 3 can give rise to degenerate BernsteinB'ezier patches. That means the parametrization at vertices is not regular in the sense that the length of the tangent vector to any curve passing through a vertex
Intersecting biquadratic Bézier surface patches
 IN BERT JUETLLER AND RAGNI PIENE, EDITORS, COMPUTATIONAL METHODS FOR ALGEBRAIC SPLINE SURFACES
, 2007
"... We present three symbolic–numeric techniques for computing the intersection and self–intersection curve(s) of two Bézier surface patches of bidegree (2,2). In particular, we discuss algorithms, implementation, illustrative examples and provide a comparison of the methods. ..."
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Cited by 1 (0 self)
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We present three symbolic–numeric techniques for computing the intersection and self–intersection curve(s) of two Bézier surface patches of bidegree (2,2). In particular, we discuss algorithms, implementation, illustrative examples and provide a comparison of the methods.
LINEAR PRECISION FOR TORIC SURFACE PATCHES
, 2008
"... We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification also includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the wellknow ..."
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Cited by 2 (1 self)
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We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification also includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well
Uniform Coverage of Automotive Surface Patches
 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2005; 24; 883
, 2005
"... In spray painting applications, it is essential to generate a spray gun trajectory such that the entire surface is completely covered and receives an acceptably uniform layer of paint deposition; we call this the “uniform coverage” problem. The uniform coverage problem is challenging because the ato ..."
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Cited by 11 (0 self)
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the atomizer emits a nontrivial paint distribution, thus making the relationships between the spray gun trajectory and the deposition uniformity complex. To understand the key issues involved in uniform coverage, we consider surface patches that are geodesically convex and topologically simple
Planning Paths for a Flexible Surface Patch
 Proc. IEEE Int. Conf. on Robotics and Automation
, 1998
"... This paper presents a probabilistic planner capable of finding paths for a flexible surface patch. The planner is based on the Probabilistic Roadmap approach to path planning while the surface patch is modeled as a low degree Bézier surface. We assume that we are dealing with an elastic part and def ..."
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Cited by 38 (6 self)
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This paper presents a probabilistic planner capable of finding paths for a flexible surface patch. The planner is based on the Probabilistic Roadmap approach to path planning while the surface patch is modeled as a low degree Bézier surface. We assume that we are dealing with an elastic part
On the existence of biharmonic tensor–product Bézier surface patches
, 2006
"... A tensor–product Bézier surface patch x of degree (m, n) is called biharmonic if it satisfies ∆²x = 0. As shown by Monterde and Ugail (2004), these surface patches are fully determined by their four boundaries. In this note we derive necessary conditions for their existence. ..."
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A tensor–product Bézier surface patch x of degree (m, n) is called biharmonic if it satisfies ∆²x = 0. As shown by Monterde and Ugail (2004), these surface patches are fully determined by their four boundaries. In this note we derive necessary conditions for their existence.
Freeform deformation of solid geometric models
 IN PROC. SIGGRAPH 86
, 1986
"... A technique is presented for deforming solid geometric models in a freeform manner. The technique can be used with any solid modeling system, such as CSG or Brep. It can deform surface primitives of any type or degree: planes, quadrics, parametric surface patches, or implicitly defined surfaces, f ..."
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Cited by 701 (1 self)
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A technique is presented for deforming solid geometric models in a freeform manner. The technique can be used with any solid modeling system, such as CSG or Brep. It can deform surface primitives of any type or degree: planes, quadrics, parametric surface patches, or implicitly defined surfaces
Parameterization of 3D Surface Patches by Straightest Distances
"... Abstract. In this paper, we introduce a new piecewise linear parameterization of 3D surface patches which provides a basis for texture mapping, morphing, remeshing, and geometry imaging. To lower distortion when flatting a 3D surface patch, we propose a new method to locally calculate straightest di ..."
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Abstract. In this paper, we introduce a new piecewise linear parameterization of 3D surface patches which provides a basis for texture mapping, morphing, remeshing, and geometry imaging. To lower distortion when flatting a 3D surface patch, we propose a new method to locally calculate straightest
Results 1  10
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