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93
Adaptive Parametrization of Multivariate Bsplines for Image Registration
"... We present an adaptive parametrization scheme for dynamic mesh refinement in the application of parametric image registration. The scheme is based on a refinement measure ensuring that the control points give an efficient representation of the warp fields, in terms of minimizing the registration cos ..."
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cost function. In the current work we introduce multivariate Bsplines as a novel alternative to the widely used tensor Bsplines enabling us to make efficient use of the derived measure. The multivariate Bsplines of order n are C n−1 smooth and are based on Delaunay configurations of arbitrary 2D
Geometric Modelling With Multivariate BSplines
, 1986
"... The tensor product Bspline surface, while regarded as a powerful boundary representation for computer aided geometric design (CAGD), still suffers restrictions because of its inherent rectangular nature. One manifestation of this problem is the difficulty of modelling nonrectangular regions. The ne ..."
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. The need for three, five, and sixsided regions often arises naturally in CAGD. In recent years, the theory of univariate Bsplines has been extended to multidimensional spaces. These multivariate splines provide generalizations of the univariate spline that preserve desirable features while providing more
Multivariate Bsplines with (almost) arbitrary knots
, 1993
"... Abstract. The multivariate B–spline scheme, due to Dahmen, Micchelli and Seidel [1] imposes some restrictions on the knots which have to be placed such that certain regions have a nonempty interior. Here it will be shown that these conditions can be almost completely dropped without losing the abil ..."
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Abstract. The multivariate B–spline scheme, due to Dahmen, Micchelli and Seidel [1] imposes some restrictions on the knots which have to be placed such that certain regions have a nonempty interior. Here it will be shown that these conditions can be almost completely dropped without losing
Modelling Robot Manipulators with Multivariate Bsplines.
, 1998
"... In programming robot manipulators to carry out a wide variety of tasks it would be desirable to create a cad system in which these tasks can be programmed at the task level, leaving the finegrained detail of path planning and collision detection to the system. This paper describes the theoretical b ..."
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background to such a system, by providing a model in which robot motions are represented using multivariate Bsplines, a standard representation for freeform shapes in the cad environment. The paper also describes algorithms which take this representation and apply it to collision detection and path
On the evaluation of box splines
"... The first (and for some still the only) multivariate Bspline is what today one would call the simplex spline, since it is derived from a simplex, and in distinction to other polyhedral splines, such as the cone spline and the box spline. The simplex spline was first talked about in 1976. However, i ..."
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Cited by 201 (8 self)
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The first (and for some still the only) multivariate Bspline is what today one would call the simplex spline, since it is derived from a simplex, and in distinction to other polyhedral splines, such as the cone spline and the box spline. The simplex spline was first talked about in 1976. However
An Algorithm for Direct Multiplication of Bsplines
"... Bspline multiplication, that is, finding the coefficients of the product Bspline of two given Bsplines is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on Bsplines. Algorithms for Bspline multiplication standardl ..."
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surfaces, or any two general multivariate Bsplines. Note to Practitioners: Geometric kernels in commercial CAD systems typically use Bsplines to represent smooth curves and surfaces. Geometric inquiry (such as curvature) on such curves and surfaces requires the fundamental mathematical operation
Multivariate complex Bsplines, Dirichlet . . .
, 2009
"... For the Schoenberg Bsplines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the Bsplines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representati ..."
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Cited by 5 (2 self)
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For the Schoenberg Bsplines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the Bsplines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain
An Implementation of Triangular BSpline Surfaces over Arbitrary Triangulations
, 1993
"... . A new multivariate Bspline scheme based on blending functions and control vertices has recently been developed by Dahmen, Micchelli, and Seidel [4]. This surface scheme allows to model piecewise polynomial surfaces of degree k over arbitrary triangulations, such that the resulting surfaces are C ..."
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Cited by 21 (2 self)
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. A new multivariate Bspline scheme based on blending functions and control vertices has recently been developed by Dahmen, Micchelli, and Seidel [4]. This surface scheme allows to model piecewise polynomial surfaces of degree k over arbitrary triangulations, such that the resulting surfaces are C
Bsplines and quasiinterpolants
, 2012
"... We present the construction of a multivariate normalized Bspline basis for the quadratic C 1continuous spline space defined over a triangulation in R s (s ≥ 1) with a generalized PowellSabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of u ..."
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We present the construction of a multivariate normalized Bspline basis for the quadratic C 1continuous spline space defined over a triangulation in R s (s ≥ 1) with a generalized PowellSabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition
CONSTRUCTING EXPLICIT BSPLINE
"... Abstract. We introduce here a direct method to construct multivariate explicit Bspline bases. Bsplines are piecewise polynomials, which are defined on adjacent tetrahedra and which are Cr continuous throughout. The Cr continuity is enforced by making sure that all directional derivatives of order ..."
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Abstract. We introduce here a direct method to construct multivariate explicit Bspline bases. Bsplines are piecewise polynomials, which are defined on adjacent tetrahedra and which are Cr continuous throughout. The Cr continuity is enforced by making sure that all directional derivatives
Results 1  10
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93