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Points on Algebraic Curves and the Parametrization Problem
 In Automated Deduction in
, 1997
"... A plane algebraic curve is given as the zeros of a bivariate polynomial. However, this implicit representation is badly suited for many applications, for instance in computer aided geometric design. What we want in many of these applications is a rational parametrization of an algebraic curve. There ..."
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Cited by 3 (2 self)
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A plane algebraic curve is given as the zeros of a bivariate polynomial. However, this implicit representation is badly suited for many applications, for instance in computer aided geometric design. What we want in many of these applications is a rational parametrization of an algebraic curve
Adaptive Polygonal Approximation of Parametric Curves
"... We present methods for constructing polygonal approximation of parametric curves based on adaptively sampling the parameter domain with respect to curvature. An important feature of these methods is the use of random probing for handling aliasing. We also discuss numerical applications of this me ..."
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We present methods for constructing polygonal approximation of parametric curves based on adaptively sampling the parameter domain with respect to curvature. An important feature of these methods is the use of random probing for handling aliasing. We also discuss numerical applications
Extremal Distance Maintenance for Parametric Curves and Surfaces
 In IEEE International Conference on Robotics and Automation
, 2002
"... A new extremal distance tracking algorithm is presented for parametric curves and surfaces undergoing rigid body motion. The essentially geometric extremization problem is transformed into a dynamical control problem by differentiating with respect to time. Extremization is then solved with the desi ..."
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Cited by 10 (2 self)
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A new extremal distance tracking algorithm is presented for parametric curves and surfaces undergoing rigid body motion. The essentially geometric extremization problem is transformed into a dynamical control problem by differentiating with respect to time. Extremization is then solved
Hierarchical modeling with parametric surfaces
"... We present a hierarchical triangular surface of arbitrary topology and its application to adaptive surface fitting. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent plan ..."
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We present a hierarchical triangular surface of arbitrary topology and its application to adaptive surface fitting. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent
�� � �� � � � Clifford Algebra, Pythagorean Hodograph, and Rational Parametrization of Curves and Surfaces ( �������� � ����� � ���������� � ��������כ�,
, 2004
"... We study the Pythagorean hodograph (PH) curves in the Euclidean or Minkowski spaces of various dimensions in the Clifford algebra framework. After the introductory chapter (Chapter 1) and the preliminaries on the basic setup (Chapter 2), we study, in Chapter 3, the topological selection problem of t ..."
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of the planar quintic Hermite interpolants, culminating in the complete resolution of the problem. In Chapter 4, we continue the study of the Hermite interpolation problem of the space quintic PH curves. This study heavily relies on the Clifford algebra framework within which a complete description
From Edgels to Parametric Curves
 Proc. of the 9 th Scandinavian Conf. on Image Analysis, SCIA'95
, 1995
"... In many applications more than one curve type is needed to explain the edge data reasonably well. In this paper we present a robust algorithm which is designed to work concurrently with different curve types where each curve type selects its own domain of applicability. The major components of o ..."
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Cited by 2 (0 self)
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In many applications more than one curve type is needed to explain the edge data reasonably well. In this paper we present a robust algorithm which is designed to work concurrently with different curve types where each curve type selects its own domain of applicability. The major components
Robust Fitting of Parametric Curves
, 2008
"... We consider the problem of fitting a parametric curve to a given point cloud (e.g., measurement data). Leastsquares approximation, i.e., minimization of the ℓ2 norm of residuals (the Euclidean distances to the data points), is the most common approach. This is due to its computational simplicity [1 ..."
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We consider the problem of fitting a parametric curve to a given point cloud (e.g., measurement data). Leastsquares approximation, i.e., minimization of the ℓ2 norm of residuals (the Euclidean distances to the data points), is the most common approach. This is due to its computational simplicity
Results 11  20
of
192,374