155 research outputs found

    Polynomial cubic splines with tension properties

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    In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems

    Geometric properties and algorithms for rational q-BĂ©zier curves and surfaces

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    In this paper, properties and algorithms of q-BĂ©zier curves and surfaces are analyzed. It is proven that the only q-BĂ©zier and rational q-BĂ©zier curves satisfying the boundary tangent property are the BĂ©zier and rational BĂ©zier curves, respectively. Evaluation algorithms formed by steps in barycentric form for rational q-BĂ©zier curves and surfaces are provided

    Approximating tensor product BĂ©zier surfaces with tangent plane continuity

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    AbstractWe present a simple method for degree reduction of tensor product BĂ©zier surfaces with tangent plane continuity in L2-norm. Continuity constraints at the four corners of surfaces are considered, so that the boundary curves preserve endpoints continuity of any order α. We obtain matrix representations for the control points of the degree reduced surfaces by the least-squares method. A simple optimization scheme that minimizes the perturbations of some related control points is proposed, and the surface patches after adjustment are C∞ continuous in the interior and G1 continuous at the common boundaries. We show that this scheme is applicable to surface patches defined on chessboard-like domains

    Proximity Queries for Absolutely Continuous Parametric Curves

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    In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is generally non-convex and serves as a significant computational bottleneck for motion planning algorithms. In this paper, we present methods for a general class of absolutely continuous parametric curves to compute: (i) the minimum separating distance, (ii) tolerance verification, and (iii) collision detection. Our methods efficiently compute bounds on obstacle proximity by bounding the curve in a convex region. This bound is based on an upper bound on the curve arc length that can be expressed in closed form for a useful class of parametric curves including curves with trigonometric or polynomial bases. We demonstrate the computational efficiency and accuracy of our approach through numerical simulations of several proximity problems.Comment: Proceedings of Robotics: Science and System

    Algorithms for curve design and accurate computations with totally positive matrices

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    Esta tesis doctoral se enmarca dentro de la teoría de la Positividad Total. Las matrices totalmente positivas han aparecido en aplicaciones de campos tan diversos como la Teoría de la Aproximación, la Biología, la Economía, la Combinatoria, la Estadística, las Ecuaciones Diferenciales, la Mecånica, el Diseño Geométrico Asistido por Ordenador o el Álgebra Numérica Lineal. En esta tesis nos centraremos en dos de los campos que estån relacionados con matrices totalmente positivas.This doctoral thesis is framed within the theory of Total Positivity. Totally positive matrices have appeared in applications from fields as diverse as Approximation Theory, Biology, Economics, Combinatorics, Statistics, Differential Equations, Mechanics, Computer Aided Geometric Design or Linear Numerical Algebra. In this thesis, we will focus on two of the fields that are related to totally positive matrices.<br /

    BĂ©zier Method For Image Processing

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    This project concerns about BĂ©zier method in Computer Aided GeometricDesign (CAGD) involving BĂ©zier Curve and BĂ©zier Surface which widely related to the other theorem and method. The aim of this project is to introduce the basic of BĂ©zier method and then generate the BĂ©zier curves, BĂ©zier surfaces, theory and properties and develop BĂ©zier method in image processing application specifically image compression by using MATLAB
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