Abstract
The computation of the minimum distance between a point and a planar implicit curve is a very important problem in geometric modeling and graphics. An integrated hybrid second order algorithm to facilitate the computation is presented. The proofs indicate that the convergence of the algorithm is independent of the initial value and demonstrate that its convergence order is up to two. Some numerical examples further confirm that the algorithm is more robust and efficient than the existing methods.
Highlights
Due to its great properties, the implicit curve has many applications
This paper investigates the problem related to a point projection onto a planar implicit curve
The integrated hybrid second order algorithm is proposed, which is composed of two sub-algorithms
Summary
Due to its great properties, the implicit curve has many applications. Using approximate distance tests to replace the Euclidean distance test, a practical rendering algorithm is proposed to rasterize algebraic curves in [2]. Employing the idea that field functions can be combined both on their values and gradients, a set of binary composition operators is developed to tackle four major problems in constructive modeling in [3]. As a powerful tool for implicit shape modeling, a new type of bivariate spline function is applied in [4], and it can be created from any given set of 2D polygons that divides the 2D plane into any required degree of smoothness. The spline basis functions created by the proposed procedure are piecewise polynomials and explicit in an analytical form
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