A trigonometric curve is a real plane curve where each coordinate is given parametri-cally by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can be also represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric repre...

An algorithm is presented to approximate planar ooset curves within an arbitrary tolerance > 0. Given a planar parametric curve C(t) and an ooset radius r, the circle of radius r is rst approximated by piecewise quadratic B ezier curve segments within the tolerance. The exact ooset curve C r (t) is then approximated by the convolution of C(t) with the quadratic B ezier curve segments. For a pol...

An algorithm for surface reconstruction from a polyhedron with arbitrary topology consisting of triangular faces is presented. The rst variant of the algorithm constructs a curve network consisting of cubic B ezier curves meeting with tangent plane continuity at the vertices. This curve network is extended to a smooth surface by replacing each of the networks facets with a split patch consistin...

Due to some important properties of B ezier splines, they have great potential use in computer-aided mammogram diagnosis. In this paper, B ezier splines are applied in both lesion detection and characterization processes, where lesion detection is achieved by segmentation using a natural threshold computed from B ezier smoothed histogram; and lesion characterization is achieved by measuring the...

Computing the intersection of parametric and algebraic curves and surfaces is a fun damental problem in computer graphics and geometric modeling This problem has been extensively studied in the literature and di erent techniques based on subdivision interval analysis and algebraic formulation are known For low degree curves and surfaces algebraic methods are considered to be the fastest whereas...

A piecewise quintic G spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular B ezier representation, is a ne invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G continuously around a common vertex is solved by constructi...

In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data points. A maximum error has been determined to preserve the absolute fitting error less than a criterion and it administers the process of curv...

Given a nite curvilinear simplicial complex in R3, made up of properlyjoined parametric patches de ned in terms of control points, it is of interest to know under what conditions the complex will retain its original topological form when the control points are perturbed. For example, the patches might be triangular B ezier surface patches, and the complex may represent the boundary of a solid i...

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We develop a spectrum of physical A-spline curve models using various energy formulations based on the theory of elasticity. Our bending and stretching energy formulations yield interactive physically based modeling with A-splines while preserving the advantages of free-form modeling of complex shapes. ...

In this paper we discuss a natural way to deene barycentric coordinates on general sphere-like surfaces. This leads to a theory of Bernstein-B ezier polynomials which parallels the familiar planar case. Our constructions are based on a study of homogeneous polynomials on trihedra in IR 3. The special case of Bernstein-B ezier polynomials on a sphere is considered in detail.