In this paper we present an efficient technique for piecewise cubic Bézier approximation of digitized curve. An adaptive breakpoint detection method divides a digital curve into a number of segments and each segment is approximated by a cubic Bézier curve so that the approximation error is minimized. Initial approximated Bézier control points for each of the segments are obtained by interpolati...

This paper presents an algorithm for optimal multi-degree reduction of rational disk Bézier curve in the L norm. We start by introducing a novel disk rational Bézier based on parallel projection, whose properties are also discussed. Then we transform multi-degree reduction of the error radius curve and the weight curve of the disk rational Bézier curve into solving a constrained quadratic progr...

A geometric interpretation of the diagonal of a tensor-product trivariate Bézier volume using degree elevation of Bézier triangles is given. A brief discussion of the diagonal curve of a tensor-product bivariate Bézier surface will help to motivate our geometric interpretation for the diagonal curve of a Bézier volume. Suppose we have a tensor-product Bézier surface, x(u, v), given by x(u, v) =...

1. An image’s outline cannot be fitted by a single cubic Bézier curve piece if it contains corners. Corners are points In this paper, a new curve-fitting algorithm is presented. This algorithm can automatically fit a set of data points with at which the outline’s directions take a sharp turn, or the piecewise geometrically continuous (G) cubic Bézier curves. outlines have discontinuous tangent ...

This paper presents an accurate and efficient method to solve both point projection and point inversion for NURBS curves and surfaces. We first subdivide the NURBS curve or surface into a set of Bézier subcurves or patches. Based on the relationship between the test point and the control polygon of Bézier curve or the control point net of the Bézier patch, we extract candidate Bézier subcurves ...

We study the problem of identifying those cubic Bézier curves that are close in the L2 norm to planar elastic curves. We identify an easily computable quantity, which we call the λ residual eλ , that accurately predicts a small L2 distance. Using this, we identify geometric criteria on the control polygon that guarantee that a Bézier curve is within 1% of its arc-length to an elastic curve. Fin...

This paper studies the problem of designing a rational Bézier developable surface pencil with a common isogeodesic, and provides an algorithm for the representation of complicated geometric models in industrial applications which need to satisfy that the shape surface can be developed and a given curve is geodesic. By employing the local Frenet orthonormal frame, the explicit expression of the ...

An example is presented of a cubic Bézier curve that is the unknot (a knot with no crossings), but whose control polygon is knotted. It is also shown that there is no upper bound on the number of crossings in the control polygon for an unknotted Bézier curve. These examples complement known upper bounds on the number of subdivisions sufficient for a control polygon to be ambient isotopic to its...

It is frequently important to approximate a rational Bézier curve by an integral, i.e., polynomial one. This need will arise when a rational Bézier curve is produced in one CAD system and is to be imported into another system, which can only handle polynomial curves. The objective of this paper is to present an algorithm to approximate rational Bézier curves with polynomial curves of higher deg...