Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the to...

The distance between two objects is an important problem in CAGD, CAD and CG etc. It will be presented in this paper that a simple and quick method to estimate the distance between a point and a Bezier curve on a Bezier surface. Keywords—Geodesic-like curve, distance, projection, Bezier.

The objective of this paper is to study and construct matrix-valued templates for interpolatory curve subdivision. Since our investigation of this problem was motivated by the need of such subdivision stencils as boundary templates for interpolatory surface subdivision, we provide both spline and non-spline templates that are necessarily symmetric, due to the lack of direction-orientation in ca...

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using aC piecewise rational cubic trigonometric spline with fo...

In this paper we present an approximation method for the convolution of two planar curves using a pair of two cubic Bézier curves with linear normals (LN). We characterize the necessary and sufficient conditions for two compatible cubic Bézier LN curves to have the same linear normal map. Using this characterization, we obtain the cubic spline approximation of the convolution curve. As illustra...

When fitting a parametric curve through a sequence of points, it is important in applications that the curve should not exhibit unwanted oscillations. In this paper we take the view that a good curve is one that does not deviate too far from the data polygon: the polygon formed by the data points. From this point of view, we study periodic cubic spline interpolation and derive bounds on the dev...

This paper describes the use of cubic splines for interpolating monotonic data sets. Interpolating cubic splines are popular for 1tting data because they use low-order polynomials and have C continuity, a property that permits them to satisfy a desirable smoothness constraint. Unfortunately, that same constraint often violates another desirable property: monotonicity. It is possible for a set o...

This paper presents a simple matrix form for degree elevation of interval Bezier curve using LegendreBernstein basis transformations. The four fixed Kharitonov's polynomials (four fixed Bezier curves) associated with the original interval Bezier curve are obtained. These four fixed Bezier curves are expressed in terms of the Legendre polynomials. The process of degree elevations r times are app...

.This paper is concerned with the range restricted interpolation of 'data on rectangular grids. The interpolant is constrained to lie on the same side of the constraint surface as the data. Sufficient non-negativity conditions on the Bezier ordinates are derived to ensure the non-negativity of a bicubic Bezier patch. The method modifies Bezier ordinates locally to fulfill the sufficient non-neg...