In this paper, we present the exact Hausdorff distance between the offset curve of quadratic Bézier curve and its quadratic GC1 approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic GC1 approximation of the offset curve of a quadratic Bézier curve. 1. Preliminaries Quadratic Bézier curves and their offset curves are widely used in CAD/CAM or Co...

In order to eliminate the weakness of large volumes data in 3D modeling process, a fast and efficient sampling method based on curvature analysis of cubic Bézier curve is presented. With the method, the characteristic points and curvature maximum value of cubic Bézier curve are used as the reference standard of the sampling interval and density. For cubic B-spline curves, the sampling data can ...

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 ...

Well-defined image can assist user to identify region of interest during segmentation. However, complex medical image is usually characterized by poor tissue contrast and low background luminance. The contrast improvement can lift image visual quality, but the fundamental contrast enhancement methods often overlook the sudden jump problem. In this work, the proposed bihistogram Bezier curve con...

A new heuristic method of geometric Hermite interpolation is presented to construct a planar cubic rational Bézier curve with two points and two unit tangent directions. The integral, which shows the change rate of the curvature, is taken as the energy function to measure the fairness of the parameter curve. Hence the curvature of the new curve is more stable. Since that the energy function of ...

This paper considers the shape control of the cubic H-Bézier curve, which can represent hyperbolas and catenaries accurately. We fix all the control points while let one vary. The locus of the moving control point that yields a cusp on the cubic H-Bézier curve is a planar curve; The tangent surface of the planar curve is the locus of the positions of the moving control point that yield inflecti...