2. MAIN RESULTS In this paper, subdivision methods for rectangular Bézier A rectangular Bézier surface of degree n 3 m can be surfaces are generalized to subdivide a rectangular Bézier surface patch of degree n 3 m into two rectangular Bézier surrepresented by face patches of degree n 3 (m 1 n), while the parameter domain of the Bézier surface is decomposed into two trapezoids. As an applicatio...

When designers begin a product design, they create their ideas and expand them. This process is performed on paper, and designers’ hand-drawn lines are called sketches. If the designers’ hand-drawn sketches can be realized as real curves, it would be effective in shortening the design period. We have developed a method to extract five degree Bézier curves based on a hand-drawn sketch. The basic...

This paper presents a geometric interpolation method for curve approximation in 3 R space. Given a curve, the new method is to find an approximation Bézier curve of degree 4 tangent with the given curve at the two end points and at an inner point as well. The resulting Bézier curve is explicitly expressed in the parameters of the tangent inner point of both the given curve and the approximation...

Approximating a hand-written curve by a Bézier curve can be performed by two main processes: (1) the selection of the significant points on the curve and (2) the curve approximation. This paper focuses on finding a set of featured points, which is an important component for curve fitting into a Bézier curve. This new approach is an extension of the authors’ previous work by reducing the weaknes...

We present a new string method for finding the most probable transition pathway and optimal reaction coordinate in complex chemical systems. Our approach evolves an analytic parametric curve, known as a Bézier curve, to the most probable transition path between metastable regions in configuration space. In addition, we demonstrate that the geometric properties of the Bézier curve can be used to...

In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...

A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. W...

This paper considers planar cubic Bézier curves in three-dimensional Minkowski space. We shall consider the conditions for the control points A,C,D,B of the Bézier curve such that the Bézier segment is pointwise space-like. For the control point C, we shall give a geometrical interpretation of the feasibility condition provided the rest of the control points are fixed.