Constructing G1 quadratic Bézier curves with arbitrary endpoint tangent vectors
نویسندگان
چکیده
Quadratice Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G quadratic Bézier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the G quadratic Bézier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.”
منابع مشابه
Constructing G quadratic Bézier curves with arbitrary endpoint tangent vectors
Quadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G quadratic Bézier curves satisfying given endpoint (positions and ...
متن کاملAn Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves
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...
متن کاملInterpolating G1 Bézier surfaces over irregular curve networks for ship hull design
We propose a local method of constructing piecewise G Bézier patches to span an irregular curve network, without modifying the given curves at oddand 4-valent node points. Topologically irregular regions of the network are approximated by implicit surfaces, which are used to generate split curves, which subdivide the regions into triangular and/or rectangular sub-regions. The subdivided regions...
متن کاملGeometric Hermite curves with minimum strain energy
The purpose of this paper is to provide yet another solution to a fundamental problem in computer aided geometric design, i.e., constructing a smooth curve satisfying given endpoint (position and tangent) conditions. A new class of curves, called optimized geometric Hermite (OGH) curves, is introduced. An OGH curve is defined by optimizing the magnitudes of the endpoint tangent vectors in the H...
متن کاملGeometric constraints on quadratic Bézier curves using minimal length and energy
This paper derives expressions for the arc length and the bending energy of quadratic Bézier curves. The formulae are in terms of the control point coordinates. For fixed start and end points of the Bézier curve, the locus of the middle control point is analyzed for curves of fixed arc length or bending energy. In the case of arc length this locus is convex. For bending energy it is not. Given ...
متن کامل