Weighted G-Multi-Degree Reduction of Bézier Curves
نویسندگان
چکیده
In this paper, weighted G-multi-degree reduction of Bézier curves is considered. The degree reduction of a given Bézier curve of degree n is used to write it as a Bézier curve of degree m,m < n. Exact degree reduction is not possible, and, therefore, approximation methods are used. The weight function w(t) = 2t(1 − t), t ∈ [0, 1] is used with the L2-norm in multidegree reduction with G-continuity at the end points of the curve. Since we consider boundary conditions this weight function improves approximation in the middle of the curve. Numerical results and comparisons show that the proposed method produces fewer errors and outperform all existing methods. Keywords—Bézier curves; multiple degree reduction; Gcontinuity; geometric continuity
منابع مشابه
Degree Reduction of Disk Rational Bézier Curves Using Multi-objective Optimization Techniques
In this paper, we start by introducing a novel disk rational Bézier based on parallel projection, whose properties are also discussed. Then applying weighted least squares, multiobjective optimization techniques and constrained quadratic programming, we achieve multi-degree reduction of this kind of disk rational Bézier curve. The paper also gives error estimation and shows some numerical examp...
متن کاملExplicit Multi-degree Reduction of Said-Bézier Generalized Ball Curves with Endpoints Constraints ?
Theoretical study shows that Said-Bézier generalized Ball curves (SBGB curves) are distinctly superior to Bézier curves in evaluation, degree elevation and reduction. However in practical engineering, there is no effective algorithm for explicit multi-degree reduction of SBGB curves with endpoints constraints in the world. It is going against designing and applying generalized Ball curves. In o...
متن کاملOptimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer
We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacob...
متن کاملMulti-Degree Reduction of Bézier Curves with Distance and Energy Optimization
In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure o...
متن کاملMulti-degree Reduction of Disk Bézier Curves in L2 Norm ?
A planar Bézier curve whose control points are disks is called a disk Bézier curve. It can be looked as a parametric curve with tolerance in the plane. It is an effective tool to measure or control the error. Based on minimum mean square error, this paper presents an algorithm for optimal multi-degree reduction of disk Bézier curves in L2 norm. First, applying the orthogonal property of Jacobi ...
متن کامل