Approximate conversion of spline curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Unified and extended form of three types of splines
Journal of Computational and Applied Mathematics
Constrained multi-degree reduction of Bézier surfaces using Jacobi polynomials
Computer Aided Geometric Design
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
Computer Aided Geometric Design
Approximating tensor product Bézier surfaces with tangent plane continuity
Journal of Computational and Applied Mathematics
Merging multiple B-spline surface patches in a virtual reality environment
Computer-Aided Design
Constrained multi-degree reduction of triangular Bézier surfaces using dual Bernstein polynomials
Journal of Computational and Applied Mathematics
Multi-degree reduction of Bézier curves using reparameterization
Computer-Aided Design
Spherical DCB-Spline Surfaces with Hierarchical and Adaptive Knot Insertion
IEEE Transactions on Visualization and Computer Graphics
Matrix Analysis
Explicit G2-constrained degree reduction of Bézier curves by quadratic optimization
Journal of Computational and Applied Mathematics
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This paper presents an explicit method for the G^3 merging problem of two Bezier curves. The main idea is to express the L"2 distance as a quadratic function of some parameters provided by G^3 continuity conditions. An efficient non-iterative algorithm is proposed to obtain the optimal merged curve when the L"2 distance is minimized. The uniqueness of the global minimum is also proven. This method can be applied to two adjacent curves with different degrees and has the ability to obtain satisfactory merging results by using curves of lower degree. The efficiency and accuracy of the proposed explicit method are illustrated through several comparative examples.