Abstract
A piecewise algebraic curve is defined as the zero contour of a bivariate spline. In this paper, we present a new method for fittingC1piecewise algebraic curves of degree 2 over type-2 triangulation to the given scattered data. By simultaneously approximating points, associated normals and tangents, and points constraints, the energy term is also considered in the method. Moreover, some examples are presented.
Highlights
A piecewise algebraic curve is defined as the zero contour of a bivariate spline
We present a new method for fitting C1 piecewise algebraic curves of degree 2 over type-2 triangulation to the given scattered data
By simultaneously approximating points, associated normals and tangents, and points constraints, the energy term is considered in the method
Summary
The curve fitting problem is very important in CAD (computer-aided design) and CAGD (computer-aided geometric design). Juttler [4, 5] described an algorithm for fitting implicit defined tensor-product spline curves and surfaces to scattered data. Wang et al [10] and Yang et al [11] used the implicit defined tensor-product spline curves and surfaces for fitting and blending. The approximation curve is to be described as the zero contour of a nontensor product C1 bivariate spline of degree 2 over type-2 triangulation. We use the piecewise algebraic curves for fitting the given points
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