Denote a point in the plane by z=(z,y) and a polynomial of nth degree in z by f(z) /spl Sigma//sub i,j//spl ges/o/sub 1/i+j/spl les/n(a/sub ij/x/sup i/y/sup j/). Denote by Z(f) the set of points for which f(z)=0. Z(f) is the 2D curve represented by f(z). In this paper, we present a new approach to fitting 2D curves to data in the plane (or 3D surfaces to range data) which has significant advantages over presently known methods. It requires considerably less computation and the resulting curve can be forced to lie close to the data set at prescribed points provided that there is an nth degree polynomial that can reasonably approximate the data. Linear programming is used to do the fitting. The approach can incorporate a variety of distance measures and global geometric constraints.
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机译:在z =(z,y)和f(z)/ spl sigma //子I,j // spl ges / sig1 / i + j / SPL LES / N(A / SUB IJ / X / SUP I / Y / SUP J /)。表示由z(f)f(z)= 0的一组点。 z(f)是由f(z)表示的2d曲线。在本文中,我们向平面(或3D表面到范围数据)中的数据拟合了拟合2D曲线的新方法,这与当前已知的方法具有显着的优点。它需要相当较少的计算,并且可以强制得到的曲线可以被迫靠近规定点设置的数据,条件是存在可以合理地近似数据的第n度多项式。线性编程用于进行配件。该方法可以包含各种距离测量和全局几何约束。
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