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On approximating contours of the piecewise trilinear interpolant using triangular rational quadratic Bezier patches

机译:用三角有理二次贝塞尔曲线补丁逼近分段三线性插值的轮廓

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Given a three dimensional (3D) array of function values F/sub i,j,k/ on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x, y, z)=T. We describe the construction of a C/sup 0/ continuous surface consisting of rational quadratic surface patches interpolating the triangles in T. We determine the Bezier control points of a single rational quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices.
机译:给定直线网格上函数值F / sub i,j,k /的三维(3D)数组,行进立方体(MC)方法是用于计算近似轮廓(等值面)的表面三角剖分T的最常用技术F(x,y,z)= T。我们描述了一个C / sup 0 /连续曲面的构造,该曲面由插在T中的三角形的有理二次曲面补丁组成。我们根据基础三角形和顶点的顶点坐标确定单个有理二次曲面补丁的Bezier控制点。与顶点相关的渐变和粗麻布。

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