Loop细分曲面精确求值新公式

A New Exact Evaluation Formula for Loop Subdivision Surfaces

利用控制网格拓扑结构的对称性,通过将奇异点周围1-环和2-环的控制顶点进行离散Fourier变换(DFT)得到分块对角阵,将其进行特征分解及排序之后,再通过离散Fourier逆变换(IDFT)和截断等操作得到细分矩阵的高次幂的表达式,从而得到Loop细分曲面新的精确参数化公式.

A block diagonal matrix can be obtained by utilizing the discrete Fourier transform （DFT） and the symmetrical structure called 1-ring and 2-ring in the vicinity of an extraordinary point on a mesh. By using in a sequence the eigen-decomposition, a permutation, the inverse discrete Fourier transform （IDFT） and a truncation on the matrix, an exact and explicit parametrization formula for Loop subdivision surfaces is proposed.