双变量张量积Bernstein基下的曲线隐式化
Curve implicitization in the bivariate tensor-product Bernstein basis
AI总结：
将Sylvester和Bezout结式矩阵及双变量插值方法从幂基扩展到Bernstein基，通过Bernstein-Bezoutian矩阵计算隐式方程系数，并利用全正矩阵逆的双对角分解。
摘要：
通过Sylvester和Bezout结式矩阵以及通常幂基下的双变量插值进行曲线隐式化的方法被扩展到Bernstein基下构造的Bernstein-Bezoutian矩阵的情形。隐式方程的系数也在双变量张量积Bernstein基下计算，其计算涉及某些全正矩阵逆的双对角分解。
英文摘要：
The approach to curve implicitization through Sylvester and Bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case of Bernstein-Bezoutian matrices constructed when the polynomials are given in the Bernstein basis. The coefficients of the implicit equation are also computed in the bivariate tensor-product Bernstein basis, and their computation involves the bidiagonal factorization of the inverses of certain totally positive matrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
