...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Computer Aided Geometric Design >An efficient method to integrate polynomials over polytopes and curved solids
【24h】

An efficient method to integrate polynomials over polytopes and curved solids

机译：一种高效的方法，用于将多项式整合到多项式和弯曲固体上

获取原文
获取原文并翻译 | 示例
   

获取外文期刊封面封底 >>

       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In this paper, we present an efficient approach to compute the integral of monomials and polynomials over polyhedra and regions defined by parametric curved boundary surfaces. We use Euler's theorem for homogeneous functions in combination with Stokes's theorem to reduce the integration of a monomial over a three-dimensional solid to its boundary. If the solid is a polytope, through a recursive application of these theorems, the integral is further reduced to just the evaluation of the monomial and its derivatives at the vertices of the polytope. The present approach is simpler than existing techniques that rely on repeated use of the divergence theorem, which require the antiderivative of the monomials and the projection of these functions onto hyperplanes. For convex and nonconvex polytopes, our approach does not introduce any approximation for the integration of monomials. For curved solid regions bounded by surfaces that admit a parameterization, the same approach yields simplified formulas to compute the integral of any homogeneous function, including monomials. For surfaces parameterized by polynomial surfaces (such as Bezier surface triangles and B-spline patches), the method yields machine-precision accuracy for the volumetric integration of monomials with an appropriate quadrature rule. Numerical examples over regions bounded by polynomial surfaces and rational surfaces are presented to establish the accuracy and efficiency of the method.
机译：在本文中，我们提出了一种有效的方法来计算通过参数弯曲边界表面定义的多面体和区域的单体和多项式的整体。我们使用Euler的定理与斯托克斯定理结合使用斯托克斯定理，以减少单项在三维固体上的整合到其边界。如果固体是多孔渗，通过这些定理的递归施用，进一步减少了积分，仅仅降低到多种渗透镜的顶点的单体及其衍生物的评估。本方法比现有技术更简单，依赖于反复使用发散定理，这需要单项式的反导体和这些功能的投影到超平面上。对于凸和非凸多粒子，我们的方法不会引入单体整合的任何近似。对于被承认参数化的表面有界面的弯曲固体区域，相同的方法产生简化的公式，以计算任何均匀函数的积分，包括单体。对于由多项式表面（例如Bezier Surface Trigles和B样条贴片）参数化的表面，该方法产生机器精度精度，用于具有适当的正交规则的单体体积的体积集成。提出了由多项式表面和合理表面界定的区域的数值例子来确定该方法的精度和效率。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号