赵辉助理研究员, 北京雁栖湖应用数学研究院

Consumer expenditures in the United Kingdom account for over 50% of Gross Domestic Product on the expenditure side, yet their impact on economic activity is often Global geometric structures live on manifolds, which contain geometry and topology informations. Their discretization will provide powerful tools for various engineering fields by introducing advanced geometry and topology concepts. Foliation is one of global geometric structures. In this talk, we present an algorithm to produce a discrete harmonic foliation. A closed, not yet harmonic foliation on a surface could evolve to a harmonic foliation by optimizing a certain kind of Dirichlet energy. The optimization procedure needs take the topology of the surface into consideration, otherwise, it will fail to arrive at the optimal values. we propose a novel discrete foliation graph stripe structure, and constrains the diffusion of optimization by foliation graph stripe, such that we can achieve the optimal value of the Dirichlet energy of discrete harmonic foliations. We also demonstrate our algorithms of the harmornic foliation and holomorphic quadratic differentials in the applicaiton of quad mesh generation which is key components in CAD and CAE.