In this paper we are concerned with the modified conjugate direction method for computing the pseudoinverse by using an orthogonal basis of the range space of A. Numerical results show that the new method retains some...In this paper we are concerned with the modified conjugate direction method for computing the pseudoinverse by using an orthogonal basis of the range space of A. Numerical results show that the new method retains some main advantages in terms of efficiency and accuracy.展开更多
We present a simple yet effective method for constructing 3D self-supporting surfaces with planar quadrilateral(PQ)elements.Starting with a triangular discretization of a self-supporting surface,we firstcompute the pr...We present a simple yet effective method for constructing 3D self-supporting surfaces with planar quadrilateral(PQ)elements.Starting with a triangular discretization of a self-supporting surface,we firstcompute the principal curvatures and directions of each triangular face using a new discrete differential geometryapproach,yielding more accurate results than existing methods.Then,we smooth the principal direction field to reduce the number of singularities.Next,we partition all faces into two groups in terms of principalcurvature difference.For each face with small curvature difference,we compute a stretch matrix that turns the principal directions into a pair of conjugate directions.For the remaining triangular faces,we simply keep their smoothed principal directions.Finally,applying a mixed-integer programming solver to the mixed principal and conjugate direction field,we obtain a planar quadrilateral mesh.Experimental results show that our method is computationally efficient and can yield high-quality PQ meshes that well approximate the geometry of the input surfaces and maintain their self-supporting properties.展开更多
文摘In this paper we are concerned with the modified conjugate direction method for computing the pseudoinverse by using an orthogonal basis of the range space of A. Numerical results show that the new method retains some main advantages in terms of efficiency and accuracy.
基金partially supported by National Natural Science Foundation of China(62172257,61802228)Singapore Ministry of Education(T2EP20220-0014)+1 种基金the RIE2020 Industry Alignment Fund-Industry Collaboration Projects(IAF-ICP)Funding Initiativecash and in-kind contribution from the industrial partner,Rolls-Royce.
文摘We present a simple yet effective method for constructing 3D self-supporting surfaces with planar quadrilateral(PQ)elements.Starting with a triangular discretization of a self-supporting surface,we firstcompute the principal curvatures and directions of each triangular face using a new discrete differential geometryapproach,yielding more accurate results than existing methods.Then,we smooth the principal direction field to reduce the number of singularities.Next,we partition all faces into two groups in terms of principalcurvature difference.For each face with small curvature difference,we compute a stretch matrix that turns the principal directions into a pair of conjugate directions.For the remaining triangular faces,we simply keep their smoothed principal directions.Finally,applying a mixed-integer programming solver to the mixed principal and conjugate direction field,we obtain a planar quadrilateral mesh.Experimental results show that our method is computationally efficient and can yield high-quality PQ meshes that well approximate the geometry of the input surfaces and maintain their self-supporting properties.
