Search Results

You can just solve the equation you display directly. For example, let $$ P_0=(0,0),\;\; P_2=(1,0),\;\; P_1=(0.4,0.8) \;, $$ and suppose $B=(0.174,0.168)$:           Then your equation $$ B=P_0+t( …

There is a thread of work that derives from W.-T. Wu's work on geometry theorem proving, and this seminal paper by Schwartz, Schwartz, Jacob T. "Fast probabilistic algorithms for verification of p …

Mathematica implements an algorithm: see the manual here: (Added in response to a comment query.) The paper Hochbaum, Dorit S., and Anu Pathria. "Can a System of Linear Diophantine Equations b …

Maybe these images will help?            (Image by Ruye Wang at this link.)            (Image at this link.) If you prefer dynamic illustrations, there is this YouTube video:      

This paper seems to directly address your question: Art Owen. "Latin supercube sampling for very high-dimensional simulations." ACM Transactions on Modeling and Computer Simulation (TOMACS). V …

There is literature on how to represent T-meshes. For example, the paper below acknowledges that the flexibility of T-meshes make them difficult to represent in a data structure. So they "recommend …

"Is it possible to construct a triangulation by choosing the points in the space as we go along?": The answer is Yes. This is known as the incremental algorithm. First, the Delaunay triangulation of …

This may not be what you seek, but in the 1996 paper, "Anisotropic refinement algorithms for finite elements" by Goodman, Samuelsson, and Szepessy (.ps link), they show an example of a function $u(x,y …

I do not believe this is exactly what you seek, but there is literature in computer graphics that starts with a mesh of "traditional triangles" as you describe them, and "remeshes" the surface with ge …

Perhaps there is a result along these lines? Given any set of distinct points in the plane, there exists a simple (nonintersecting) path through them in a specified order, with the path composed …

Nothing can surpass the Li and Vitányi book in both readability and comprehensiveness, but that is a significant undertaking, and you might need alternatives. "A Short Introduction to Kolmogorov Compl …

Select any edge $e_1$, and orient it arbitrarily. Now orient the next edge $e_2$ (the one that uniquely shares the head endpoint of $e_1$) to be consistent with $e_1$. Continuing in this manner, you …

The paper you cite, "On the multivariate Horner scheme" (Pena, Sauer) has an explicit algorithm specified on p.3. The remaining challenge is to penetrate the notation and conventions in the paper lai …