The points P0, P1 and P2 are the vertices of the triangle. P is a point at which interpolation will be performed. For purposes of this document, point P0 has cartesian coordinates (x0,y0,w0), color coordinates (r0,g0,b0) and texture coordinates (u0,v0). Points P1 and P2 are similarly defined. The cartesian coordinates are defined in perspective space, i.e., they have been multiplied by a perspe...

This paper is concerned with the problem of characterizing those functions of minimum LP-norm on their nth derivative, <=p=<, that sequentially take on the given values (ei). For p = the unique minimizing function is characterized. For p < fairly explicit necessary conditions are given.

We propose a generalized curvature that is motivated by the optimal transport problem on $\mathbb{R}^d$ with cost induced Tonelli Lagrangian $L$. show non-negativity of implies displacement convexity entropy functional $L-$Wasserstein space along $C^2$ interpolants.