In order to transmit or store three-dimensional (3-D) mesh models efficiently, we need to simplify them. Although the quadric error metric (QEM) provides fast and accurate geometric simplification of 3-D mesh models, it cannot capture discontinuities faithfully. Recently, an enhanced QEM based on subdivided edge classification has been proposed to handle this problem. Although it can capture di...

We study the multi-dimensional re ection map on the spaces D([0; T ];Rk ) and D([0;1);Rk ) of right-continuous Rk -valued functions on [0; T ] or [0;1) with left limits, endowed with variants of the Skorohod(1956) M1 topology. The re ection map was used with the continuous mapping theorem by Harrison and Reiman (1981) and Reiman (1984) to establish heavy-tra c limit theorems with re ected Brown...

We introduce a new texture representation that combines standard bi-linearly interpolated samples, for smoothly varying regions, with customizable discontinuities for sharp boundaries between these regions. It consists in a standard signal texture, plus a second texture we call pinchmap, which encodes discontinuities along generally curved lines; this structure is stored in texture memory as a ...