Elements of Coordinate Geometry

A Coordinate Free Geometry

An algebra for geometric reasoning is developed that is amenable to software implementation. The features of the algebra are chosen to support geometric programming of the variety found in computer graphics and computer aided geometric design applications. The implementation of the algebra in C++ is described, and several examples illustrating the use of this software are given.

Coordinate-Free Projective Geometry for Computer Vision

Elements of Computer Vision: Multiple View Geometry

It is worth reminding the reader that geometry is an important but not the only important aspect of computer vision, and in particular of multi-view vision. The information brought by each image pixel is twofold: its position and its colour (or brightness, for a monochrome image). Ultimately, each computer vision system must start with brightness values, and, to smaller or greater depth, link s...

Remarks on the Geometry of Coordinate Projections in Rn

We investigate some properties of coordinate projections. Among other results, we show that if a body K ⊂ Rn has an “almost extremal” volume ratio, then it has a projection of proportional dimension which is close to the cube. We also establish a sharp estimate on the shattering dimension of a convex hull of a class of functions.

Remarks on the Geometry of Coordinate Projections in R

We study geometric properties of coordinate projections. Among other results, we show that if a body K ⊂ R has an “almost extremal” volume ratio, then it has a projection of proportional dimension which is close to the cube. We also establish a sharp estimate on the shattering dimension of the convex hull of a class of functions in terms of the shattering dimension of the class itself.