We present a generalization of the Bogomolov-Miyaoka-Yau inequality to Deligne-Mumford surfaces of general type.

We use Seidel representation for symplectic orbifolds to compute the quantum cohomology ring of a compact symplectic toric orbifold (X , ω).

We give a new, simple algorithm for simultaneous degree elevation and knot insertion for B-spline curves. The method is based on the simple approach of computing derivatives using the control points, resampling the knot vector, and then computing the new control points from the derivatives. We compare our approach with previous algorithms and illustrate it with examples.

In this paper we analyze an algorithm which solves the point projection and the “inversion” problems for parametric curves and surfaces. It consists of a geometric second order iteration which converges faster than existing first order methods, and whose sensitivity to the choice of initial values is small. Applications include the ICP algorithm for shape registration.

We study error propagation through implicit geometric problems by linearizing and estimating the linearization error. The method is particularly useful for quadratic constraints, which turns out to be no big restriction for many geometric problems in applications.