93.55 Constructing a quadrilateral inside another one

Largest Placement of One Convex Polygon Inside Another

We show that the largest similar copy of a convex polygon P with m edges inside a convex polygon Q with n edges can be computed in O mn logn time We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O mn and that it can also be computed in O mn logn time Let P be a convex polygon with m edges and Q a convex polygon with n edges Our goal is to nd the...

Exact 2-D Integration inside Quadrilateral Boundaries

This short paper shows how to shift, add, scale and multiply a few small matrices to compute the integral of any 2-D polynomial f x y within any specified quadrilateral boundaries, including non-convex chevrons and triangles. The solution is exact, general, and might be suitable for parallel implementation on graphics hardware. It can aid in many graphical tasks, including compositing, anisotro...

Constructing Hamiltonian Triangle Strips on Quadrilateral Meshes

Because of their improved numerical properties, quadrilateral meshes have become a popular representation for finite elements computations and computer animation. In this paper we address the problem of optimally representing quadrilateral meshes as generalized triangle strips (with one swap bit per triangle). This is important because 3D rendering hardware is optimized for rendering triangle m...

Give Me Another One!

We investigate the complexity of an optimization problem in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfying assignment with minimal Hamming distance to a given assignment that satisfies the formula (NearestOtherSolution, NOSol). We present a complete classification with respect to the relations admitted in the for...

Inside the Buy - One Give - One Model