A geometric look at corner cutting

A geometric look at corner cutting

G. de Rham (1947), Un peu de math ematiques a propos d'une courbe plane, Elemente der Mathematik, 2(4):89{104. G. de Rham (1956), Sur une courbe plane, Journal de Math ematiques pures et appliqu ees, 35:25{42. 27 Figure 28: Each point in the shaded area carries a continuum of lines such that the associated aane standard cut produces C 1-curves without line segments. Hence for each contact point...

A Geometric Look at Manipulation

We take a fresh look at voting theory, in particular at the notion of manipulation, by employing the geometry of the Saari triangle. This yields a geometric proof of the Gibbard/Satterthwaite theorem, and new insight into what it means to manipulate the vote. Next, we propose two possible strengthenings of the notion of manipulability (or weakenings of the notion of non-manipulability), and ana...

A Principled Look at Cost Cutting

Rectangular Corner Cutting Sylvester

This paper presents a way to construct the Sylvester A-resultant matrix for three bi-degree (m; n) polynomials whose exponent set is cut oo by rectangles at the corners. The paper also shows that the determinant of this matrix does give the resultant of the three polynomials.

Corner cutting systems

If we can evaluate a curve by means of a corner cutting algorithm, we call the corresponding system of functions a corner cutting system. We prove that corner cutting systems are always monotonicity preserving. We obtain weak sufficient conditions for corner cutting systems. Optimal stability properties and properties concerning the supports of the basis functions of corner cutting systems are ...