Graphics Evolutionary Computations in Higher Order Parametric Bezier Curves

Computations of Bezier Geodesic-like Curves on Spheres

It is an important problem to compute the geodesics on a surface in many fields. To find the geodesics in practice, however, the traditional discrete algorithms or numerical approaches can only find a list of discrete points. The first author proposed in 2010 a new, elegant and accurate method, the geodesic-like method, for approximating geodesics on a regular surface. This paper will present b...

Bezier curves

i=0 aix , ai ∈ R. We will denote by πn the linear (vector) space of all such polynomials. The actual degree of p is the largest i for which ai is non-zero. The functions 1, x, . . . , x form a basis for πn, known as the monomial basis, and the dimension of the space πn is therefore n + 1. Bernstein polynomials are an alternative basis for πn, and are used to construct Bezier curves. The i-th Be...

Parametric Pricing of Higher Order

A general parametric framework based on the generalized Student t distribution is developed for pricing S&P500 options. Higher order moments in stock returns as well as time-varying volatility are priced. An important computational advantage of the proposed framework over Monte Carlo-based pricing methods is that options can be priced using one-dimensional quadrature integration. The empirical ...

5 Rational Bezier Curves Andrelief

Evolutionary Higher-Order Concept Learning

Current concept learners are limited in their applicability as they generally rely on comparatively poor knowledge representation facilities (e.g. attribute value pairs, flattened horn clauses). The work carried out in support of my thesis has involved extending concept learning to a higher order setting by developing a novel representation based on closed Escher terms for highly structured dat...