This paper presents a scale method for developing high dimensional scale functions to blend implicitly defined objects. Scale functions are differentiable on the entire domain except the origin, provide blending range control, and behave like Min/Max operators everywhere, so even a successive composition of blending operations containing overlapped blending regions can be generated smoothly. Be...

Method of deviation was introduced in [1] for drawing implicit curves. This paper develops algorithms for drawing lines and conic sections using method of deviation. All computations are performed in integer mode. The lines and conic sections drawn are compared with those drawn using mid point algorithm.

We determine all point-sets of minimum size in PG(2, q), q odd that meet every external line to a conic in PG(2, q). The proof uses a result on the linear system of polynomials vanishing at every internal point to the conic and a corollary to the classification theorem of all subgroups of PGL(2, q).

For large q we characterize the (q + 1)-sets in PG(2, q), q odd, having more than 0.326q nuclei on a conic. In the process more information about the structure of (q + 1)-sets having a large number of nuclei on a conic is obtained.

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A NOVEL CONIC SECTION CLASSIFIER WITH TRACTABLE GEOMETRIC LEARNING ALGORITHMS By Santhosh Kodipaka August 2009 Chair: Baba C. Vemuri Cochair: Arunava Banerjee Major: Computer Engineering Several pattern recognition problems in computer v...

Received: date / Revised version: date Abstract. We investigate the relation between interior-point algorithms applied to two homogeneous self-dual approaches to linear programming, one of which was proposed by Ye, Todd, and Mizuno and the other by Nesterov, Todd, and Ye. We obtain only a partial equivalence of path-following methods (the centering parameter for the first approach needs to be e...

Highly localized kernels constructed by orthogonal polynomials have been fundamental in the recent development of approximation and computational analysis on unit sphere, ball, several other regular domains. In this work, we first study homogeneous spaces that are assumed to contain highly establish a framework for tight frames such spaces, which extends works bounded We then show is applicable...