Symbolic Manipulation of Bspline Basis Functions with Mathematica

Abstract

Abstract. Bspline curves and surfaces are the most common and most important geometric entities in many fields, such as computer design and manufacturing (CAD/CAM) and computer graphics. However, up to our knowledge no computer algebra package includes especialized symbolic routines for dealing with Bsplines so far. In this paper, we describe a new Mathematica program to compute the Bspline basis functions symbolically. The performance of the code along with the description of the main commands are discussed by using some illustrative examples.

New Package in Maxima for Single-Valued Interval Computation on Real Numbers

“…in this regard, intervals are used to handle uncertainties, mathematical approximations, and arithmetic roundoff on values of physical and technical parameters obtained from measurement errors. Applications of intervals also extend to many other fields of theoretical and applied mathematics, such as optimization and linear programming [7,13], functional equations [2,3], complex variable [23], inequalities solving [9,11] equation systems solving [22], robust control and robotics [12], geometric modeling and processing [6,8,10,24,25,26], statistics [28], circuit analysis [14], computer graphics and CAD [29], data processing [17], dynamical systems [4] and so on.…”