2010/06/25 by Luis David Garcia-Puente, Garcia-Puente, Luis David, Frank Sottile +3
Computer Science · Mathematics · #14M25 #65D17 #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #I.3.5 #acm:14M25 #acm:65D17 #cs.GR #math.AG #msc:14M25 #msc:65D17
paper · pdf · doi:10.48550/arxiv.1006.4903
21 pages, many .eps figures
arxiv created 2010/12/30 · arxiv updated 2011/01/04
The control polygon of a Bezier curve is well-defined and has geometric significance---there is a sequence of weights under which the limiting position of the curve is the control polygon. For a Bezier surface patch, there are many possible polyhedral control structures, and none are canonical. We propose a not necessarily polyhedral control structure for surface patches, regular control surfaces, which are certain C0 spline surfaces. While not unique, regular control surfaces are exactly the possible limiting positions of a Bezier patch when the weights are allowed to vary.