词条 | Control point (mathematics) |
释义 |
In computer-aided geometric design a control point is a member of a set of points used to determine the shape of a spline curve or, more generally, a surface or higher-dimensional object.[1] For Bézier curves, it has become customary to refer to the -vectors p in a parametric representation p of a curve or surface in -space as control points, while the scalar-valued functions , defined over the relevant parameter domain, are the corresponding weight or blending functions. Some would reasonably insist, in order to give intuitive geometric meaning to the word `control', that the blending functions form a partition of unity, i.e., that the are nonnegative and sum to one. This property implies that the curve lies within the convex hull of its control points.[2] This is the case for Bézier's representation of a polynomial curve as well as for the B-spline representation of a spline curve or tensor-product spline surface. References1. ^{{citation|title=Curves and Surfaces for Computer Graphics|first=David|last=Salomon|publisher=Springer|year=2007|isbn=9780387284521|page=11|url=https://books.google.com/books?id=r5o5biZPDKEC&pg=PA11}}. {{geometry-stub}}2. ^{{citation|title=Computer Graphics Through OpenGL: From Theory to Experiments|first=Sumanta|last=Guha|publisher=CRC Press|year=2010|isbn=9781439846209|page=663|url=https://books.google.com/books?id=7bCiFepXle0C&pg=PA663}}. 1 : Splines (mathematics) |
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