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Cubic algebraic curves based on geometric constraints
Methods for curve modeling with cubic algebraic curves based on geometric constraints are introduced in this paper. A 1-parameter family of cubic curves with four given points as well as two tangent lines at the endpoints is constructed in the first ...
Algebraic and geometric characterizations of a class of Algebraic-Hyperbolic Pythagorean-Hodograph curves
AbstractIn this paper, we study algebraic and geometric characteristics of a class of Algebraic-Hyperbolic curves that possess Pythagorean-Hodograph (PH) properties, which are called AHPH curves. These curves are defined on the space Γ n = ...
Graphical abstractHighlights- A particular class of PH curves in the space span { 1 , t , … , t n − 3 , sinh t , cosh t } is defined as AHPH curves.
Changeable degree spline basis functions
A B-spline basis function is a piecewise function of polynomials of equal degree on its support interval. This paper extends B-spline basis functions to changeable degree spline (CD-spline for short) basis functions, each of which may consist of ...
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