Concepts inVoronoi diagram computations for planar NURBS curves
Non-uniform rational B-spline
Non-uniform rational basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces which offers great flexibility and precision for handling both analytic and modeled shapes.
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Voronoi diagram
In mathematics, a Voronoi diagram is a special kind of decomposition of a given space, e.g. , a metric space, determined by distances to a specified family of objects (subsets) in the space.
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Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature. Often curves in two-dimensional or three-dimensional (space curves) Euclidean space are of interest.
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Bisection
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. The most often considered types of bisectors are the segment bisector (a line that passes through the midpoint of a given segment) and the angle bisector (a line that passes through the apex of an angle, that divides it into two equal angles). In three dimensional space, bisection is usually done by a plane, also called the bisector or bisecting plane.
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Plane curve
In mathematics, a plane curve is a curve in a Euclidean plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. A smooth plane curve is a curve in a real Euclidean plane R and is a one-dimensional smooth manifold. Equivalently, a smooth plane curve can be given locally by an equation {{{1}}} where ¿ : R ¿ R is a smooth function, and the partial derivatives ¿¿/¿x and ¿¿/¿y are never both 0.
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Algebraic curve
In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections.
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In mathematics, a piecewise-defined function (also called a piecewise function) is a function whose definition changes depending on the value of the independent variable. Mathematically, a real-valued function f of a real variable x is a relationship whose definition is given differently on disjoint subsets of its domain (known as subdomains).
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