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DEFINITION OF A B-SPLINE CURVE - Computer Science

On-Line Geometric Modeling NotesDEFINITION OF A B-SPLINE CURVEK enneth I. JoyVisualization and Graphics Research GroupDepartment of Computer ScienceUniversity of California, DavisOverviewThese notes present the direct DEFINITION of the B-SPLINE CURVE . This DEFINITION is given in two ways: firstby an analytical DEFINITION using the normalized B-SPLINE blending functions, and then through a B-SPLINE CURVE Analytical DefinitionA B-SPLINE curveP(t), is defined byP(t) =n i=0 PiNi,k(t)where the{Pi:i= 0,1, .., n}are the control points, kis the order of the polynomial segments of the B-SPLINE CURVE . Orderkmeans that the CURVE is madeup of piecewise polynomial segments of degreek 1, theNi,k(t)are the normalized B-SPLINE blending functions . They are described by the orderkandby a non-decreasing sequence of real numbers{ti:i= 0.}

and geometric definitions of B-splines. Starting with the definition of the normalized B-spline blending functions, these two researchers were able to develop the geometric definition of the B-spline. It is this calculation that is discussed in this paper. Definition of the B-Spline Curve A B-spline curveP(t), is defined by P(t) = Xn i=0 P ...

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