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ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 1982, Vol. 3 ›› Issue (3): 97-104.
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Shi Fazhong, Wu Junheng
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Abstract: In this paper, taking the plotting theorem as the point of departure, we analyze in detail the geometrical characteristics of plane cubic Bezier curves, including whether a cusp ( a cusp of class one) or one inflexion point or two inflexion points exist on the ( 0, 1 ); whether double point occurs on [0, 1 ) or ( 0 , 1 ] and whether the curve is convex or not.The geometrical characteristics of plane cubic Bezier curve can be determined uniquely by two parameters λ , μ or λ,μ(see Fig. 2)on the diagram(fig. 3). The single inflexion curve in Fig. 3 represents the cases when the curve can be transformed into general cubic polynomial. The single inflexion region indicates the cases when the curve has only one inflexion point on ( 0, 1 )and another is not on ( 0, 1 ).We may obtain the parameter uc of cusp, uI of inflexion point and u1, u2 of double point.By using plotting theorem we can also make the conclusion that a space cubic Bezier curve has not cusp, double point and its spiral direction doesn't change.
Shi Fazhong;Wu Junheng. BEZIER'S PLOTTING THEOREM AND GEOMETRICAL CHARACTERISTICS OF CUBIC BEZIER CURVES[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1982, 3(3): 97-104.
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