2D Graphics - Techniques

A cubic spline curve is a piecewise cubic curve with continuous 2nd derivative.

Computing a curve to approximate data points is a problem encountered frequently in many applications in computer graphics, computer vision, CAD/CAM, and image processing. We present a novel and effcient method, called squared distance minimization (SDM), for computing a planar B-spline curve, closed or open, to approximate a target shape de?ned by a point cloud, i.e., a set of unorganized, possibly noisy data points. We show that SDM outperforms signifcantly other optimization methods used currently in common practice of curve fitting.

A good description of how to find the Cube Bezier control points given 4 points on the curve. If P0...P3 are 4 points known on your curve, then y0...y3 are the control points that define the Bezier Curve.

        [y0] = 1/27 * [ 27  0  0  0 ] * [ P0 ]
        [y1]                [  8 12  6  1 ]    [ P1 ]
        [y2]                [  1  6 12  8 ]    [ P2 ]
        [y3]                [  0  0  0 27 ]    [ P3 ]

Bezier Cubic Splines are an excellent and preferred method to draw the smooth continuous curves often found in typography, CAD/CAM, and graphics in general.