Animation of the construction of a fifth-order Bézier curve
Bézier curves are widely used in computer graphics to model smooth curves. As the curve is completely contained in the convex hull of its control points, the points can be graphically displayed and used to manipulate the curve intuitively.
Reference:
http://math.stackexchange.com/questions/1032883/maximum-of-a-5th-order-bezier-curve-with-restrictions
Animation via wikipedia commons
#math #animation #beziercurve
I have to go back and study bezier curves. The primary curve in this, as a product of the the visible control points, is straight forward, but the rest of what's going on has me lost.
ReplyDeleteScott: it is common to use a matrix representation of spline interpolation over a “polyline“ of control points. But this is a recursive geometric construction. Watch the green circles, they each linearly interpolate along one edge of the gray polyline. Connect two adjacent green circles with a green line, then simultaneously linearly interpolate along that to trace out a green parabola (quadratic curve). It touches (“interpolates”) vertices 0 and 2 while “approximating” vertex 1. Repeat this process on the green polyline to form blue cubic splines, then purple quartic curves, and finally the orange/red quintic.
ReplyDeleteOh yeah I think I see it now. The lines from the recursive interpolation points are sort of bounding the points along the curve.
ReplyDelete