These interactive demos illustrate various concepts in applied mathematics. Most initial examples are from the field of computational geometry. All demos required the Flash 9 player.
:: Parameterization Demo - Illustrate the difference bewteen uniform and arc-length parameterization on a cubic Bezier spline.
::Quadratic Bezier Parameterization - illustrates the difference in natural vs arc-length parameterization for a simple quadratic Bezier curve.
::Quad. Bezier, 3-point interpolation - The classic formula familiar to many Flash programmers is actually a simplified version of a more general parameterization, called 'midpoint' parameterization or 'midpoint interpolation'. The more general formula is discussed in the Cubic Bezier TechNote. This demo illustrates the difference between midpoint, chord-length, and arbitrary parameterizations.
::Catmull-Rom Spline animation - a simple example illustrating the animation of a Catmull-Rom spline from beginning to end, as if it were being drawn by hand. Also a subtle introduction to spline parameterization.
::Closed-Loop Catmull-Rom spline - a simple method for setting outer control points for a smooth, continuous-loop Catmull-Rom spline.
::Path Animation with Papervision 3D - a simple demo illustrating path animation with Papervision 3D and the 3D Catmull-Rom spline.
::Lemniscate of Bernoulli - how to use a closed-loop Catmull-Rom spline to animate sprites around a Lemniscate of Bernoulli (infinity or fiture-8 shape).
::Papervision 3D Figure-8's- builds upon the 2D Lemniscate of Bernoulli example to animate markers along figure-8 paths in the XY, XZ, and YZ planes.
::Papervision 3D Path Animation from 3ds max - uses spline data exported from 3ds max (in XML) and the Singularity 3D Bezier spline for path animation in Papervision 3D.
::Quadratic Bezier y at x - computes (t,y) values along a quadratic Bezier curve at a given x-coordinate.
::Cubic Bezier y at x - computes (t,y) values along a cubic Bezier curve at a given x-coordinate.
::Closest Point on Cubic - closest point on a cubic Bezier to an arbitrary point (port of class Graphic Gem algorithm).
::Closest Point on Quadratic - closest point on a quadratic Bezier to an arbitrary point (Graphic Gem algorithm generalized to work with quads or cubics).
::Easing Along a Cubic Bezier Curve- Penner easing functions applied to easing along a parametric curve. Another practical application of arc-length parameterization.
::Cubic Bezier 4-point Interpolation-Interpolating four points with a cubic Bezier curve.