This example illustrates how to use a closed-loop Catmull-Rom spline to animate square markers along a figure-8 path using Papervision 3D. It was generated using the PV3D 1.5 release. Working with the source code requires a bit of prior knowledge of how to use PV3D with FlexBuilder.

The code builds on the 2D Lemniscate of Bernoulli example. Three splines are used to aproximate figure-8 paths in the XY, XZ, and YZ planes. Arc-length parameterization is used to animate along the path with constant velocity.

Click the 'Animate' button to watch a series of ten markers animate along each of the three paths.

This example requires the Flash™ 9 player.

For further reading,

:: Catmull-Rom Splines - An introduction to Catmull-Rom Splines.

:: Arc-Length Parameterization - Introduction to curve parameterization and how to reparameterize a curve on arc length. Techniques applied to a Catmull-Rom spline. Examples include how to distribute sprites evenly along a curve and path animation (including path following and orientation).

:: Arc Length of a Catmull-Rom Spline - Arc Length of parametric curves and derivative evaluation, applied to Catmull-Rom splines.

Source Code. Download the Singularity package (this example is in Singularity/demos/P3D/PV3DFigure8.mxml). You must install the PV3D 1.5 code and make sure the Canvas3D.as file is in the org.papervision3d.flex folder. The Figure8.as file must be placed in the org.papervision3d.examples folder.

You may obtain more PV3D AS3 example source from the SVN repository.