## Demos

Online demos are interactive demonstrations of individual concepts in applied mathematics, mostly from the areas of numerical analysis and computational geometry. Interactive feedback reinforces mathematical principals and can be helpful in enhancing the understanding of complex formulas. Actual demo topics are largely a function of reader feedback.

For Degrafa-specific demos and tutorials, check the Degrafa page.  For specific posts detailing client work, click on the ‘Portfolio’ post category.

Spark/Flex 4 demos

Tron Clock – Styling, skinning, dynamic drawing, integration of artist-generated assets … and more 🙂

Custom Animation Clases and Path Animation – How to create a custom Spark Animation applied to path animation.

FlashBuilder and PureMVC series, which covers creating Actionscript components in Flex.

Demo::Dynamic Bezier Spline Scroller – Illustrate the use of a quadratic Bezier spline to dynamically draw an organic scroller track and thumb.  Companion demo illustrates how to use splines to bound the width of an element.

Demo::Bezier Curvature Explorer – Illustrates computation of the extrinsic curvature of a quadratic Bezier curve, natural parameter at maximum curvature, and displays osculating circle.

Demo::Spline Parameterization – Illlustrates the difference between uniform and arc-length parameterization of a cubic bezier spline (composite curve).

Demo::Quadratic Bezier Parameterization – illustrates the difference in natural vs arc-length parameterization for a simple quadratic Bezier curve. Shows some issues with approximate arc-length parameterization.

Demo::Quad. Bezier 3-Point Interpolation – Illustrates how parameterization can affect the shape of the curve. Midpoint, chord-length, and arbitrary parameterizations are simulaneously illustrated. The classic formula is not all you may think 🙂

Demo::Catmull-Rom Spline Animation – a simple demo illustrating how to animation a C-R spline from beginning to end in an ENTER_FRAME handler.

Demo::Closed-Loop Catmull-Rom spline – a simple method for setting outer control points for a smooth, continuous-loop Catmull-Rom spline.

Demo::Path Animation with Papervision 3D – a simple demo illustrating path animation with Papervision 3D and the 3D Catmull-Rom spline.

Demo::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).

Demo::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.

Demo::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.

Demo::Papervision Renderable Spline with Path Following – get Phunky, baby. This demo illustrates the new Singularity PV3DSpline class which uses methods from the Phunky branch to draw splines in 3D space with some path following control.

Demo::Quadratic Bezier y at x – Illustrates the quadratic Bezier’s yAtX() method, returning the (t,y) values for a specified x-coordinate on a quadratic Bezier curve.

Demo::Cubic Bezier y at x – Illustrates the quadratic Bezier’s yAtX() method, returning the (t,y) values for a specified x-coordinate on a quadratic Bezier curve.

Demo::Closest Point on a Cubic Bezier – Illustrates the classic Graphic Gems algorithm for computing the closest point on a cubic Bezier to an arbitrary point.

Demo::Closest Point on a Quadratic Bezier – Classic Graphic Gems algorithm for computing the closest point on a cubic Bezier to an arbitrary point, extended to work with quad. Beziers.

Demo::Easing Along a Cubic Bezier Curve – Penner easing functions applied to easing along a parametric curve. Another practical application of arc-length parameterization.

1. October 15, 2008 at 9:13 pm

Those closest point demos are awesome. Any idea how to calculate the closest point on a Catmull Rom? Can’t find an example anywhere…

2. July 16, 2011 at 6:15 am

hello，I am from china，What is your code is open book how to write it results？

1. December 17, 2008 at 10:12 am