This library illustrates many practical Actionscript 3 concepts via the development of a 2D parametric curve library. The current library consists of a base set of Classes for constructing single-segment and composite (piecewise) parametric curves. For more information and regular updates, visit Jim Armstrong's personal blog.
Flex MXML files are provided to illustrate the application of the library. Check back often as I expect new Classes to be added.
Current Release (9/08): 1.0 - Baseline functionality is frozen - added cubic Bezier 4-point interpolation.
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All classes in the parametric curve library are in the Singularity package, which must be added to your path when building a new Flex project. The current package organization is as follows,
Singularity.Events
Dispatcher - Illustrates how to apply an event dispatcher via Composition
SingularityEvent - Common event management for all Classes in Singularity package
Singularity.Geom
Bezier - K-th order Bezier curve
Bezier2 - Base quadratic Bezier (includes 3-point, auto-parametrized interpolation)
Bezier3 - Base cubic Bezier with recursive midpoint subdivision for drawing
BezierFactory - Returns appropriate Bezier instance based on number of control points
BezierSpline - Piecewise cubic bezier that interpolates a set of knots
BezierSplineControl - Tangent construction control-point generation for bezier spline
CatmullRom - Catmull-Rom spline with uniform or arc-length parameterization
Composite - Base, pseudo-abstract class for composite or piecewise parametric curves
Coef - Manages creation, evaluation, and differentiation of a arbitrary-order polynomial
Cubic - Manages creation, evaluation, and differentiation of a cubic polynomial
CubicCage - Control cage for a single cubic segment in a piecewise Bezier curve
Ellipse - Arc-length parametrized Ellipse (useful for distributing sprites evenly around an ellipse
FastCubicSpline - Natural cubic spline without error checking and does not subclass Composite
FastBezier - Cubic bezier with customized subdivision trading quality for faster drawing
IParametric - Interface for all single-segment parametric curves
IPoly - Interface for polynomials of arbitrary degree
Knot - Visual representation of a point
Quad - Manages creation, evaluation, and differentiation of a quadratic polynomial
Spline3 - Natural cubic spline (non-overlapping intervals)
PSpline3 - Parametric cubic spline (abitrary knots)
Wedge - Draw pie-shaped wedges using quad. bezier for circular arcs
Singularity.Geom.P3D
The following methods have been ported for use in 3D applications such as Papervision 3D. Online demos for these methods and
those from the 2D Parameteric curve library, along with supporting TechNotes, may be found here.
BezierSpline
CatmullRom
Composite
Cubic
CubicCage
FastCubicSpline
FastBezier
IPoly
Knot
PV3DSpline - Spline designed to work with knot data exported from a package such as 3ds max
Singularity.Interactive
PointSelector - Enable point selection by mouse over a colored background 'drawing area'
RectangleSelector - Click and drag to define a rectangular selection inside 'drawing area'
Singularity.Numeric
Binomial - Generates Binomial coefficients (forward- and backward-recursion of Pascal's triangle)
Bisect - Recursive bisection method to isolate root in an interval
Consts - Absolute and machine-dependent constants
Gauss - Gauss-Legendre Integration
Newton - AS3 Implementation of Newton's method
Halley - AS3 Implementation of Halley's method
SimpleRoot - AS3 Implementation of Jack Crenshaw's TWBRF
Solve2x2 - Solves 2x2 systems of equations using Cramer's rule
Singularity.Utils
BezierUtils - Bezier utilities class (currently contains methods for general Bezier subdivision and closest point algorithm)
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Test programs consist of MXML files from which you may create a new project (make sure the Singularity package is in your build path). All MXML files are contained in the Singularity\demos folder.
BezierClosedSpline - Test driver for cubic Bezier spline with arc-length parameterization and closed-loop support (auto-closure)
BezierEasing - Penner easing functions applied to easing along a parametric curve with arc-length parametrization
BezierNumeric - Demo [in progress] to illustrate k-th order Bezier curves and compare naive formula vs. coefficient generation and numerical issues. Long-term goal is to illustrate general application of deCasteljau's method.
BezierSplineTest - Test driver for cubic Bezier spline
BezierParameterization - Illustrate difference between uniform and arc-length parameterization for a cubic bezier spline
BezierTest - Test driver for quadratic and cubic Bezier curves and BZFactory class
CatmullRomTest - Test driver for Catmull-Rom splline
ClosestToCubic - Closest point on a cubic Bezier to an arbitrary point
ClosestToQuad - Closest point on a quadratic Bezier to an arbitrary point
CRAnimation - Illustrate drawing C-R spline from beginning to end
CRClosedSpline - Illustrate closed-loop Catmull-Rom Spline
CRClosed2 - Closed-loop Catmull-Rom Spline used to approximate a figure-8 or infinity shape
CubicBezierInterpolation - Cubic Bezier, 4-point interpolation
EllipseTest - Test driver illustrating ellipse creation and parametrizations (polar and arc-length)
PSplineTest - Test driver for cubic parametric spline
SplineTest - Test driver for natural cubic spline
PathTween - Illustrates constant-velocity sprite animation along a Catmull-Rom spline
PathTween2 - Illustrates direct scripting of embedded image instead of mx:Image control
QuadInterpolation - Illustrates effect of parameterization on 3-point quad. Bezier interpolation
QuadBezierParam - Illustrates natural vs. arc-length parameterization of a quadratic Beizer curve
WedgeTest - Interactive drawing and modification of pie-shaped wedge
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The Singularity AS 3 parametric curve library requires the Flash 9 player and a development environment supporting Actionscript 3. All demonstration programs were created with FlexBuilder 2. The AS 3 parametric curve library is copyrighted and licensed for personal, experimental usage. Please contact me to obtain authorization for commercial use. My primary interest is to ensure that the library is not commericalized and resold as a standalone library or packaged as a standalone component.
The download includes the entire Singularity package (which includes the rigging classes).
Download library (.zip) here. Before running any example programs, place the Singularity package in your build path. |
AS 3 Parametric Curve Library