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Degrafa Cardinal Spline

October 20, 2009

The Degrafa Cardinal spline is now available from the Origin branch.  Usage is very similar to the Catmull-Rom spline with the exception of the tension parameter.  The Cardinal spline is based on the C-R code base, so it supports closure.  The algorithm is the same as the C-R spline, so it is best used for tensions in the [0,1] range.  For example,

<mx:Application xmlns:mx=”http://www.adobe.com/2006/mxml&#8221;
xmlns:comp=”components.*”
xmlns:degrafa=”com.degrafa.*”
xmlns:paint=”com.degrafa.paint.*”
xmlns:geom=”com.degrafa.geometry.*”
xmlns:splines=”com.degrafa.geometry.splines.*”
layout=”absolute”
width=”600″ height=”500″
pageTitle=”Cardinal Spline”
applicationComplete=”test()” viewSourceURL=”srcview/index.html”>

.
.
.

<paint:SolidStroke id=”redstroke” weight=”2″ color=”#FF0000″/>

<splines:CardinalSpline id=”crspline” graphicsTarget=”{[splineLayer1]}” stroke=”{redstroke}” knots=”453,159 350,302 218,202 146,297 400,110″ tension=”0″ closed=”true” />

produces the same fit as the Catmull-Rom spline,

Closure with Zero Tension

Closure with Zero Tension

Changing the tension to 1 ‘pulls’ the spline to the point where the fit is line-to-line,

<splines:CardinalSpline id=”crspline” graphicsTarget=”{[splineLayer1]}” stroke=”{redstroke}” knots=”453,159 350,302 218,202 146,297 400,110″ tension=”1″ closed=”true” />

Closure with Tension = 1

Closure with Tension = 1

Tensions in the range -1 to 3 are supported.  Negative tension ‘loosens’ the fit.  Tensions greater than 1 cause the spline to loop in on itself going into and out of each knot.  The effect at initial and terminal knots depends on how the auxiliary control points are chosen (same options as the C-R spline).

Splines are open by default.  For example,

<splines:CardinalSpline id=”crspline” graphicsTarget=”{[splineLayer1]}” stroke=”{redstroke}” knots=”453,159 350,302 218,202 146,297 400,110″ tension=”-0.5″ />

produces the following

Loosening the tension in a Cardinal spline

Loosening the tension in a Cardinal spline

I’m preparing for a long business trip, so posts and Degrafa updates will be sparse over the next several weeks.

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