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Degrafa Quadratic Hermite Spline

September 17, 2009

The quadratic Hermite spline is now available in the Origin branch.  It works pretty much like any of the other splines with the exception of the method to manually assign the start tangent.  The default is automatic selection of start tangent, which uses the reflection discussed in this post.  A screenshot is provided below.

Automatic Selection of Start Tangent

Automatic Selection of Start Tangent

The blue curve results from plotting the low-level utility upon which the Degrafa spline is based.  It is plotted old-school, point-to-point with manual start tangent.  The red curve is the Degrafa spline fitting the same set of points in MXML with automatic selection of start tangent, and approximated by quadratic Beziers in the Degrafa command stack.

The relevant MXML is

<?xml version="1.0" encoding="utf-8"?>
 <mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"
 xmlns:paint="com.degrafa.paint.*"
 xmlns:splines="com.degrafa.geometry.splines.*"
 layout="absolute"
 width="600" height="500" >

 <mx:Canvas id="quadSpline" />
 <paint:SolidStroke id="redstroke" weight="2" color="#FF0000"/>
 <splines:QuadraticHermiteSpline id="hermiteSpline" graphicsTarget="{[quadSpline]}"
 stroke="{redstroke}" knots="90,250 250,230 330,320 410,250" />

The next screenshot shows what happens if the start tangent is arbitrarily set to the point (100,100).

Assigning 100,100 as the start tangent

Assigning 100,100 as the start tangent

The only change to the MXML is the line

<splines:QuadraticHermiteSpline id=”hermiteSpline” graphicsTarget=”{[quadSpline]}” stroke=”{redstroke}” knots=”90,250 250,230 330,320 410,250″ startTangent=”100,100″ />

A very wide variety of interesting curves can be created by changing knot coordinates and the start tangent point.  Update your SVN and enjoy🙂

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