Difference between revisions of "Transformations"

From JSXGraph Wiki
Jump to navigationJump to search
Line 1: Line 1:
 
In JSXGraph it is possible to apply plane projective transformations to point elements. A projective transformation is a multiplication by a 3x3 matrix to the homogeneous coordinates of a point. To make life easier some standard transformation are predefined.
 
In JSXGraph it is possible to apply plane projective transformations to point elements. A projective transformation is a multiplication by a 3x3 matrix to the homogeneous coordinates of a point. To make life easier some standard transformation are predefined.
====Available transformation types====
+
===Available transformation types===
 
* Translation
 
* Translation
 
* Scaling
 
* Scaling
Line 8: Line 8:
 
* Generic transformation
 
* Generic transformation
  
====Using transformations====
+
===Using transformations===
 
There are three possibilities to apply transformations:
 
There are three possibilities to apply transformations:
* One point is the result of applying a transformation to another point.
+
====One point is the result of applying a transformation to another point.====
 
First, the transformation has to be time, for example
 
First, the transformation has to be time, for example
 
<source lang="javascript">
 
<source lang="javascript">
Line 27: Line 27:
 
</source>
 
</source>
  
* One-time application of a transformation to a point.
+
====One-time application of a transformation to a point.====
 
Here, we start with the same setting as above: There are points ''p1'', ''p2'' and the transformation ''t''.
 
Here, we start with the same setting as above: There are points ''p1'', ''p2'' and the transformation ''t''.
 
But here, ''p2'' is rotated once.  
 
But here, ''p2'' is rotated once.  

Revision as of 01:26, 15 February 2010

In JSXGraph it is possible to apply plane projective transformations to point elements. A projective transformation is a multiplication by a 3x3 matrix to the homogeneous coordinates of a point. To make life easier some standard transformation are predefined.

Available transformation types

  • Translation
  • Scaling
  • Reflection
  • Rotation
  • Shear transformation
  • Generic transformation

Using transformations

There are three possibilities to apply transformations:

One point is the result of applying a transformation to another point.

First, the transformation has to be time, for example

var p1 = board.create('point', [1,1], {style:6, name:'C'}); 
var t = board.create('transform', [Math.PI/3,p1], {type:'rotate'});  // angle, rotation center

The transformation t is the rotation by 60 degrees around the point p1. Alternatively, the rotation can also be defined by giving the name of the rotation center.

var p1 = board.create('point', [1,1], {style:6, name:'C'}); 
var t = board.create('transform', [Math.PI/3,'C'], {type:'rotate'});  // angle, rotation center

Now, two more points p2 and p3 are created. p3 has the coordinates of p2 rotated by 60 degrees around p1.

var p2 = board.create('point', [3,1]); 
var p3 = board.create('point', [p2,t]);

One-time application of a transformation to a point.

Here, we start with the same setting as above: There are points p1, p2 and the transformation t. But here, p2 is rotated once.

var p1 = board.create('point', [1,1], {style:6, name:'C'}); 
var t = board.create('transform', [Math.PI/3,'C'], {type:'rotate'});  // angle, rotation center
var p2 = board.create('point', [3,1]); 
t.applyOnce(p2);

If there are more than one point to be rotated, an array can be supplied

var p1 = board.create('point', [1,1], {style:6, name:'C'}); 
var t = board.create('transform', [Math.PI/3,'C'], {type:'rotate'});  // angle, rotation center
var p2 = board.create('point', [3,1]); 
var p3 = board.create('point', [4,1]); 
t.applyOnce([p2,p3]);
  • Points may have