# Images and Transformations

Here is an example where images are combined with transformations.
The point *offset* determines the lower left corner of the image.
Additionally the point *offset* (p0) determines the position of the point *rotate+scale* (p1).
This is realized by defining the transformation *tOff*. It is a translation by the vector *offset*.

The transformation *tRot* rotates the images around the point *offset*. For this, the angle (slope) of the line
[p0,p1] is determined.

Finally, we scale the image with the help of the point *rotate+scale*.
This is done by moving the lower left corner of the image back to the origin. This is necessary, because
all transformatiuon start from the origin. Then, the scaling is done and the image is moved back to its original position.

### The JavaScript code

Here is the complete code to accomplish this behaviour.

```
var brd = JXG.JSXGraph.initBoard('box1', {boundingbox:[-5,5,5,-5], axis:true});
var urlImg = "http://jsxgraph.uni-bayreuth.de/distrib/images/uccellino.jpg";
var p0 = brd.create('point', [-2,-1], {size:8, name:'offset', opacity:0.3});
// Initially we put the lower left corner of the image to (0,0) and
// p1 to (3,0)
// After applying the transformation tOff to the image and the point p1, they are moved to
// (-2,-1) and (1,-1), respectively.
var p1 = brd.create('point', [3,-1], {size:8, name:'rotate+scale', opacity:0.3});
var im = brd.create('image',[urlImg, [0,0], [3,3]]);
var li = brd.create('segment', [p0,p1], {dash:2}); // Just for illustration
//
// Translate image and point "rotate+scale" by dragging point "offset"
var tOff = brd.create('transform', [function(){return p0.X()},function(){return p0.Y()}], {type:'translate'});
tOff.bindTo(im);
tOff.bindTo(p1);
// Rotate image around point "offset" by dragging point "rot+scale"
var tRot = brd.create('transform', [function(){return Math.atan2(p1.Y()-p0.Y(),p1.X()-p0.X())}, p0], {type:'rotate'});
tRot.bindTo(im);
// Scale image by dragging point "rot+scale"
// We do this by moving the image back to the origin (inverse of transformation tOff),
// then scale the image (because scaling "starts from (0,0))
// Finally, we move the image back to point "Offset"
// The scaling factor is divided by three, because the original image size is (3,3).
var tOffInv = brd.create('transform', [function(){return -p0.X()},function(){return -p0.Y()}], {type:'translate'});
var tScale = brd.create('transform', [function(){return p1.Dist(p0)/3;},
function(){return p1.Dist(p0)/3;}], {type:'scale'});
tOffInv.bindTo(im); tScale.bindTo(im); tOff.bindTo(im);
brd.update();
```