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1. Re: Transform shape
James_D Jan 2, 2013 3:42 AM (in response to user8929955)user8929955 wrote:
You can't use Affine Transformations to map a rectangle into an arbitrary quadrilateral. Affine Transformations preserve parallelism: so you can only transform a rectangle into another parallelogram.
I'm trying to figure out how to create a transformation to deform a rectangle into a quadrangle, where one corner stays the same. The basic mathematical solution is clear as described in [this Wiki articlehttp://en.wikipedia.org/wiki/Affine_transformation] .
There are two questions I would like to pose:
The API defines Affine Transformations, and then Translations, Scales, Rotations, and Shears. You can (if I remember my Linear Algebra correctly) construct any Affine Transformation by composing translations, scale transformations, rotations, and shears. There's no API for nonaffine transformations that I am aware of.
1. Has anyone done this already?
2. Basically this could also be achieved by concatenating simpler transformation (scale, rotation, projection). While scale and rotation is available in JavaFX I wonder how to define projection in a simple way? Projection in this context would mean that I have one edge and then scale the opposing edge in or outward. This would make a trapeze out of the rectangle. How would such a transformation matrix look like? 
2. Re: Transform shape
jsmith Jan 2, 2013 7:19 AM (in response to user8929955)Assuming it's a perspective projection you want . . .1 person found this helpful
Do a PerspectiveTransform on your shape.
http://docs.oracle.com/javafx/2/api/javafx/scene/effect/PerspectiveTransform.html
Or (simplest) enable the PerspectiveCamera on your Scene and set different z coordinates for the corners of your shape.
http://docs.oracle.com/javafx/2/api/javafx/scene/PerspectiveCamera.html
If you want the mathematics behind the perspective camera or want to do perspective calculations to setup your PerspectiveTransform then you can look at:
http://en.wikipedia.org/wiki/Perspective_projection#Perspective_projection (unless you are really keen, just use the simple formula from the Diagram section of the article). 
3. Re: Transform shape
user8929955 Jan 4, 2013 8:51 AM (in response to jsmith)Thanks for your replies, especially the link
http://docs.oracle.com/javafx/2/api/javafx/scene/effect/PerspectiveTransform.html
was helpful. That was exactly what I was looking for. I then took it one step further, as I needed the transformed shapes to be clickable. I documented this in the following three blog entries:
http://sahits.ch/blog/?p=2286 (JavaFX: Deformation)
http://sahits.ch/blog/?p=2307 (JavaFX: Deformation with offscreen image)
http://sahits.ch/blog/?p=2314 (JavaFX: Perspective Transformation)