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I am trying to figure out how to apply the proper sequence of translate and scale commands (or a single .transform command) so that the default pixel grid (0,0,1920,1080) for instance is setup so that the coordinate system (minx,miny,maxx,maxy) can be used where for instance minx=100 maxx=200 miny=-5 maxy=5

I am trying to render mathematical functions and map the results to pixels and use the mouse to select certain regions to zoom in on.. my current code is at

https://bitbucket.org/stephenc214/fastmath/src/default/src/fastmath/fx/HardyZMap.java

I would really appreciate any help... I know this is simple but I just can't seem to get it to work properly

crow
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2 Answers2

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You can map [x, y] pixel coordinates in an image of size [width, height] to your given range as follows:

x'=minx+(maxx-minx)*(x+0.5)/width;
y'=miny+(maxy-miny)*(y+0.5)/height;
JarkkoL
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  • I'm looking for the inverse of that. but cant do it that way.. need to do it as an affine transform. I'm setting up the coordinate system apriori with translate() and scale commands applied to the http://docs.oracle.com/javafx/2/api/javafx/scene/canvas/GraphicsContext.html associated with the Canvas object which takes up the whole window and whose coordinate (0,0) is the upper-left hand of the window... currently im using something like this 
    gc.restore();
gc.translate( 0, height / 2 );
gc.scale( width / xrange, height / yrange )
gc.translate( -minx, 0 );
    – crow Nov 15 '16 at 05:13
  • Usually you don't want the inverse to map each pixel on the screen exactly once to your function. Here's similar question to yours: http://computergraphics.stackexchange.com/questions/4193/what-is-the-correct-order-of-transformations-scale-rotate-and-translate-and-why/4194#4194 Would have voted for close, but this is a more generic answer. – JarkkoL Nov 15 '16 at 13:30
  • Thank you. I'm actually doing the opposite of that, I'm looping thru each pixel x,y and mapping that to precisely one point in the complex plane to evaluate something like the Mandelbrot set. Also, the mouse click handler returns point clicked in pixels, and I need to map that onto the complex plane as well. I realize each "pixel" is actually a rectangle on the complex plane but the resolution is small enough that just sampling the center of this rectangle is fine for display purposes. – crow Nov 15 '16 at 22:04
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import javafx.scene.canvas.GraphicsContext;
import javafx.scene.transform.Affine;
import javafx.scene.transform.NonInvertibleTransformException;
double xrange = maxx - minx;
double yrange = maxy - miny;
// width and height are in units of pixels
// gc is the GraphicsContext object from javafx
Affine t = new Affine();
double xratio = xrange / width;
double yratio = yrange / height;
t.appendTranslation( minx, miny );
t.appendScale( xratio, yratio );
try
{
  t.invert();
}
catch( NonInvertibleTransformException e )
{
  throw new RuntimeException( e.getMessage(), e );
}
gc.setTransform( t );
crow
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