Create transform to map from one rectangle to another?

问题:

What is the simplest way to create AffineTransform which maps coordinates from one rectangle to another (float/double rectangles are given)?

UPDATE 1

Rectangles can be absolutely different. For example [(0,0)-(1,1)] and [(150,-14)-(-1000,-14.1)]. And transformation should transform uniformly. For example, rectangle corners should be transformed one to one. For example coordinates (0,0) should turn to (150,-14).

UPDATE 2

I need AffineTransform object, not just calculation. Because I want to apply it to Graphics object. Also I would like to have in the form of some concatenation of simple transforms.

UPDATE 3

All the following 3 tests are failed:

public class RectangleTransformTest {      private static final double delta = 0.001;      Rectangle2D r1 = new Rectangle2D.Double(-1, 0, 2, 0.01);     Rectangle2D r2 = new Rectangle2D.Double(10, 20, 400, 300);      AffineTransform t;      Point2D src;     Point2D dst1, dst2;      @Test     public void test1() {          t = new AffineTransform();         t.translate(+r2.getMinX()-r1.getMinX(), +r2.getMinY()-r1.getMinY());         t.scale(r2.getWidth()/r1.getWidth(), r2.getHeight()/r1.getHeight());      }      @Test     public void test2() {          t = new AffineTransform();          t.scale(r2.getWidth()/r1.getWidth(), r2.getHeight()/r1.getHeight());         t.translate(+r2.getMinX()-r1.getMinX(), +r2.getMinY()-r1.getMinY());      }      @Test     public void test3() {          t = new AffineTransform();          t.scale((r2.getMaxX()-r2.getMinX())/(r1.getMaxX()-r1.getMinX()), (r2.getMaxY()-r2.getMinY())/(r1.getMaxY()-r1.getMinY()));         t.translate(+r2.getMinX()-r1.getMinX(), +r2.getMinY()-r1.getMinY());      }      @After     public void comparePoints() {          src = new Point2D.Double(r1.getMinX(), r1.getMinY());         dst1 =  new Point2D.Double();         t.transform(src, dst1);         dst2 = new Point2D.Double(r2.getMinX(), r2.getMinY());          assertEquals(dst2.getX(), dst1.getX(), delta);         assertEquals(dst2.getY(), dst1.getY(), delta);          src = new Point2D.Double(r1.getMinX(), r1.getMaxY());         dst1 =  new Point2D.Double();         t.transform(src, dst1);         dst2 = new Point2D.Double(r2.getMinX(), r2.getMaxY());          assertEquals(dst2.getX(), dst1.getX(), delta);         assertEquals(dst2.getY(), dst1.getY(), delta);          src = new Point2D.Double(r1.getMaxX(), r1.getMinY());         dst1 =  new Point2D.Double();         t.transform(src, dst1);         dst2 = new Point2D.Double(r2.getMaxX(), r2.getMinY());          assertEquals(dst2.getX(), dst1.getX(), delta);         assertEquals(dst2.getY(), dst1.getY(), delta);          src = new Point2D.Double(r1.getMaxX(), r1.getMaxY());         dst1 =  new Point2D.Double();         t.transform(src, dst1);         dst2 = new Point2D.Double(r2.getMaxX(), r2.getMaxY());          assertEquals(dst2.getX(), dst1.getX(), delta);         assertEquals(dst2.getY(), dst1.getY(), delta);      }  } 

回答1:

To transform from [(a,b)-(c,d)] to [(e,f)-(g,h)] you can perform the following computation:

x' = e + (x - a) * (g - e) / (c - a); y' = f + (y - b) * (h - f) / (d - b); 

Here is the corresponding AffineTransform code, where r1 is being transformed to r2:

t = new AffineTransform(); t.translate(r2.getMinX(), r2.getMinY()); t.scale(r2.getWidth()/r1.getWidth(), r2.getHeight()/r1.getHeight());     t.translate(-r1.getMinX(), -r1.getMinY()); 

文章来源: Create transform to map from one rectangle to another?