Reflect Geometric Node around arbitrary axis in JavaFX - javafx

Question

Is there a way in javafx to reflect/mirror a geometric node (line for example) around an arbitrary axis-- one that is user-defined?
I see rotation, scale, shear, and translation methods, but no reflect(mirror).
I stumpled upon a post that suggests using alignment Left to right , or Right to left, but it is not quit what I am looking for.
I didn't build the application yet to post sample code, as I am still looking for quite a few libraries before starting.
Any tips would be great from the community!
EDIT: Not sure how to add images to comments. I tried the code by James below, I get the result in the image below, but I am trying to get it where noted in read.

Answer 1

If you have a line segment defined by two points p1 and p2, then reflecting in that line segment is equivalent to
Translate p1 to the origin (T)
Rotate p2 to the positive x-axis (R)
Reflect in the x-axis (which you can do with a scale with x=1 and y=-1)
Inverse of R
Inverse of T
So this looks something like
private Transform createReflection(Point2D p1, Point2D p2) {
Translate translation = new Translate(-p1.getX(), -p1.getY());
double deltaX = p2.getX() - p1.getX();
double deltaY = p2.getY() - p1.getY();
Rotate rotate = new Rotate(-Math.toDegrees(Math.atan2(deltaY, deltaX)));
Scale scale = new Scale(1, -1);
Affine reflection = new Affine();
reflection.append(translation.createInverse());
try {
// not sure how a rotation could possibly be non-invertible:
reflection.append(rotate.createInverse());
} catch (NonInvertibleTransformException e) {
throw new RuntimeException(e);
}
reflection.append(scale);
reflection.append(rotate);
reflection.append(translation);
return reflection ;
}
SSCCE:
import javafx.application.Application;
import javafx.geometry.Point2D;
import javafx.scene.Group;
import javafx.scene.Scene;
import javafx.scene.layout.Pane;
import javafx.scene.shape.Line;
import javafx.scene.text.Text;
import javafx.scene.transform.Affine;
import javafx.scene.transform.NonInvertibleTransformException;
import javafx.scene.transform.Rotate;
import javafx.scene.transform.Scale;
import javafx.scene.transform.Transform;
import javafx.scene.transform.Translate;
import javafx.stage.Stage;
public class ArbitraryReflection extends Application {
#Override
public void start(Stage primaryStage) {
Text original = new Text("Through the looking glass");
original.relocate(200, 350);
Text reflected = new Text("Through the looking glass");
reflected.relocate(200, 350);
Group reflectedGp = new Group(reflected);
Point2D start = new Point2D(0, 400);
Point2D end = new Point2D(400, 150);
Line axis = new Line(start.getX(), start.getY(), end.getX(), end.getY());
Pane root = new Pane(original, reflectedGp, axis);
reflectedGp.getTransforms().add(createReflection(start, end));
Scene scene = new Scene(root, 400, 400);
primaryStage.setScene(scene);
primaryStage.show();
}
private Transform createReflection(Point2D p1, Point2D p2) {
Translate translation = new Translate(-p1.getX(), -p1.getY());
double deltaX = p2.getX() - p1.getX();
double deltaY = p2.getY() - p1.getY();
Rotate rotate = new Rotate(-Math.toDegrees(Math.atan2(deltaY, deltaX)));
Scale scale = new Scale(1, -1);
Affine reflection = new Affine();
reflection.append(translation.createInverse());
try {
// not sure how a rotation could possibly be non-invertible:
reflection.append(rotate.createInverse());
} catch (NonInvertibleTransformException e) {
throw new RuntimeException(e);
}
reflection.append(scale);
reflection.append(rotate);
reflection.append(translation);
return reflection ;
}
public static void main(String[] args) {
launch(args);
}
}