transform update for generic transforms (#60)

Co-authored-by: Todd Keeler <tdk@meta.com>

Author: tdk-meta

examples/transforms.rs

@@ -34,11 +34,10 @@ fn main() {
     // Create transformation matrix
     let x = 0.5 * (cameraman.cols() as f64) - 0.5;
     let y = 0.5 * (cameraman.rows() as f64) - 0.5;
-    let trans = rotate_around_centre(FRAC_PI_4, (x, y)).dot(&scale(0.7, 0.7));
+    let trans =
+        transform_from_2dmatrix(rotate_around_centre(FRAC_PI_4, (x, y)).dot(&scale(0.7, 0.7)));
 
-    let transformed = cameraman
-        .transform(trans.view(), None)
-        .expect("Transform failed");
+    let transformed = cameraman.transform(&trans, None).expect("Transform failed");
 
     // save
     let path = Path::new("transformed_cameraman.png");

src/transform/affine.rs

@@ -1,23 +1,94 @@
+use super::Transform;
 use ndarray::{array, prelude::*};
+use ndarray_linalg::Inverse;
 
+/// converts a matrix into an equivalent `AffineTransform`
+pub fn transform_from_2dmatrix(in_array: Array2<f64>) -> AffineTransform {
+    let transform = match in_array.inv() {
+        Ok(inv) => AffineTransform {
+            matrix2d_transform: in_array.clone(),
+            matrix2d_transform_inverse: inv,
+            inverse_exists: true,
+        },
+        Err(e) => AffineTransform {
+            matrix2d_transform: in_array.clone(),
+            matrix2d_transform_inverse: Array2::zeros((2, 2)),
+            inverse_exists: false,
+        },
+    };
+    return transform;
+}
+
+/// a linear transform of an image represented by either size 2x2
+/// or 3x3 ( right column is a translation and projection ) matrix applied to the image index
+/// coordinates
+pub struct AffineTransform {
+    matrix2d_transform: Array2<f64>,
+    matrix2d_transform_inverse: Array2<f64>,
+    inverse_exists: bool,
+}
+
+fn source_coordinate(p: (f64, f64), trans: ArrayView2<f64>) -> (f64, f64) {
+    let p = match trans.shape()[0] {
+        2 => array![[p.0], [p.1]],
+        3 => array![[p.0], [p.1], [1.0]],
+        _ => unreachable!(),
+    };
+
+    let result = trans.dot(&p);
+    let x = result[[0, 0]];
+    let y = result[[1, 0]];
+    let w = match trans.shape()[0] {
+        2 => 1.0,
+        3 => result[[2, 0]],
+        _ => unreachable!(),
+    };
+    if (w - 1.0).abs() > std::f64::EPSILON {
+        (x / w, y / w)
+    } else {
+        (x, y)
+    }
+}
+
+impl Transform for AffineTransform {
+    fn apply(&self, p: (f64, f64)) -> (f64, f64) {
+        return source_coordinate(p, self.matrix2d_transform.view());
+    }
+
+    fn apply_inverse(&self, p: (f64, f64)) -> (f64, f64) {
+        return source_coordinate(p, self.matrix2d_transform_inverse.view());
+    }
+
+    fn inverse_exists(&self) -> bool {
+        return self.inverse_exists;
+    }
+}
+
+/// describes the Axes to use in rotation_3d
+/// X and Y correspond to the image index coordinates and
+/// Z is perpendicular out of the image plane
 pub enum Axes {
     X,
     Y,
     Z,
 }
 
+/// generates a 2d matrix describing a rotation around a 2d coordinate
 pub fn rotate_around_centre(radians: f64, centre: (f64, f64)) -> Array2<f64> {
     translation(centre.0, centre.1)
         .dot(&rotation_3d(radians, Axes::Z))
         .dot(&translation(-centre.0, -centre.1))
 }
 
+/// generates a matrix describing 2d rotation around origin
 pub fn rotation_2d(radians: f64) -> Array2<f64> {
     let s = radians.sin();
     let c = radians.cos();
     array![[c, -s], [s, c]]
 }
 
+/// generates a 3x3 matrix describing a rotation around either the index coordinate axes
+/// (X,Y) or in the perpendicular axes to the image (Z)
 pub fn rotation_3d(radians: f64, ax: Axes) -> Array2<f64> {
     let s = radians.sin();
     let c = radians.cos();
@@ -29,14 +100,17 @@ pub fn rotation_3d(radians: f64, ax: Axes) -> Array2<f64> {
     }
 }
 
+/// generates a matrix describing translation in the image index space
 pub fn translation(x: f64, y: f64) -> Array2<f64> {
     array![[1.0, 0.0, x], [0.0, 1.0, y], [0.0, 0.0, 1.0]]
 }
 
+/// generates a matrix describing scaling in image index space
 pub fn scale(x: f64, y: f64) -> Array2<f64> {
     array![[x, 0.0, 0.0], [0.0, y, 0.0], [0.0, 0.0, 1.0]]
 }
 
+/// generates a matrix describing shear in image index space
 pub fn shear(x: f64, y: f64) -> Array2<f64> {
     array![[1.0, x, 0.0], [y, 1.0, 0.0], [0.0, 0.0, 1.0]]
 }