Optimize the transformRect and transformPoint methods in matrix_utils. (#36396)

Primarily these methods no longer allocate any objects other than their
return values.

Additionally, the math in the methods is reduced compared to the general
case math based on known input conditions.

packages/flutter/test/painting/matrix_utils_test.dart

@@ -121,4 +121,78 @@ void main() {
       forcedOffset,
     );
   });
+
+  test('transformRect with no perspective (w = 1)', () {
+    const Rect rectangle20x20 = Rect.fromLTRB(10, 20, 30, 40);
+
+    // Identity
+    expect(
+      MatrixUtils.transformRect(Matrix4.identity(), rectangle20x20),
+      rectangle20x20,
+    );
+
+    // 2D Scaling
+    expect(
+      MatrixUtils.transformRect(Matrix4.diagonal3Values(2, 2, 2), rectangle20x20),
+      const Rect.fromLTRB(20, 40, 60, 80),
+    );
+
+    // Rotation
+    expect(
+      MatrixUtils.transformRect(Matrix4.rotationZ(pi / 2.0), rectangle20x20),
+      within<Rect>(distance: 0.00001, from: const Rect.fromLTRB(-40.0, 10.0, -20.0, 30.0)),
+    );
+  });
+
+  test('transformRect with perspective (w != 1)', () {
+    final Matrix4 transform = MatrixUtils.createCylindricalProjectionTransform(
+      radius: 10.0,
+      angle: pi / 8.0,
+      perspective: 0.3,
+    );
+
+    for (int i = 1; i < 10000; i++) {
+      final Rect rect = Rect.fromLTRB(11.0 * i, 12.0 * i, 15.0 * i, 18.0 * i);
+      final Rect golden = _vectorWiseTransformRect(transform, rect);
+      expect(
+        MatrixUtils.transformRect(transform, rect),
+        within<Rect>(distance: 0.00001, from: golden),
+      );
+    }
+  });
+}
+
+// Produces the same computation as `MatrixUtils.transformPoint` but it uses
+// the built-in perspective transform methods in the Matrix4 class as a
+// golden implementation of the optimized `MatrixUtils.transformPoint`
+// to make sure optimizations do not contain bugs.
+Offset _transformPoint(Matrix4 transform, Offset point) {
+  final Vector3 position3 = Vector3(point.dx, point.dy, 0.0);
+  final Vector3 transformed3 = transform.perspectiveTransform(position3);
+  return Offset(transformed3.x, transformed3.y);
+}
+
+// Produces the same computation as `MatrixUtils.transformRect` but it does this
+// one point at a time. This function is used as the golden implementation of the
+// optimized `MatrixUtils.transformRect` to make sure optimizations do not contain
+// bugs.
+Rect _vectorWiseTransformRect(Matrix4 transform, Rect rect) {
+  final Offset point1 = _transformPoint(transform, rect.topLeft);
+  final Offset point2 = _transformPoint(transform, rect.topRight);
+  final Offset point3 = _transformPoint(transform, rect.bottomLeft);
+  final Offset point4 = _transformPoint(transform, rect.bottomRight);
+  return Rect.fromLTRB(
+    _min4(point1.dx, point2.dx, point3.dx, point4.dx),
+    _min4(point1.dy, point2.dy, point3.dy, point4.dy),
+    _max4(point1.dx, point2.dx, point3.dx, point4.dx),
+    _max4(point1.dy, point2.dy, point3.dy, point4.dy),
+  );
+}
+
+double _min4(double a, double b, double c, double d) {
+  return min(a, min(b, min(c, d)));
+}
+
+double _max4(double a, double b, double c, double d) {
+  return max(a, max(b, max(c, d)));
 }