[Core] Move Rect2 and Transform2D to their own files

Math2D includes Transform2D, which includes Rect2, which includes Vector2.

1 files changed, 201 insertions, 0 deletions

diff --git a/core/math/transform_2d.h b/core/math/transform_2d.h
new file mode 100644
index 0000000000..bf73755f0d
--- /dev/null
+++ b/core/math/transform_2d.h
@@ -0,0 +1,201 @@
+/*************************************************************************/
+/*  transform_2d.h                                                       */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md)    */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef TRANSFORM_2D_H
+#define TRANSFORM_2D_H
+
+#include "rect2.h" // also includes vector2, math_funcs, and ustring
+
+struct Transform2D {
+	// Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper":
+	// M = (elements[0][0] elements[1][0])
+	//     (elements[0][1] elements[1][1])
+	// This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i].
+	// Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here.
+	// This requires additional care when working with explicit indices.
+	// See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
+
+	// Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
+	// and angle is measure from +X to +Y in a clockwise-fashion.
+
+	Vector2 elements[3];
+
+	_FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
+	_FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return elements[0][1] * v.x + elements[1][1] * v.y; }
+
+	const Vector2 &operator[](int p_idx) const { return elements[p_idx]; }
+	Vector2 &operator[](int p_idx) { return elements[p_idx]; }
+
+	_FORCE_INLINE_ Vector2 get_axis(int p_axis) const {
+		ERR_FAIL_INDEX_V(p_axis, 3, Vector2());
+		return elements[p_axis];
+	}
+	_FORCE_INLINE_ void set_axis(int p_axis, const Vector2 &p_vec) {
+		ERR_FAIL_INDEX(p_axis, 3);
+		elements[p_axis] = p_vec;
+	}
+
+	void invert();
+	Transform2D inverse() const;
+
+	void affine_invert();
+	Transform2D affine_inverse() const;
+
+	void set_rotation(real_t p_rot);
+	real_t get_rotation() const;
+	_FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale);
+	void rotate(real_t p_phi);
+
+	void scale(const Size2 &p_scale);
+	void scale_basis(const Size2 &p_scale);
+	void translate(real_t p_tx, real_t p_ty);
+	void translate(const Vector2 &p_translation);
+
+	real_t basis_determinant() const;
+
+	Size2 get_scale() const;
+
+	_FORCE_INLINE_ const Vector2 &get_origin() const { return elements[2]; }
+	_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { elements[2] = p_origin; }
+
+	Transform2D scaled(const Size2 &p_scale) const;
+	Transform2D basis_scaled(const Size2 &p_scale) const;
+	Transform2D translated(const Vector2 &p_offset) const;
+	Transform2D rotated(real_t p_phi) const;
+
+	Transform2D untranslated() const;
+
+	void orthonormalize();
+	Transform2D orthonormalized() const;
+
+	bool operator==(const Transform2D &p_transform) const;
+	bool operator!=(const Transform2D &p_transform) const;
+
+	void operator*=(const Transform2D &p_transform);
+	Transform2D operator*(const Transform2D &p_transform) const;
+
+	Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const;
+
+	_FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const;
+	_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const;
+	_FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const;
+	_FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const;
+	_FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const;
+	_FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const;
+
+	operator String() const;
+
+	Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) {
+
+		elements[0][0] = xx;
+		elements[0][1] = xy;
+		elements[1][0] = yx;
+		elements[1][1] = yy;
+		elements[2][0] = ox;
+		elements[2][1] = oy;
+	}
+
+	Transform2D(real_t p_rot, const Vector2 &p_pos);
+	Transform2D() {
+		elements[0][0] = 1.0;
+		elements[1][1] = 1.0;
+	}
+};
+
+Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const {
+
+	return Vector2(
+			tdotx(p_vec),
+			tdoty(p_vec));
+}
+
+Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const {
+
+	return Vector2(
+			elements[0].dot(p_vec),
+			elements[1].dot(p_vec));
+}
+
+Vector2 Transform2D::xform(const Vector2 &p_vec) const {
+
+	return Vector2(
+				   tdotx(p_vec),
+				   tdoty(p_vec)) +
+		   elements[2];
+}
+Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const {
+
+	Vector2 v = p_vec - elements[2];
+
+	return Vector2(
+			elements[0].dot(v),
+			elements[1].dot(v));
+}
+Rect2 Transform2D::xform(const Rect2 &p_rect) const {
+
+	Vector2 x = elements[0] * p_rect.size.x;
+	Vector2 y = elements[1] * p_rect.size.y;
+	Vector2 pos = xform(p_rect.position);
+
+	Rect2 new_rect;
+	new_rect.position = pos;
+	new_rect.expand_to(pos + x);
+	new_rect.expand_to(pos + y);
+	new_rect.expand_to(pos + x + y);
+	return new_rect;
+}
+
+void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) {
+
+	elements[0][0] = Math::cos(p_rot) * p_scale.x;
+	elements[1][1] = Math::cos(p_rot) * p_scale.y;
+	elements[1][0] = -Math::sin(p_rot) * p_scale.y;
+	elements[0][1] = Math::sin(p_rot) * p_scale.x;
+}
+
+Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const {
+
+	Vector2 ends[4] = {
+		xform_inv(p_rect.position),
+		xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
+		xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
+		xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y))
+	};
+
+	Rect2 new_rect;
+	new_rect.position = ends[0];
+	new_rect.expand_to(ends[1]);
+	new_rect.expand_to(ends[2]);
+	new_rect.expand_to(ends[3]);
+
+	return new_rect;
+}
+
+#endif // TRANSFORM_2D_H