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-rw-r--r--core/math/camera_matrix.h2
-rw-r--r--core/math/delaunay.h2
-rw-r--r--core/math/geometry.h2
-rw-r--r--core/math/math_2d.h1002
-rw-r--r--core/math/math_defs.h59
-rw-r--r--core/math/math_funcs.h7
-rw-r--r--core/math/rect2.cpp240
-rw-r--r--core/math/rect2.h371
-rw-r--r--core/math/transform_2d.cpp (renamed from core/math/math_2d.cpp)284
-rw-r--r--core/math/transform_2d.h201
-rw-r--r--core/math/triangulate.h2
-rw-r--r--core/math/vector2.cpp253
-rw-r--r--core/math/vector2.h316
13 files changed, 1437 insertions, 1304 deletions
diff --git a/core/math/camera_matrix.h b/core/math/camera_matrix.h
index 226b4d572b..a689c7238a 100644
--- a/core/math/camera_matrix.h
+++ b/core/math/camera_matrix.h
@@ -31,7 +31,7 @@
#ifndef CAMERA_MATRIX_H
#define CAMERA_MATRIX_H
-#include "math_2d.h"
+#include "rect2.h"
#include "transform.h"
/**
@author Juan Linietsky <reduzio@gmail.com>
diff --git a/core/math/delaunay.h b/core/math/delaunay.h
index 13fbc0c6ae..46535d5ce9 100644
--- a/core/math/delaunay.h
+++ b/core/math/delaunay.h
@@ -1,7 +1,7 @@
#ifndef DELAUNAY_H
#define DELAUNAY_H
-#include "math_2d.h"
+#include "rect2.h"
class Delaunay2D {
public:
diff --git a/core/math/geometry.h b/core/math/geometry.h
index 186a05fb37..83b9467a30 100644
--- a/core/math/geometry.h
+++ b/core/math/geometry.h
@@ -33,9 +33,9 @@
#include "dvector.h"
#include "face3.h"
-#include "math_2d.h"
#include "object.h"
#include "print_string.h"
+#include "rect2.h"
#include "triangulate.h"
#include "vector.h"
#include "vector3.h"
diff --git a/core/math/math_2d.h b/core/math/math_2d.h
deleted file mode 100644
index 25c39e5d7a..0000000000
--- a/core/math/math_2d.h
+++ /dev/null
@@ -1,1002 +0,0 @@
-/*************************************************************************/
-/* math_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 MATH_2D_H
-#define MATH_2D_H
-
-#include "math_funcs.h"
-#include "ustring.h"
-/**
- @author Juan Linietsky <reduzio@gmail.com>
-*/
-enum Margin {
-
- MARGIN_LEFT,
- MARGIN_TOP,
- MARGIN_RIGHT,
- MARGIN_BOTTOM
-};
-
-enum Corner {
-
- CORNER_TOP_LEFT,
- CORNER_TOP_RIGHT,
- CORNER_BOTTOM_RIGHT,
- CORNER_BOTTOM_LEFT
-};
-
-enum Orientation {
-
- HORIZONTAL,
- VERTICAL
-};
-
-enum HAlign {
-
- HALIGN_LEFT,
- HALIGN_CENTER,
- HALIGN_RIGHT
-};
-
-enum VAlign {
-
- VALIGN_TOP,
- VALIGN_CENTER,
- VALIGN_BOTTOM
-};
-
-struct Vector2 {
-
- union {
- real_t x;
- real_t width;
- };
- union {
- real_t y;
- real_t height;
- };
-
- _FORCE_INLINE_ real_t &operator[](int p_idx) {
- return p_idx ? y : x;
- }
- _FORCE_INLINE_ const real_t &operator[](int p_idx) const {
- return p_idx ? y : x;
- }
-
- void normalize();
- Vector2 normalized() const;
- bool is_normalized() const;
-
- real_t length() const;
- real_t length_squared() const;
-
- real_t distance_to(const Vector2 &p_vector2) const;
- real_t distance_squared_to(const Vector2 &p_vector2) const;
- real_t angle_to(const Vector2 &p_vector2) const;
- real_t angle_to_point(const Vector2 &p_vector2) const;
-
- real_t dot(const Vector2 &p_other) const;
- real_t cross(const Vector2 &p_other) const;
- Vector2 project(const Vector2 &p_vec) const;
-
- Vector2 plane_project(real_t p_d, const Vector2 &p_vec) const;
-
- Vector2 clamped(real_t p_len) const;
-
- _FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_t);
- _FORCE_INLINE_ Vector2 linear_interpolate(const Vector2 &p_b, real_t p_t) const;
- _FORCE_INLINE_ Vector2 slerp(const Vector2 &p_b, real_t p_t) const;
- Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_t) const;
-
- Vector2 slide(const Vector2 &p_normal) const;
- Vector2 bounce(const Vector2 &p_normal) const;
- Vector2 reflect(const Vector2 &p_normal) const;
-
- Vector2 operator+(const Vector2 &p_v) const;
- void operator+=(const Vector2 &p_v);
- Vector2 operator-(const Vector2 &p_v) const;
- void operator-=(const Vector2 &p_v);
- Vector2 operator*(const Vector2 &p_v1) const;
-
- Vector2 operator*(const real_t &rvalue) const;
- void operator*=(const real_t &rvalue);
- void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }
-
- Vector2 operator/(const Vector2 &p_v1) const;
-
- Vector2 operator/(const real_t &rvalue) const;
-
- void operator/=(const real_t &rvalue);
-
- Vector2 operator-() const;
-
- bool operator==(const Vector2 &p_vec2) const;
- bool operator!=(const Vector2 &p_vec2) const;
-
- bool operator<(const Vector2 &p_vec2) const { return (x == p_vec2.x) ? (y < p_vec2.y) : (x < p_vec2.x); }
- bool operator<=(const Vector2 &p_vec2) const { return (x == p_vec2.x) ? (y <= p_vec2.y) : (x <= p_vec2.x); }
-
- real_t angle() const;
-
- void set_rotation(real_t p_radians) {
-
- x = Math::cos(p_radians);
- y = Math::sin(p_radians);
- }
-
- _FORCE_INLINE_ Vector2 abs() const {
-
- return Vector2(Math::abs(x), Math::abs(y));
- }
-
- Vector2 rotated(real_t p_by) const;
- Vector2 tangent() const {
-
- return Vector2(y, -x);
- }
-
- Vector2 floor() const;
- Vector2 ceil() const;
- Vector2 round() const;
- Vector2 snapped(const Vector2 &p_by) const;
- real_t aspect() const { return width / height; }
-
- operator String() const { return String::num(x) + ", " + String::num(y); }
-
- _FORCE_INLINE_ Vector2(real_t p_x, real_t p_y) {
- x = p_x;
- y = p_y;
- }
- _FORCE_INLINE_ Vector2() {
- x = 0;
- y = 0;
- }
-};
-
-_FORCE_INLINE_ Vector2 Vector2::plane_project(real_t p_d, const Vector2 &p_vec) const {
-
- return p_vec - *this * (dot(p_vec) - p_d);
-}
-
-_FORCE_INLINE_ Vector2 operator*(real_t p_scalar, const Vector2 &p_vec) {
-
- return p_vec * p_scalar;
-}
-
-_FORCE_INLINE_ Vector2 Vector2::operator+(const Vector2 &p_v) const {
-
- return Vector2(x + p_v.x, y + p_v.y);
-}
-_FORCE_INLINE_ void Vector2::operator+=(const Vector2 &p_v) {
-
- x += p_v.x;
- y += p_v.y;
-}
-_FORCE_INLINE_ Vector2 Vector2::operator-(const Vector2 &p_v) const {
-
- return Vector2(x - p_v.x, y - p_v.y);
-}
-_FORCE_INLINE_ void Vector2::operator-=(const Vector2 &p_v) {
-
- x -= p_v.x;
- y -= p_v.y;
-}
-
-_FORCE_INLINE_ Vector2 Vector2::operator*(const Vector2 &p_v1) const {
-
- return Vector2(x * p_v1.x, y * p_v1.y);
-};
-
-_FORCE_INLINE_ Vector2 Vector2::operator*(const real_t &rvalue) const {
-
- return Vector2(x * rvalue, y * rvalue);
-};
-_FORCE_INLINE_ void Vector2::operator*=(const real_t &rvalue) {
-
- x *= rvalue;
- y *= rvalue;
-};
-
-_FORCE_INLINE_ Vector2 Vector2::operator/(const Vector2 &p_v1) const {
-
- return Vector2(x / p_v1.x, y / p_v1.y);
-};
-
-_FORCE_INLINE_ Vector2 Vector2::operator/(const real_t &rvalue) const {
-
- return Vector2(x / rvalue, y / rvalue);
-};
-
-_FORCE_INLINE_ void Vector2::operator/=(const real_t &rvalue) {
-
- x /= rvalue;
- y /= rvalue;
-};
-
-_FORCE_INLINE_ Vector2 Vector2::operator-() const {
-
- return Vector2(-x, -y);
-}
-
-_FORCE_INLINE_ bool Vector2::operator==(const Vector2 &p_vec2) const {
-
- return x == p_vec2.x && y == p_vec2.y;
-}
-_FORCE_INLINE_ bool Vector2::operator!=(const Vector2 &p_vec2) const {
-
- return x != p_vec2.x || y != p_vec2.y;
-}
-
-Vector2 Vector2::linear_interpolate(const Vector2 &p_b, real_t p_t) const {
-
- Vector2 res = *this;
-
- res.x += (p_t * (p_b.x - x));
- res.y += (p_t * (p_b.y - y));
-
- return res;
-}
-
-Vector2 Vector2::slerp(const Vector2 &p_b, real_t p_t) const {
-#ifdef MATH_CHECKS
- ERR_FAIL_COND_V(is_normalized() == false, Vector2());
-#endif
- real_t theta = angle_to(p_b);
- return rotated(theta * p_t);
-}
-
-Vector2 Vector2::linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_t) {
-
- Vector2 res = p_a;
-
- res.x += (p_t * (p_b.x - p_a.x));
- res.y += (p_t * (p_b.y - p_a.y));
-
- return res;
-}
-
-typedef Vector2 Size2;
-typedef Vector2 Point2;
-
-struct Transform2D;
-
-struct Rect2 {
-
- Point2 position;
- Size2 size;
-
- const Vector2 &get_position() const { return position; }
- void set_position(const Vector2 &p_pos) { position = p_pos; }
- const Vector2 &get_size() const { return size; }
- void set_size(const Vector2 &p_size) { size = p_size; }
-
- real_t get_area() const { return size.width * size.height; }
-
- inline bool intersects(const Rect2 &p_rect) const {
- if (position.x >= (p_rect.position.x + p_rect.size.width))
- return false;
- if ((position.x + size.width) <= p_rect.position.x)
- return false;
- if (position.y >= (p_rect.position.y + p_rect.size.height))
- return false;
- if ((position.y + size.height) <= p_rect.position.y)
- return false;
-
- return true;
- }
-
- inline real_t distance_to(const Vector2 &p_point) const {
-
- real_t dist = 0.0;
- bool inside = true;
-
- if (p_point.x < position.x) {
- real_t d = position.x - p_point.x;
- dist = inside ? d : MIN(dist, d);
- inside = false;
- }
- if (p_point.y < position.y) {
- real_t d = position.y - p_point.y;
- dist = inside ? d : MIN(dist, d);
- inside = false;
- }
- if (p_point.x >= (position.x + size.x)) {
- real_t d = p_point.x - (position.x + size.x);
- dist = inside ? d : MIN(dist, d);
- inside = false;
- }
- if (p_point.y >= (position.y + size.y)) {
- real_t d = p_point.y - (position.y + size.y);
- dist = inside ? d : MIN(dist, d);
- inside = false;
- }
-
- if (inside)
- return 0;
- else
- return dist;
- }
-
- _FORCE_INLINE_ bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const;
-
- bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = NULL, Point2 *r_normal = NULL) const;
-
- inline bool encloses(const Rect2 &p_rect) const {
-
- return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
- ((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
- ((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
- }
-
- inline bool has_no_area() const {
-
- return (size.x <= 0 || size.y <= 0);
- }
- inline Rect2 clip(const Rect2 &p_rect) const { /// return a clipped rect
-
- Rect2 new_rect = p_rect;
-
- if (!intersects(new_rect))
- return Rect2();
-
- new_rect.position.x = MAX(p_rect.position.x, position.x);
- new_rect.position.y = MAX(p_rect.position.y, position.y);
-
- Point2 p_rect_end = p_rect.position + p_rect.size;
- Point2 end = position + size;
-
- new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x;
- new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y;
-
- return new_rect;
- }
-
- inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect
-
- Rect2 new_rect;
-
- new_rect.position.x = MIN(p_rect.position.x, position.x);
- new_rect.position.y = MIN(p_rect.position.y, position.y);
-
- new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
- new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
-
- new_rect.size = new_rect.size - new_rect.position; //make relative again
-
- return new_rect;
- };
- inline bool has_point(const Point2 &p_point) const {
- if (p_point.x < position.x)
- return false;
- if (p_point.y < position.y)
- return false;
-
- if (p_point.x >= (position.x + size.x))
- return false;
- if (p_point.y >= (position.y + size.y))
- return false;
-
- return true;
- }
-
- inline bool no_area() const { return (size.width <= 0 || size.height <= 0); }
-
- bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; }
- bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; }
-
- inline Rect2 grow(real_t p_by) const {
-
- Rect2 g = *this;
- g.position.x -= p_by;
- g.position.y -= p_by;
- g.size.width += p_by * 2;
- g.size.height += p_by * 2;
- return g;
- }
-
- inline Rect2 grow_margin(Margin p_margin, real_t p_amount) const {
- Rect2 g = *this;
- g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0,
- (MARGIN_TOP == p_margin) ? p_amount : 0,
- (MARGIN_RIGHT == p_margin) ? p_amount : 0,
- (MARGIN_BOTTOM == p_margin) ? p_amount : 0);
- return g;
- }
-
- inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const {
-
- Rect2 g = *this;
- g.position.x -= p_left;
- g.position.y -= p_top;
- g.size.width += p_left + p_right;
- g.size.height += p_top + p_bottom;
-
- return g;
- }
-
- inline Rect2 expand(const Vector2 &p_vector) const {
-
- Rect2 r = *this;
- r.expand_to(p_vector);
- return r;
- }
-
- inline void expand_to(const Vector2 &p_vector) { //in place function for speed
-
- Vector2 begin = position;
- Vector2 end = position + size;
-
- if (p_vector.x < begin.x)
- begin.x = p_vector.x;
- if (p_vector.y < begin.y)
- begin.y = p_vector.y;
-
- if (p_vector.x > end.x)
- end.x = p_vector.x;
- if (p_vector.y > end.y)
- end.y = p_vector.y;
-
- position = begin;
- size = end - begin;
- }
-
- inline Rect2 abs() const {
-
- return Rect2(Point2(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs());
- }
-
- operator String() const { return String(position) + ", " + String(size); }
-
- Rect2() {}
- Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) :
- position(Point2(p_x, p_y)),
- size(Size2(p_width, p_height)) {
- }
- Rect2(const Point2 &p_pos, const Size2 &p_size) :
- position(p_pos),
- size(p_size) {
- }
-};
-
-/* INTEGER STUFF */
-
-struct Point2i {
-
- union {
- int x;
- int width;
- };
- union {
- int y;
- int height;
- };
-
- _FORCE_INLINE_ int &operator[](int p_idx) {
- return p_idx ? y : x;
- }
- _FORCE_INLINE_ const int &operator[](int p_idx) const {
- return p_idx ? y : x;
- }
-
- Point2i operator+(const Point2i &p_v) const;
- void operator+=(const Point2i &p_v);
- Point2i operator-(const Point2i &p_v) const;
- void operator-=(const Point2i &p_v);
- Point2i operator*(const Point2i &p_v1) const;
-
- Point2i operator*(const int &rvalue) const;
- void operator*=(const int &rvalue);
-
- Point2i operator/(const Point2i &p_v1) const;
-
- Point2i operator/(const int &rvalue) const;
-
- void operator/=(const int &rvalue);
-
- Point2i operator-() const;
- bool operator<(const Point2i &p_vec2) const { return (x == p_vec2.x) ? (y < p_vec2.y) : (x < p_vec2.x); }
- bool operator>(const Point2i &p_vec2) const { return (x == p_vec2.x) ? (y > p_vec2.y) : (x > p_vec2.x); }
-
- bool operator==(const Point2i &p_vec2) const;
- bool operator!=(const Point2i &p_vec2) const;
-
- real_t get_aspect() const { return width / (real_t)height; }
-
- operator String() const { return String::num(x) + ", " + String::num(y); }
-
- operator Vector2() const { return Vector2(x, y); }
- inline Point2i(const Vector2 &p_vec2) {
- x = (int)p_vec2.x;
- y = (int)p_vec2.y;
- }
- inline Point2i(int p_x, int p_y) {
- x = p_x;
- y = p_y;
- }
- inline Point2i() {
- x = 0;
- y = 0;
- }
-};
-
-typedef Point2i Size2i;
-
-struct Rect2i {
-
- Point2i position;
- Size2i size;
-
- const Point2i &get_position() const { return position; }
- void set_position(const Point2i &p_pos) { position = p_pos; }
- const Point2i &get_size() const { return size; }
- void set_size(const Point2i &p_size) { size = p_size; }
-
- int get_area() const { return size.width * size.height; }
-
- inline bool intersects(const Rect2i &p_rect) const {
- if (position.x > (p_rect.position.x + p_rect.size.width))
- return false;
- if ((position.x + size.width) < p_rect.position.x)
- return false;
- if (position.y > (p_rect.position.y + p_rect.size.height))
- return false;
- if ((position.y + size.height) < p_rect.position.y)
- return false;
-
- return true;
- }
-
- inline bool encloses(const Rect2i &p_rect) const {
-
- return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
- ((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
- ((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
- }
-
- inline bool has_no_area() const {
-
- return (size.x <= 0 || size.y <= 0);
- }
- inline Rect2i clip(const Rect2i &p_rect) const { /// return a clipped rect
-
- Rect2i new_rect = p_rect;
-
- if (!intersects(new_rect))
- return Rect2i();
-
- new_rect.position.x = MAX(p_rect.position.x, position.x);
- new_rect.position.y = MAX(p_rect.position.y, position.y);
-
- Point2 p_rect_end = p_rect.position + p_rect.size;
- Point2 end = position + size;
-
- new_rect.size.x = (int)(MIN(p_rect_end.x, end.x) - new_rect.position.x);
- new_rect.size.y = (int)(MIN(p_rect_end.y, end.y) - new_rect.position.y);
-
- return new_rect;
- }
-
- inline Rect2i merge(const Rect2i &p_rect) const { ///< return a merged rect
-
- Rect2i new_rect;
-
- new_rect.position.x = MIN(p_rect.position.x, position.x);
- new_rect.position.y = MIN(p_rect.position.y, position.y);
-
- new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
- new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
-
- new_rect.size = new_rect.size - new_rect.position; //make relative again
-
- return new_rect;
- };
- bool has_point(const Point2 &p_point) const {
- if (p_point.x < position.x)
- return false;
- if (p_point.y < position.y)
- return false;
-
- if (p_point.x >= (position.x + size.x))
- return false;
- if (p_point.y >= (position.y + size.y))
- return false;
-
- return true;
- }
-
- bool no_area() { return (size.width <= 0 || size.height <= 0); }
-
- bool operator==(const Rect2i &p_rect) const { return position == p_rect.position && size == p_rect.size; }
- bool operator!=(const Rect2i &p_rect) const { return position != p_rect.position || size != p_rect.size; }
-
- Rect2i grow(int p_by) const {
-
- Rect2i g = *this;
- g.position.x -= p_by;
- g.position.y -= p_by;
- g.size.width += p_by * 2;
- g.size.height += p_by * 2;
- return g;
- }
-
- inline void expand_to(const Point2i &p_vector) {
-
- Point2i begin = position;
- Point2i end = position + size;
-
- if (p_vector.x < begin.x)
- begin.x = p_vector.x;
- if (p_vector.y < begin.y)
- begin.y = p_vector.y;
-
- if (p_vector.x > end.x)
- end.x = p_vector.x;
- if (p_vector.y > end.y)
- end.y = p_vector.y;
-
- position = begin;
- size = end - begin;
- }
-
- operator String() const { return String(position) + ", " + String(size); }
-
- operator Rect2() const { return Rect2(position, size); }
- Rect2i(const Rect2 &p_r2) :
- position(p_r2.position),
- size(p_r2.size) {
- }
- Rect2i() {}
- Rect2i(int p_x, int p_y, int p_width, int p_height) :
- position(Point2(p_x, p_y)),
- size(Size2(p_width, p_height)) {
- }
- Rect2i(const Point2 &p_pos, const Size2 &p_size) :
- position(p_pos),
- size(p_size) {
- }
-};
-
-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;
- }
-};
-
-bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const {
-
- //SAT intersection between local and transformed rect2
-
- Vector2 xf_points[4] = {
- p_xform.xform(p_rect.position),
- p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)),
- p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
- p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
- };
-
- real_t low_limit;
-
- //base rect2 first (faster)
-
- if (xf_points[0].y > position.y)
- goto next1;
- if (xf_points[1].y > position.y)
- goto next1;
- if (xf_points[2].y > position.y)
- goto next1;
- if (xf_points[3].y > position.y)
- goto next1;
-
- return false;
-
-next1:
-
- low_limit = position.y + size.y;
-
- if (xf_points[0].y < low_limit)
- goto next2;
- if (xf_points[1].y < low_limit)
- goto next2;
- if (xf_points[2].y < low_limit)
- goto next2;
- if (xf_points[3].y < low_limit)
- goto next2;
-
- return false;
-
-next2:
-
- if (xf_points[0].x > position.x)
- goto next3;
- if (xf_points[1].x > position.x)
- goto next3;
- if (xf_points[2].x > position.x)
- goto next3;
- if (xf_points[3].x > position.x)
- goto next3;
-
- return false;
-
-next3:
-
- low_limit = position.x + size.x;
-
- if (xf_points[0].x < low_limit)
- goto next4;
- if (xf_points[1].x < low_limit)
- goto next4;
- if (xf_points[2].x < low_limit)
- goto next4;
- if (xf_points[3].x < low_limit)
- goto next4;
-
- return false;
-
-next4:
-
- Vector2 xf_points2[4] = {
- position,
- Vector2(position.x + size.x, position.y),
- Vector2(position.x, position.y + size.y),
- Vector2(position.x + size.x, position.y + size.y),
- };
-
- real_t maxa = p_xform.elements[0].dot(xf_points2[0]);
- real_t mina = maxa;
-
- real_t dp = p_xform.elements[0].dot(xf_points2[1]);
- maxa = MAX(dp, maxa);
- mina = MIN(dp, mina);
-
- dp = p_xform.elements[0].dot(xf_points2[2]);
- maxa = MAX(dp, maxa);
- mina = MIN(dp, mina);
-
- dp = p_xform.elements[0].dot(xf_points2[3]);
- maxa = MAX(dp, maxa);
- mina = MIN(dp, mina);
-
- real_t maxb = p_xform.elements[0].dot(xf_points[0]);
- real_t minb = maxb;
-
- dp = p_xform.elements[0].dot(xf_points[1]);
- maxb = MAX(dp, maxb);
- minb = MIN(dp, minb);
-
- dp = p_xform.elements[0].dot(xf_points[2]);
- maxb = MAX(dp, maxb);
- minb = MIN(dp, minb);
-
- dp = p_xform.elements[0].dot(xf_points[3]);
- maxb = MAX(dp, maxb);
- minb = MIN(dp, minb);
-
- if (mina > maxb)
- return false;
- if (minb > maxa)
- return false;
-
- maxa = p_xform.elements[1].dot(xf_points2[0]);
- mina = maxa;
-
- dp = p_xform.elements[1].dot(xf_points2[1]);
- maxa = MAX(dp, maxa);
- mina = MIN(dp, mina);
-
- dp = p_xform.elements[1].dot(xf_points2[2]);
- maxa = MAX(dp, maxa);
- mina = MIN(dp, mina);
-
- dp = p_xform.elements[1].dot(xf_points2[3]);
- maxa = MAX(dp, maxa);
- mina = MIN(dp, mina);
-
- maxb = p_xform.elements[1].dot(xf_points[0]);
- minb = maxb;
-
- dp = p_xform.elements[1].dot(xf_points[1]);
- maxb = MAX(dp, maxb);
- minb = MIN(dp, minb);
-
- dp = p_xform.elements[1].dot(xf_points[2]);
- maxb = MAX(dp, maxb);
- minb = MIN(dp, minb);
-
- dp = p_xform.elements[1].dot(xf_points[3]);
- maxb = MAX(dp, maxb);
- minb = MIN(dp, minb);
-
- if (mina > maxb)
- return false;
- if (minb > maxa)
- return false;
-
- return true;
-}
-
-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
diff --git a/core/math/math_defs.h b/core/math/math_defs.h
index d3484d8d02..a5feee6eb5 100644
--- a/core/math/math_defs.h
+++ b/core/math/math_defs.h
@@ -36,30 +36,71 @@
#define CMP_NORMALIZE_TOLERANCE 0.000001
#define CMP_POINT_IN_PLANE_EPSILON 0.00001
+#define Math_SQRT12 0.7071067811865475244008443621048490
+#define Math_SQRT2 1.4142135623730950488016887242
+#define Math_LN2 0.6931471805599453094172321215
+#define Math_TAU 6.2831853071795864769252867666
+#define Math_PI 3.1415926535897932384626433833
+#define Math_E 2.7182818284590452353602874714
+#define Math_INF INFINITY
+#define Math_NAN NAN
+
#ifdef DEBUG_ENABLED
#define MATH_CHECKS
#endif
#define USEC_TO_SEC(m_usec) ((m_usec) / 1000000.0)
-/**
- * "Real" is a type that will be translated to either floats or fixed depending
- * on the compilation setting
- */
enum ClockDirection {
-
CLOCKWISE,
COUNTERCLOCKWISE
};
-#ifdef REAL_T_IS_DOUBLE
+enum Orientation {
-typedef double real_t;
+ HORIZONTAL,
+ VERTICAL
+};
-#else
+enum HAlign {
-typedef float real_t;
+ HALIGN_LEFT,
+ HALIGN_CENTER,
+ HALIGN_RIGHT
+};
+
+enum VAlign {
+
+ VALIGN_TOP,
+ VALIGN_CENTER,
+ VALIGN_BOTTOM
+};
+enum Margin {
+
+ MARGIN_LEFT,
+ MARGIN_TOP,
+ MARGIN_RIGHT,
+ MARGIN_BOTTOM
+};
+
+enum Corner {
+
+ CORNER_TOP_LEFT,
+ CORNER_TOP_RIGHT,
+ CORNER_BOTTOM_RIGHT,
+ CORNER_BOTTOM_LEFT
+};
+
+/**
+ * The "Real" type is an abstract type used for real numbers, such as 1.5,
+ * in contrast to integer numbers. Precision can be controlled with the
+ * presence or absence of the REAL_T_IS_DOUBLE define.
+ */
+#ifdef REAL_T_IS_DOUBLE
+typedef double real_t;
+#else
+typedef float real_t;
#endif
#endif // MATH_DEFS_H
diff --git a/core/math/math_funcs.h b/core/math/math_funcs.h
index f0c0268f31..992084a653 100644
--- a/core/math/math_funcs.h
+++ b/core/math/math_funcs.h
@@ -39,13 +39,6 @@
#include <float.h>
#include <math.h>
-#define Math_PI 3.14159265358979323846
-#define Math_TAU 6.28318530717958647692
-#define Math_SQRT12 0.7071067811865475244008443621048490
-#define Math_LN2 0.693147180559945309417
-#define Math_INF INFINITY
-#define Math_NAN NAN
-
class Math {
static pcg32_random_t default_pcg;
diff --git a/core/math/rect2.cpp b/core/math/rect2.cpp
new file mode 100644
index 0000000000..480bccdff1
--- /dev/null
+++ b/core/math/rect2.cpp
@@ -0,0 +1,240 @@
+/*************************************************************************/
+/* rect2.cpp */
+/*************************************************************************/
+/* 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. */
+/*************************************************************************/
+
+#include "transform_2d.h" // Includes rect2.h but Rect2 needs Transform2D
+
+bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const {
+
+ real_t min = 0, max = 1;
+ int axis = 0;
+ real_t sign = 0;
+
+ for (int i = 0; i < 2; i++) {
+ real_t seg_from = p_from[i];
+ real_t seg_to = p_to[i];
+ real_t box_begin = position[i];
+ real_t box_end = box_begin + size[i];
+ real_t cmin, cmax;
+ real_t csign;
+
+ if (seg_from < seg_to) {
+
+ if (seg_from > box_end || seg_to < box_begin)
+ return false;
+ real_t length = seg_to - seg_from;
+ cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
+ cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
+ csign = -1.0;
+
+ } else {
+
+ if (seg_to > box_end || seg_from < box_begin)
+ return false;
+ real_t length = seg_to - seg_from;
+ cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
+ cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
+ csign = 1.0;
+ }
+
+ if (cmin > min) {
+ min = cmin;
+ axis = i;
+ sign = csign;
+ }
+ if (cmax < max)
+ max = cmax;
+ if (max < min)
+ return false;
+ }
+
+ Vector2 rel = p_to - p_from;
+
+ if (r_normal) {
+ Vector2 normal;
+ normal[axis] = sign;
+ *r_normal = normal;
+ }
+
+ if (r_pos)
+ *r_pos = p_from + rel * min;
+
+ return true;
+}
+
+bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const {
+
+ //SAT intersection between local and transformed rect2
+
+ Vector2 xf_points[4] = {
+ p_xform.xform(p_rect.position),
+ p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)),
+ p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
+ p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
+ };
+
+ real_t low_limit;
+
+ //base rect2 first (faster)
+
+ if (xf_points[0].y > position.y)
+ goto next1;
+ if (xf_points[1].y > position.y)
+ goto next1;
+ if (xf_points[2].y > position.y)
+ goto next1;
+ if (xf_points[3].y > position.y)
+ goto next1;
+
+ return false;
+
+next1:
+
+ low_limit = position.y + size.y;
+
+ if (xf_points[0].y < low_limit)
+ goto next2;
+ if (xf_points[1].y < low_limit)
+ goto next2;
+ if (xf_points[2].y < low_limit)
+ goto next2;
+ if (xf_points[3].y < low_limit)
+ goto next2;
+
+ return false;
+
+next2:
+
+ if (xf_points[0].x > position.x)
+ goto next3;
+ if (xf_points[1].x > position.x)
+ goto next3;
+ if (xf_points[2].x > position.x)
+ goto next3;
+ if (xf_points[3].x > position.x)
+ goto next3;
+
+ return false;
+
+next3:
+
+ low_limit = position.x + size.x;
+
+ if (xf_points[0].x < low_limit)
+ goto next4;
+ if (xf_points[1].x < low_limit)
+ goto next4;
+ if (xf_points[2].x < low_limit)
+ goto next4;
+ if (xf_points[3].x < low_limit)
+ goto next4;
+
+ return false;
+
+next4:
+
+ Vector2 xf_points2[4] = {
+ position,
+ Vector2(position.x + size.x, position.y),
+ Vector2(position.x, position.y + size.y),
+ Vector2(position.x + size.x, position.y + size.y),
+ };
+
+ real_t maxa = p_xform.elements[0].dot(xf_points2[0]);
+ real_t mina = maxa;
+
+ real_t dp = p_xform.elements[0].dot(xf_points2[1]);
+ maxa = MAX(dp, maxa);
+ mina = MIN(dp, mina);
+
+ dp = p_xform.elements[0].dot(xf_points2[2]);
+ maxa = MAX(dp, maxa);
+ mina = MIN(dp, mina);
+
+ dp = p_xform.elements[0].dot(xf_points2[3]);
+ maxa = MAX(dp, maxa);
+ mina = MIN(dp, mina);
+
+ real_t maxb = p_xform.elements[0].dot(xf_points[0]);
+ real_t minb = maxb;
+
+ dp = p_xform.elements[0].dot(xf_points[1]);
+ maxb = MAX(dp, maxb);
+ minb = MIN(dp, minb);
+
+ dp = p_xform.elements[0].dot(xf_points[2]);
+ maxb = MAX(dp, maxb);
+ minb = MIN(dp, minb);
+
+ dp = p_xform.elements[0].dot(xf_points[3]);
+ maxb = MAX(dp, maxb);
+ minb = MIN(dp, minb);
+
+ if (mina > maxb)
+ return false;
+ if (minb > maxa)
+ return false;
+
+ maxa = p_xform.elements[1].dot(xf_points2[0]);
+ mina = maxa;
+
+ dp = p_xform.elements[1].dot(xf_points2[1]);
+ maxa = MAX(dp, maxa);
+ mina = MIN(dp, mina);
+
+ dp = p_xform.elements[1].dot(xf_points2[2]);
+ maxa = MAX(dp, maxa);
+ mina = MIN(dp, mina);
+
+ dp = p_xform.elements[1].dot(xf_points2[3]);
+ maxa = MAX(dp, maxa);
+ mina = MIN(dp, mina);
+
+ maxb = p_xform.elements[1].dot(xf_points[0]);
+ minb = maxb;
+
+ dp = p_xform.elements[1].dot(xf_points[1]);
+ maxb = MAX(dp, maxb);
+ minb = MIN(dp, minb);
+
+ dp = p_xform.elements[1].dot(xf_points[2]);
+ maxb = MAX(dp, maxb);
+ minb = MIN(dp, minb);
+
+ dp = p_xform.elements[1].dot(xf_points[3]);
+ maxb = MAX(dp, maxb);
+ minb = MIN(dp, minb);
+
+ if (mina > maxb)
+ return false;
+ if (minb > maxa)
+ return false;
+
+ return true;
+}
diff --git a/core/math/rect2.h b/core/math/rect2.h
new file mode 100644
index 0000000000..20329bee0d
--- /dev/null
+++ b/core/math/rect2.h
@@ -0,0 +1,371 @@
+/*************************************************************************/
+/* rect2.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 RECT2_H
+#define RECT2_H
+
+#include "vector2.h" // also includes math_funcs and ustring
+
+struct Transform2D;
+
+struct Rect2 {
+
+ Point2 position;
+ Size2 size;
+
+ const Vector2 &get_position() const { return position; }
+ void set_position(const Vector2 &p_pos) { position = p_pos; }
+ const Vector2 &get_size() const { return size; }
+ void set_size(const Vector2 &p_size) { size = p_size; }
+
+ real_t get_area() const { return size.width * size.height; }
+
+ inline bool intersects(const Rect2 &p_rect) const {
+ if (position.x >= (p_rect.position.x + p_rect.size.width))
+ return false;
+ if ((position.x + size.width) <= p_rect.position.x)
+ return false;
+ if (position.y >= (p_rect.position.y + p_rect.size.height))
+ return false;
+ if ((position.y + size.height) <= p_rect.position.y)
+ return false;
+
+ return true;
+ }
+
+ inline real_t distance_to(const Vector2 &p_point) const {
+
+ real_t dist = 0.0;
+ bool inside = true;
+
+ if (p_point.x < position.x) {
+ real_t d = position.x - p_point.x;
+ dist = inside ? d : MIN(dist, d);
+ inside = false;
+ }
+ if (p_point.y < position.y) {
+ real_t d = position.y - p_point.y;
+ dist = inside ? d : MIN(dist, d);
+ inside = false;
+ }
+ if (p_point.x >= (position.x + size.x)) {
+ real_t d = p_point.x - (position.x + size.x);
+ dist = inside ? d : MIN(dist, d);
+ inside = false;
+ }
+ if (p_point.y >= (position.y + size.y)) {
+ real_t d = p_point.y - (position.y + size.y);
+ dist = inside ? d : MIN(dist, d);
+ inside = false;
+ }
+
+ if (inside)
+ return 0;
+ else
+ return dist;
+ }
+
+ bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const;
+
+ bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = NULL, Point2 *r_normal = NULL) const;
+
+ inline bool encloses(const Rect2 &p_rect) const {
+
+ return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
+ ((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
+ ((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
+ }
+
+ inline bool has_no_area() const {
+
+ return (size.x <= 0 || size.y <= 0);
+ }
+ inline Rect2 clip(const Rect2 &p_rect) const { /// return a clipped rect
+
+ Rect2 new_rect = p_rect;
+
+ if (!intersects(new_rect))
+ return Rect2();
+
+ new_rect.position.x = MAX(p_rect.position.x, position.x);
+ new_rect.position.y = MAX(p_rect.position.y, position.y);
+
+ Point2 p_rect_end = p_rect.position + p_rect.size;
+ Point2 end = position + size;
+
+ new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x;
+ new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y;
+
+ return new_rect;
+ }
+
+ inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect
+
+ Rect2 new_rect;
+
+ new_rect.position.x = MIN(p_rect.position.x, position.x);
+ new_rect.position.y = MIN(p_rect.position.y, position.y);
+
+ new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
+ new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
+
+ new_rect.size = new_rect.size - new_rect.position; //make relative again
+
+ return new_rect;
+ };
+ inline bool has_point(const Point2 &p_point) const {
+ if (p_point.x < position.x)
+ return false;
+ if (p_point.y < position.y)
+ return false;
+
+ if (p_point.x >= (position.x + size.x))
+ return false;
+ if (p_point.y >= (position.y + size.y))
+ return false;
+
+ return true;
+ }
+
+ inline bool no_area() const { return (size.width <= 0 || size.height <= 0); }
+
+ bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; }
+ bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; }
+
+ inline Rect2 grow(real_t p_by) const {
+
+ Rect2 g = *this;
+ g.position.x -= p_by;
+ g.position.y -= p_by;
+ g.size.width += p_by * 2;
+ g.size.height += p_by * 2;
+ return g;
+ }
+
+ inline Rect2 grow_margin(Margin p_margin, real_t p_amount) const {
+ Rect2 g = *this;
+ g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0,
+ (MARGIN_TOP == p_margin) ? p_amount : 0,
+ (MARGIN_RIGHT == p_margin) ? p_amount : 0,
+ (MARGIN_BOTTOM == p_margin) ? p_amount : 0);
+ return g;
+ }
+
+ inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const {
+
+ Rect2 g = *this;
+ g.position.x -= p_left;
+ g.position.y -= p_top;
+ g.size.width += p_left + p_right;
+ g.size.height += p_top + p_bottom;
+
+ return g;
+ }
+
+ inline Rect2 expand(const Vector2 &p_vector) const {
+
+ Rect2 r = *this;
+ r.expand_to(p_vector);
+ return r;
+ }
+
+ inline void expand_to(const Vector2 &p_vector) { //in place function for speed
+
+ Vector2 begin = position;
+ Vector2 end = position + size;
+
+ if (p_vector.x < begin.x)
+ begin.x = p_vector.x;
+ if (p_vector.y < begin.y)
+ begin.y = p_vector.y;
+
+ if (p_vector.x > end.x)
+ end.x = p_vector.x;
+ if (p_vector.y > end.y)
+ end.y = p_vector.y;
+
+ position = begin;
+ size = end - begin;
+ }
+
+ inline Rect2 abs() const {
+
+ return Rect2(Point2(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs());
+ }
+
+ operator String() const { return String(position) + ", " + String(size); }
+
+ Rect2() {}
+ Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) :
+ position(Point2(p_x, p_y)),
+ size(Size2(p_width, p_height)) {
+ }
+ Rect2(const Point2 &p_pos, const Size2 &p_size) :
+ position(p_pos),
+ size(p_size) {
+ }
+};
+
+struct Rect2i {
+
+ Point2i position;
+ Size2i size;
+
+ const Point2i &get_position() const { return position; }
+ void set_position(const Point2i &p_position) { position = p_position; }
+ const Size2i &get_size() const { return size; }
+ void set_size(const Size2i &p_size) { size = p_size; }
+
+ int get_area() const { return size.width * size.height; }
+
+ inline bool intersects(const Rect2i &p_rect) const {
+ if (position.x > (p_rect.position.x + p_rect.size.width))
+ return false;
+ if ((position.x + size.width) < p_rect.position.x)
+ return false;
+ if (position.y > (p_rect.position.y + p_rect.size.height))
+ return false;
+ if ((position.y + size.height) < p_rect.position.y)
+ return false;
+
+ return true;
+ }
+
+ inline bool encloses(const Rect2i &p_rect) const {
+
+ return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
+ ((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
+ ((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
+ }
+
+ inline bool has_no_area() const {
+
+ return (size.x <= 0 || size.y <= 0);
+ }
+ inline Rect2i clip(const Rect2i &p_rect) const { /// return a clipped rect
+
+ Rect2i new_rect = p_rect;
+
+ if (!intersects(new_rect))
+ return Rect2i();
+
+ new_rect.position.x = MAX(p_rect.position.x, position.x);
+ new_rect.position.y = MAX(p_rect.position.y, position.y);
+
+ Point2 p_rect_end = p_rect.position + p_rect.size;
+ Point2 end = position + size;
+
+ new_rect.size.x = (int)(MIN(p_rect_end.x, end.x) - new_rect.position.x);
+ new_rect.size.y = (int)(MIN(p_rect_end.y, end.y) - new_rect.position.y);
+
+ return new_rect;
+ }
+
+ inline Rect2i merge(const Rect2i &p_rect) const { ///< return a merged rect
+
+ Rect2i new_rect;
+
+ new_rect.position.x = MIN(p_rect.position.x, position.x);
+ new_rect.position.y = MIN(p_rect.position.y, position.y);
+
+ new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
+ new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
+
+ new_rect.size = new_rect.size - new_rect.position; //make relative again
+
+ return new_rect;
+ };
+ bool has_point(const Point2 &p_point) const {
+ if (p_point.x < position.x)
+ return false;
+ if (p_point.y < position.y)
+ return false;
+
+ if (p_point.x >= (position.x + size.x))
+ return false;
+ if (p_point.y >= (position.y + size.y))
+ return false;
+
+ return true;
+ }
+
+ bool no_area() { return (size.width <= 0 || size.height <= 0); }
+
+ bool operator==(const Rect2i &p_rect) const { return position == p_rect.position && size == p_rect.size; }
+ bool operator!=(const Rect2i &p_rect) const { return position != p_rect.position || size != p_rect.size; }
+
+ Rect2i grow(int p_by) const {
+
+ Rect2i g = *this;
+ g.position.x -= p_by;
+ g.position.y -= p_by;
+ g.size.width += p_by * 2;
+ g.size.height += p_by * 2;
+ return g;
+ }
+
+ inline void expand_to(const Point2i &p_vector) {
+
+ Point2i begin = position;
+ Point2i end = position + size;
+
+ if (p_vector.x < begin.x)
+ begin.x = p_vector.x;
+ if (p_vector.y < begin.y)
+ begin.y = p_vector.y;
+
+ if (p_vector.x > end.x)
+ end.x = p_vector.x;
+ if (p_vector.y > end.y)
+ end.y = p_vector.y;
+
+ position = begin;
+ size = end - begin;
+ }
+
+ operator String() const { return String(position) + ", " + String(size); }
+
+ operator Rect2() const { return Rect2(position, size); }
+ Rect2i(const Rect2 &p_r2) :
+ position(p_r2.position),
+ size(p_r2.size) {
+ }
+ Rect2i() {}
+ Rect2i(int p_x, int p_y, int p_width, int p_height) :
+ position(Point2(p_x, p_y)),
+ size(Size2(p_width, p_height)) {
+ }
+ Rect2i(const Point2 &p_pos, const Size2 &p_size) :
+ position(p_pos),
+ size(p_size) {
+ }
+};
+
+#endif // RECT2_H
diff --git a/core/math/math_2d.cpp b/core/math/transform_2d.cpp
index a053ffbd93..4bb763c879 100644
--- a/core/math/math_2d.cpp
+++ b/core/math/transform_2d.cpp
@@ -1,5 +1,5 @@
/*************************************************************************/
-/* math_2d.cpp */
+/* transform_2d.cpp */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
@@ -28,287 +28,7 @@
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/*************************************************************************/
-#include "math_2d.h"
-
-real_t Vector2::angle() const {
-
- return Math::atan2(y, x);
-}
-
-real_t Vector2::length() const {
-
- return Math::sqrt(x * x + y * y);
-}
-
-real_t Vector2::length_squared() const {
-
- return x * x + y * y;
-}
-
-void Vector2::normalize() {
-
- real_t l = x * x + y * y;
- if (l != 0) {
-
- l = Math::sqrt(l);
- x /= l;
- y /= l;
- }
-}
-
-Vector2 Vector2::normalized() const {
-
- Vector2 v = *this;
- v.normalize();
- return v;
-}
-
-bool Vector2::is_normalized() const {
- // use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
- return Math::is_equal_approx(length_squared(), 1.0);
-}
-
-real_t Vector2::distance_to(const Vector2 &p_vector2) const {
-
- return Math::sqrt((x - p_vector2.x) * (x - p_vector2.x) + (y - p_vector2.y) * (y - p_vector2.y));
-}
-
-real_t Vector2::distance_squared_to(const Vector2 &p_vector2) const {
-
- return (x - p_vector2.x) * (x - p_vector2.x) + (y - p_vector2.y) * (y - p_vector2.y);
-}
-
-real_t Vector2::angle_to(const Vector2 &p_vector2) const {
-
- return Math::atan2(cross(p_vector2), dot(p_vector2));
-}
-
-real_t Vector2::angle_to_point(const Vector2 &p_vector2) const {
-
- return Math::atan2(y - p_vector2.y, x - p_vector2.x);
-}
-
-real_t Vector2::dot(const Vector2 &p_other) const {
-
- return x * p_other.x + y * p_other.y;
-}
-
-real_t Vector2::cross(const Vector2 &p_other) const {
-
- return x * p_other.y - y * p_other.x;
-}
-
-Vector2 Vector2::floor() const {
-
- return Vector2(Math::floor(x), Math::floor(y));
-}
-
-Vector2 Vector2::ceil() const {
-
- return Vector2(Math::ceil(x), Math::ceil(y));
-}
-
-Vector2 Vector2::round() const {
-
- return Vector2(Math::round(x), Math::round(y));
-}
-
-Vector2 Vector2::rotated(real_t p_by) const {
-
- Vector2 v;
- v.set_rotation(angle() + p_by);
- v *= length();
- return v;
-}
-
-Vector2 Vector2::project(const Vector2 &p_vec) const {
-
- Vector2 v1 = p_vec;
- Vector2 v2 = *this;
- return v2 * (v1.dot(v2) / v2.dot(v2));
-}
-
-Vector2 Vector2::snapped(const Vector2 &p_by) const {
-
- return Vector2(
- Math::stepify(x, p_by.x),
- Math::stepify(y, p_by.y));
-}
-
-Vector2 Vector2::clamped(real_t p_len) const {
-
- real_t l = length();
- Vector2 v = *this;
- if (l > 0 && p_len < l) {
-
- v /= l;
- v *= p_len;
- }
-
- return v;
-}
-
-Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_t) const {
-
- Vector2 p0 = p_pre_a;
- Vector2 p1 = *this;
- Vector2 p2 = p_b;
- Vector2 p3 = p_post_b;
-
- real_t t = p_t;
- real_t t2 = t * t;
- real_t t3 = t2 * t;
-
- Vector2 out;
- out = 0.5 * ((p1 * 2.0) +
- (-p0 + p2) * t +
- (2.0 * p0 - 5.0 * p1 + 4 * p2 - p3) * t2 +
- (-p0 + 3.0 * p1 - 3.0 * p2 + p3) * t3);
- return out;
-}
-
-// slide returns the component of the vector along the given plane, specified by its normal vector.
-Vector2 Vector2::slide(const Vector2 &p_normal) const {
-#ifdef MATH_CHECKS
- ERR_FAIL_COND_V(p_normal.is_normalized() == false, Vector2());
-#endif
- return *this - p_normal * this->dot(p_normal);
-}
-
-Vector2 Vector2::bounce(const Vector2 &p_normal) const {
- return -reflect(p_normal);
-}
-
-Vector2 Vector2::reflect(const Vector2 &p_normal) const {
-#ifdef MATH_CHECKS
- ERR_FAIL_COND_V(p_normal.is_normalized() == false, Vector2());
-#endif
- return 2.0 * p_normal * this->dot(p_normal) - *this;
-}
-
-bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const {
-
- real_t min = 0, max = 1;
- int axis = 0;
- real_t sign = 0;
-
- for (int i = 0; i < 2; i++) {
- real_t seg_from = p_from[i];
- real_t seg_to = p_to[i];
- real_t box_begin = position[i];
- real_t box_end = box_begin + size[i];
- real_t cmin, cmax;
- real_t csign;
-
- if (seg_from < seg_to) {
-
- if (seg_from > box_end || seg_to < box_begin)
- return false;
- real_t length = seg_to - seg_from;
- cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
- cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
- csign = -1.0;
-
- } else {
-
- if (seg_to > box_end || seg_from < box_begin)
- return false;
- real_t length = seg_to - seg_from;
- cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
- cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
- csign = 1.0;
- }
-
- if (cmin > min) {
- min = cmin;
- axis = i;
- sign = csign;
- }
- if (cmax < max)
- max = cmax;
- if (max < min)
- return false;
- }
-
- Vector2 rel = p_to - p_from;
-
- if (r_normal) {
- Vector2 normal;
- normal[axis] = sign;
- *r_normal = normal;
- }
-
- if (r_pos)
- *r_pos = p_from + rel * min;
-
- return true;
-}
-
-/* Point2i */
-
-Point2i Point2i::operator+(const Point2i &p_v) const {
-
- return Point2i(x + p_v.x, y + p_v.y);
-}
-void Point2i::operator+=(const Point2i &p_v) {
-
- x += p_v.x;
- y += p_v.y;
-}
-Point2i Point2i::operator-(const Point2i &p_v) const {
-
- return Point2i(x - p_v.x, y - p_v.y);
-}
-void Point2i::operator-=(const Point2i &p_v) {
-
- x -= p_v.x;
- y -= p_v.y;
-}
-
-Point2i Point2i::operator*(const Point2i &p_v1) const {
-
- return Point2i(x * p_v1.x, y * p_v1.y);
-};
-
-Point2i Point2i::operator*(const int &rvalue) const {
-
- return Point2i(x * rvalue, y * rvalue);
-};
-void Point2i::operator*=(const int &rvalue) {
-
- x *= rvalue;
- y *= rvalue;
-};
-
-Point2i Point2i::operator/(const Point2i &p_v1) const {
-
- return Point2i(x / p_v1.x, y / p_v1.y);
-};
-
-Point2i Point2i::operator/(const int &rvalue) const {
-
- return Point2i(x / rvalue, y / rvalue);
-};
-
-void Point2i::operator/=(const int &rvalue) {
-
- x /= rvalue;
- y /= rvalue;
-};
-
-Point2i Point2i::operator-() const {
-
- return Point2i(-x, -y);
-}
-
-bool Point2i::operator==(const Point2i &p_vec2) const {
-
- return x == p_vec2.x && y == p_vec2.y;
-}
-bool Point2i::operator!=(const Point2i &p_vec2) const {
-
- return x != p_vec2.x || y != p_vec2.y;
-}
+#include "transform_2d.h"
void Transform2D::invert() {
// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
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
diff --git a/core/math/triangulate.h b/core/math/triangulate.h
index b1a583d0c5..a0f56f5f27 100644
--- a/core/math/triangulate.h
+++ b/core/math/triangulate.h
@@ -31,7 +31,7 @@
#ifndef TRIANGULATE_H
#define TRIANGULATE_H
-#include "math_2d.h"
+#include "vector2.h"
/*
http://www.flipcode.com/archives/Efficient_Polygon_Triangulation.shtml
diff --git a/core/math/vector2.cpp b/core/math/vector2.cpp
new file mode 100644
index 0000000000..441e7d8907
--- /dev/null
+++ b/core/math/vector2.cpp
@@ -0,0 +1,253 @@
+/*************************************************************************/
+/* vector2.cpp */
+/*************************************************************************/
+/* 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. */
+/*************************************************************************/
+
+#include "vector2.h"
+
+real_t Vector2::angle() const {
+
+ return Math::atan2(y, x);
+}
+
+real_t Vector2::length() const {
+
+ return Math::sqrt(x * x + y * y);
+}
+
+real_t Vector2::length_squared() const {
+
+ return x * x + y * y;
+}
+
+void Vector2::normalize() {
+
+ real_t l = x * x + y * y;
+ if (l != 0) {
+
+ l = Math::sqrt(l);
+ x /= l;
+ y /= l;
+ }
+}
+
+Vector2 Vector2::normalized() const {
+
+ Vector2 v = *this;
+ v.normalize();
+ return v;
+}
+
+bool Vector2::is_normalized() const {
+ // use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
+ return Math::is_equal_approx(length_squared(), 1.0);
+}
+
+real_t Vector2::distance_to(const Vector2 &p_vector2) const {
+
+ return Math::sqrt((x - p_vector2.x) * (x - p_vector2.x) + (y - p_vector2.y) * (y - p_vector2.y));
+}
+
+real_t Vector2::distance_squared_to(const Vector2 &p_vector2) const {
+
+ return (x - p_vector2.x) * (x - p_vector2.x) + (y - p_vector2.y) * (y - p_vector2.y);
+}
+
+real_t Vector2::angle_to(const Vector2 &p_vector2) const {
+
+ return Math::atan2(cross(p_vector2), dot(p_vector2));
+}
+
+real_t Vector2::angle_to_point(const Vector2 &p_vector2) const {
+
+ return Math::atan2(y - p_vector2.y, x - p_vector2.x);
+}
+
+real_t Vector2::dot(const Vector2 &p_other) const {
+
+ return x * p_other.x + y * p_other.y;
+}
+
+real_t Vector2::cross(const Vector2 &p_other) const {
+
+ return x * p_other.y - y * p_other.x;
+}
+
+Vector2 Vector2::floor() const {
+
+ return Vector2(Math::floor(x), Math::floor(y));
+}
+
+Vector2 Vector2::ceil() const {
+
+ return Vector2(Math::ceil(x), Math::ceil(y));
+}
+
+Vector2 Vector2::round() const {
+
+ return Vector2(Math::round(x), Math::round(y));
+}
+
+Vector2 Vector2::rotated(real_t p_by) const {
+
+ Vector2 v;
+ v.set_rotation(angle() + p_by);
+ v *= length();
+ return v;
+}
+
+Vector2 Vector2::project(const Vector2 &p_vec) const {
+
+ Vector2 v1 = p_vec;
+ Vector2 v2 = *this;
+ return v2 * (v1.dot(v2) / v2.dot(v2));
+}
+
+Vector2 Vector2::snapped(const Vector2 &p_by) const {
+
+ return Vector2(
+ Math::stepify(x, p_by.x),
+ Math::stepify(y, p_by.y));
+}
+
+Vector2 Vector2::clamped(real_t p_len) const {
+
+ real_t l = length();
+ Vector2 v = *this;
+ if (l > 0 && p_len < l) {
+
+ v /= l;
+ v *= p_len;
+ }
+
+ return v;
+}
+
+Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_t) const {
+
+ Vector2 p0 = p_pre_a;
+ Vector2 p1 = *this;
+ Vector2 p2 = p_b;
+ Vector2 p3 = p_post_b;
+
+ real_t t = p_t;
+ real_t t2 = t * t;
+ real_t t3 = t2 * t;
+
+ Vector2 out;
+ out = 0.5 * ((p1 * 2.0) +
+ (-p0 + p2) * t +
+ (2.0 * p0 - 5.0 * p1 + 4 * p2 - p3) * t2 +
+ (-p0 + 3.0 * p1 - 3.0 * p2 + p3) * t3);
+ return out;
+}
+
+// slide returns the component of the vector along the given plane, specified by its normal vector.
+Vector2 Vector2::slide(const Vector2 &p_normal) const {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(p_normal.is_normalized() == false, Vector2());
+#endif
+ return *this - p_normal * this->dot(p_normal);
+}
+
+Vector2 Vector2::bounce(const Vector2 &p_normal) const {
+ return -reflect(p_normal);
+}
+
+Vector2 Vector2::reflect(const Vector2 &p_normal) const {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(p_normal.is_normalized() == false, Vector2());
+#endif
+ return 2.0 * p_normal * this->dot(p_normal) - *this;
+}
+
+/* Vector2i */
+
+Vector2i Vector2i::operator+(const Vector2i &p_v) const {
+
+ return Vector2i(x + p_v.x, y + p_v.y);
+}
+void Vector2i::operator+=(const Vector2i &p_v) {
+
+ x += p_v.x;
+ y += p_v.y;
+}
+Vector2i Vector2i::operator-(const Vector2i &p_v) const {
+
+ return Vector2i(x - p_v.x, y - p_v.y);
+}
+void Vector2i::operator-=(const Vector2i &p_v) {
+
+ x -= p_v.x;
+ y -= p_v.y;
+}
+
+Vector2i Vector2i::operator*(const Vector2i &p_v1) const {
+
+ return Vector2i(x * p_v1.x, y * p_v1.y);
+};
+
+Vector2i Vector2i::operator*(const int &rvalue) const {
+
+ return Vector2i(x * rvalue, y * rvalue);
+};
+void Vector2i::operator*=(const int &rvalue) {
+
+ x *= rvalue;
+ y *= rvalue;
+};
+
+Vector2i Vector2i::operator/(const Vector2i &p_v1) const {
+
+ return Vector2i(x / p_v1.x, y / p_v1.y);
+};
+
+Vector2i Vector2i::operator/(const int &rvalue) const {
+
+ return Vector2i(x / rvalue, y / rvalue);
+};
+
+void Vector2i::operator/=(const int &rvalue) {
+
+ x /= rvalue;
+ y /= rvalue;
+};
+
+Vector2i Vector2i::operator-() const {
+
+ return Vector2i(-x, -y);
+}
+
+bool Vector2i::operator==(const Vector2i &p_vec2) const {
+
+ return x == p_vec2.x && y == p_vec2.y;
+}
+bool Vector2i::operator!=(const Vector2i &p_vec2) const {
+
+ return x != p_vec2.x || y != p_vec2.y;
+}
diff --git a/core/math/vector2.h b/core/math/vector2.h
new file mode 100644
index 0000000000..7c8882f6e2
--- /dev/null
+++ b/core/math/vector2.h
@@ -0,0 +1,316 @@
+/*************************************************************************/
+/* vector2.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 VECTOR2_H
+#define VECTOR2_H
+
+#include "math_funcs.h"
+#include "ustring.h"
+
+struct Vector2i;
+
+struct Vector2 {
+
+ union {
+ real_t x;
+ real_t width;
+ };
+ union {
+ real_t y;
+ real_t height;
+ };
+
+ _FORCE_INLINE_ real_t &operator[](int p_idx) {
+ return p_idx ? y : x;
+ }
+ _FORCE_INLINE_ const real_t &operator[](int p_idx) const {
+ return p_idx ? y : x;
+ }
+
+ void normalize();
+ Vector2 normalized() const;
+ bool is_normalized() const;
+
+ real_t length() const;
+ real_t length_squared() const;
+
+ real_t distance_to(const Vector2 &p_vector2) const;
+ real_t distance_squared_to(const Vector2 &p_vector2) const;
+ real_t angle_to(const Vector2 &p_vector2) const;
+ real_t angle_to_point(const Vector2 &p_vector2) const;
+
+ real_t dot(const Vector2 &p_other) const;
+ real_t cross(const Vector2 &p_other) const;
+ Vector2 project(const Vector2 &p_vec) const;
+
+ Vector2 plane_project(real_t p_d, const Vector2 &p_vec) const;
+
+ Vector2 clamped(real_t p_len) const;
+
+ _FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_t);
+ _FORCE_INLINE_ Vector2 linear_interpolate(const Vector2 &p_b, real_t p_t) const;
+ _FORCE_INLINE_ Vector2 slerp(const Vector2 &p_b, real_t p_t) const;
+ Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_t) const;
+
+ Vector2 slide(const Vector2 &p_normal) const;
+ Vector2 bounce(const Vector2 &p_normal) const;
+ Vector2 reflect(const Vector2 &p_normal) const;
+
+ Vector2 operator+(const Vector2 &p_v) const;
+ void operator+=(const Vector2 &p_v);
+ Vector2 operator-(const Vector2 &p_v) const;
+ void operator-=(const Vector2 &p_v);
+ Vector2 operator*(const Vector2 &p_v1) const;
+
+ Vector2 operator*(const real_t &rvalue) const;
+ void operator*=(const real_t &rvalue);
+ void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }
+
+ Vector2 operator/(const Vector2 &p_v1) const;
+
+ Vector2 operator/(const real_t &rvalue) const;
+
+ void operator/=(const real_t &rvalue);
+
+ Vector2 operator-() const;
+
+ bool operator==(const Vector2 &p_vec2) const;
+ bool operator!=(const Vector2 &p_vec2) const;
+
+ bool operator<(const Vector2 &p_vec2) const { return (x == p_vec2.x) ? (y < p_vec2.y) : (x < p_vec2.x); }
+ bool operator<=(const Vector2 &p_vec2) const { return (x == p_vec2.x) ? (y <= p_vec2.y) : (x <= p_vec2.x); }
+
+ real_t angle() const;
+
+ void set_rotation(real_t p_radians) {
+
+ x = Math::cos(p_radians);
+ y = Math::sin(p_radians);
+ }
+
+ _FORCE_INLINE_ Vector2 abs() const {
+
+ return Vector2(Math::abs(x), Math::abs(y));
+ }
+
+ Vector2 rotated(real_t p_by) const;
+ Vector2 tangent() const {
+
+ return Vector2(y, -x);
+ }
+
+ Vector2 floor() const;
+ Vector2 ceil() const;
+ Vector2 round() const;
+ Vector2 snapped(const Vector2 &p_by) const;
+ real_t aspect() const { return width / height; }
+
+ operator String() const { return String::num(x) + ", " + String::num(y); }
+
+ _FORCE_INLINE_ Vector2(real_t p_x, real_t p_y) {
+ x = p_x;
+ y = p_y;
+ }
+ _FORCE_INLINE_ Vector2() {
+ x = 0;
+ y = 0;
+ }
+};
+
+_FORCE_INLINE_ Vector2 Vector2::plane_project(real_t p_d, const Vector2 &p_vec) const {
+
+ return p_vec - *this * (dot(p_vec) - p_d);
+}
+
+_FORCE_INLINE_ Vector2 operator*(real_t p_scalar, const Vector2 &p_vec) {
+
+ return p_vec * p_scalar;
+}
+
+_FORCE_INLINE_ Vector2 Vector2::operator+(const Vector2 &p_v) const {
+
+ return Vector2(x + p_v.x, y + p_v.y);
+}
+_FORCE_INLINE_ void Vector2::operator+=(const Vector2 &p_v) {
+
+ x += p_v.x;
+ y += p_v.y;
+}
+_FORCE_INLINE_ Vector2 Vector2::operator-(const Vector2 &p_v) const {
+
+ return Vector2(x - p_v.x, y - p_v.y);
+}
+_FORCE_INLINE_ void Vector2::operator-=(const Vector2 &p_v) {
+
+ x -= p_v.x;
+ y -= p_v.y;
+}
+
+_FORCE_INLINE_ Vector2 Vector2::operator*(const Vector2 &p_v1) const {
+
+ return Vector2(x * p_v1.x, y * p_v1.y);
+};
+
+_FORCE_INLINE_ Vector2 Vector2::operator*(const real_t &rvalue) const {
+
+ return Vector2(x * rvalue, y * rvalue);
+};
+_FORCE_INLINE_ void Vector2::operator*=(const real_t &rvalue) {
+
+ x *= rvalue;
+ y *= rvalue;
+};
+
+_FORCE_INLINE_ Vector2 Vector2::operator/(const Vector2 &p_v1) const {
+
+ return Vector2(x / p_v1.x, y / p_v1.y);
+};
+
+_FORCE_INLINE_ Vector2 Vector2::operator/(const real_t &rvalue) const {
+
+ return Vector2(x / rvalue, y / rvalue);
+};
+
+_FORCE_INLINE_ void Vector2::operator/=(const real_t &rvalue) {
+
+ x /= rvalue;
+ y /= rvalue;
+};
+
+_FORCE_INLINE_ Vector2 Vector2::operator-() const {
+
+ return Vector2(-x, -y);
+}
+
+_FORCE_INLINE_ bool Vector2::operator==(const Vector2 &p_vec2) const {
+
+ return x == p_vec2.x && y == p_vec2.y;
+}
+_FORCE_INLINE_ bool Vector2::operator!=(const Vector2 &p_vec2) const {
+
+ return x != p_vec2.x || y != p_vec2.y;
+}
+
+Vector2 Vector2::linear_interpolate(const Vector2 &p_b, real_t p_t) const {
+
+ Vector2 res = *this;
+
+ res.x += (p_t * (p_b.x - x));
+ res.y += (p_t * (p_b.y - y));
+
+ return res;
+}
+
+Vector2 Vector2::slerp(const Vector2 &p_b, real_t p_t) const {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(is_normalized() == false, Vector2());
+#endif
+ real_t theta = angle_to(p_b);
+ return rotated(theta * p_t);
+}
+
+Vector2 Vector2::linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_t) {
+
+ Vector2 res = p_a;
+
+ res.x += (p_t * (p_b.x - p_a.x));
+ res.y += (p_t * (p_b.y - p_a.y));
+
+ return res;
+}
+
+typedef Vector2 Size2;
+typedef Vector2 Point2;
+
+/* INTEGER STUFF */
+
+struct Vector2i {
+
+ union {
+ int x;
+ int width;
+ };
+ union {
+ int y;
+ int height;
+ };
+
+ _FORCE_INLINE_ int &operator[](int p_idx) {
+ return p_idx ? y : x;
+ }
+ _FORCE_INLINE_ const int &operator[](int p_idx) const {
+ return p_idx ? y : x;
+ }
+
+ Vector2i operator+(const Vector2i &p_v) const;
+ void operator+=(const Vector2i &p_v);
+ Vector2i operator-(const Vector2i &p_v) const;
+ void operator-=(const Vector2i &p_v);
+ Vector2i operator*(const Vector2i &p_v1) const;
+
+ Vector2i operator*(const int &rvalue) const;
+ void operator*=(const int &rvalue);
+
+ Vector2i operator/(const Vector2i &p_v1) const;
+
+ Vector2i operator/(const int &rvalue) const;
+
+ void operator/=(const int &rvalue);
+
+ Vector2i operator-() const;
+ bool operator<(const Vector2i &p_vec2) const { return (x == p_vec2.x) ? (y < p_vec2.y) : (x < p_vec2.x); }
+ bool operator>(const Vector2i &p_vec2) const { return (x == p_vec2.x) ? (y > p_vec2.y) : (x > p_vec2.x); }
+
+ bool operator==(const Vector2i &p_vec2) const;
+ bool operator!=(const Vector2i &p_vec2) const;
+
+ real_t get_aspect() const { return width / (real_t)height; }
+
+ operator String() const { return String::num(x) + ", " + String::num(y); }
+
+ operator Vector2() const { return Vector2(x, y); }
+ inline Vector2i(const Vector2 &p_vec2) {
+ x = (int)p_vec2.x;
+ y = (int)p_vec2.y;
+ }
+ inline Vector2i(int p_x, int p_y) {
+ x = p_x;
+ y = p_y;
+ }
+ inline Vector2i() {
+ x = 0;
+ y = 0;
+ }
+};
+
+typedef Vector2i Size2i;
+typedef Vector2i Point2i;
+
+#endif // VECTOR2_H
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