1a620bd5fa
This is in alignment with other functions in vector classes. Also added checks for normalization, fixed the sign of reflect (which now corresponds to reflection along a plane mathematically), added bounce method and updated docs. Fixes #8201.
885 lines
23 KiB
C++
885 lines
23 KiB
C++
/*************************************************************************/
|
|
/* math_2d.h */
|
|
/*************************************************************************/
|
|
/* This file is part of: */
|
|
/* GODOT ENGINE */
|
|
/* http://www.godotengine.org */
|
|
/*************************************************************************/
|
|
/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur. */
|
|
/* */
|
|
/* 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 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 cross(real_t 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;
|
|
Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_t) const;
|
|
Vector2 cubic_interpolate_soft(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_t) const;
|
|
|
|
Vector2 slide(const Vector2 &p_vec) const;
|
|
Vector2 bounce(const Vector2 &p_vec) const;
|
|
Vector2 reflect(const Vector2 &p_vec) 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 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;
|
|
}
|
|
|
|
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::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 pos;
|
|
Size2 size;
|
|
|
|
const Vector2 &get_pos() const { return pos; }
|
|
void set_pos(const Vector2 &p_pos) { pos = 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 (pos.x >= (p_rect.pos.x + p_rect.size.width))
|
|
return false;
|
|
if ((pos.x + size.width) <= p_rect.pos.x)
|
|
return false;
|
|
if (pos.y >= (p_rect.pos.y + p_rect.size.height))
|
|
return false;
|
|
if ((pos.y + size.height) <= p_rect.pos.y)
|
|
return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
inline real_t distance_to(const Vector2 &p_point) const {
|
|
|
|
real_t dist = 1e20;
|
|
|
|
if (p_point.x < pos.x) {
|
|
dist = MIN(dist, pos.x - p_point.x);
|
|
}
|
|
if (p_point.y < pos.y) {
|
|
dist = MIN(dist, pos.y - p_point.y);
|
|
}
|
|
if (p_point.x >= (pos.x + size.x)) {
|
|
dist = MIN(p_point.x - (pos.x + size.x), dist);
|
|
}
|
|
if (p_point.y >= (pos.y + size.y)) {
|
|
dist = MIN(p_point.y - (pos.y + size.y), dist);
|
|
}
|
|
|
|
if (dist == 1e20)
|
|
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.pos.x >= pos.x) && (p_rect.pos.y >= pos.y) &&
|
|
((p_rect.pos.x + p_rect.size.x) < (pos.x + size.x)) &&
|
|
((p_rect.pos.y + p_rect.size.y) < (pos.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.pos.x = MAX(p_rect.pos.x, pos.x);
|
|
new_rect.pos.y = MAX(p_rect.pos.y, pos.y);
|
|
|
|
Point2 p_rect_end = p_rect.pos + p_rect.size;
|
|
Point2 end = pos + size;
|
|
|
|
new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.pos.x;
|
|
new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.pos.y;
|
|
|
|
return new_rect;
|
|
}
|
|
|
|
inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect
|
|
|
|
Rect2 new_rect;
|
|
|
|
new_rect.pos.x = MIN(p_rect.pos.x, pos.x);
|
|
new_rect.pos.y = MIN(p_rect.pos.y, pos.y);
|
|
|
|
new_rect.size.x = MAX(p_rect.pos.x + p_rect.size.x, pos.x + size.x);
|
|
new_rect.size.y = MAX(p_rect.pos.y + p_rect.size.y, pos.y + size.y);
|
|
|
|
new_rect.size = new_rect.size - new_rect.pos; //make relative again
|
|
|
|
return new_rect;
|
|
};
|
|
inline bool has_point(const Point2 &p_point) const {
|
|
if (p_point.x < pos.x)
|
|
return false;
|
|
if (p_point.y < pos.y)
|
|
return false;
|
|
|
|
if (p_point.x >= (pos.x + size.x))
|
|
return false;
|
|
if (p_point.y >= (pos.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 pos == p_rect.pos && size == p_rect.size; }
|
|
bool operator!=(const Rect2 &p_rect) const { return pos != p_rect.pos || size != p_rect.size; }
|
|
|
|
inline Rect2 grow(real_t p_by) const {
|
|
|
|
Rect2 g = *this;
|
|
g.pos.x -= p_by;
|
|
g.pos.y -= p_by;
|
|
g.size.width += p_by * 2;
|
|
g.size.height += p_by * 2;
|
|
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 = pos;
|
|
Vector2 end = pos + 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;
|
|
|
|
pos = begin;
|
|
size = end - begin;
|
|
}
|
|
|
|
operator String() const { return String(pos) + ", " + String(size); }
|
|
|
|
Rect2() {}
|
|
Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) {
|
|
pos = Point2(p_x, p_y);
|
|
size = Size2(p_width, p_height);
|
|
}
|
|
Rect2(const Point2 &p_pos, const Size2 &p_size) {
|
|
pos = 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 pos;
|
|
Size2i size;
|
|
|
|
const Point2i &get_pos() const { return pos; }
|
|
void set_pos(const Point2i &p_pos) { pos = 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 (pos.x > (p_rect.pos.x + p_rect.size.width))
|
|
return false;
|
|
if ((pos.x + size.width) < p_rect.pos.x)
|
|
return false;
|
|
if (pos.y > (p_rect.pos.y + p_rect.size.height))
|
|
return false;
|
|
if ((pos.y + size.height) < p_rect.pos.y)
|
|
return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
inline bool encloses(const Rect2i &p_rect) const {
|
|
|
|
return (p_rect.pos.x >= pos.x) && (p_rect.pos.y >= pos.y) &&
|
|
((p_rect.pos.x + p_rect.size.x) < (pos.x + size.x)) &&
|
|
((p_rect.pos.y + p_rect.size.y) < (pos.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.pos.x = MAX(p_rect.pos.x, pos.x);
|
|
new_rect.pos.y = MAX(p_rect.pos.y, pos.y);
|
|
|
|
Point2 p_rect_end = p_rect.pos + p_rect.size;
|
|
Point2 end = pos + size;
|
|
|
|
new_rect.size.x = (int)(MIN(p_rect_end.x, end.x) - new_rect.pos.x);
|
|
new_rect.size.y = (int)(MIN(p_rect_end.y, end.y) - new_rect.pos.y);
|
|
|
|
return new_rect;
|
|
}
|
|
|
|
inline Rect2i merge(const Rect2i &p_rect) const { ///< return a merged rect
|
|
|
|
Rect2i new_rect;
|
|
|
|
new_rect.pos.x = MIN(p_rect.pos.x, pos.x);
|
|
new_rect.pos.y = MIN(p_rect.pos.y, pos.y);
|
|
|
|
new_rect.size.x = MAX(p_rect.pos.x + p_rect.size.x, pos.x + size.x);
|
|
new_rect.size.y = MAX(p_rect.pos.y + p_rect.size.y, pos.y + size.y);
|
|
|
|
new_rect.size = new_rect.size - new_rect.pos; //make relative again
|
|
|
|
return new_rect;
|
|
};
|
|
bool has_point(const Point2 &p_point) const {
|
|
if (p_point.x < pos.x)
|
|
return false;
|
|
if (p_point.y < pos.y)
|
|
return false;
|
|
|
|
if (p_point.x >= (pos.x + size.x))
|
|
return false;
|
|
if (p_point.y >= (pos.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 pos == p_rect.pos && size == p_rect.size; }
|
|
bool operator!=(const Rect2i &p_rect) const { return pos != p_rect.pos || size != p_rect.size; }
|
|
|
|
Rect2i grow(int p_by) const {
|
|
|
|
Rect2i g = *this;
|
|
g.pos.x -= p_by;
|
|
g.pos.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 = pos;
|
|
Point2i end = pos + 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;
|
|
|
|
pos = begin;
|
|
size = end - begin;
|
|
}
|
|
|
|
operator String() const { return String(pos) + ", " + String(size); }
|
|
|
|
operator Rect2() const { return Rect2(pos, size); }
|
|
Rect2i(const Rect2 &p_r2) {
|
|
pos = p_r2.pos;
|
|
size = p_r2.size;
|
|
}
|
|
Rect2i() {}
|
|
Rect2i(int p_x, int p_y, int p_width, int p_height) {
|
|
pos = Point2(p_x, p_y);
|
|
size = Size2(p_width, p_height);
|
|
}
|
|
Rect2i(const Point2 &p_pos, const Size2 &p_size) {
|
|
pos = 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_phi);
|
|
real_t get_rotation() const;
|
|
_FORCE_INLINE_ void set_rotation_and_scale(real_t p_phi, 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_vec) const;
|
|
_FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_vec) 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.pos),
|
|
p_xform.xform(Vector2(p_rect.pos.x + p_rect.size.x, p_rect.pos.y)),
|
|
p_xform.xform(Vector2(p_rect.pos.x, p_rect.pos.y + p_rect.size.y)),
|
|
p_xform.xform(Vector2(p_rect.pos.x + p_rect.size.x, p_rect.pos.y + p_rect.size.y)),
|
|
};
|
|
|
|
real_t low_limit;
|
|
|
|
//base rect2 first (faster)
|
|
|
|
if (xf_points[0].y > pos.y)
|
|
goto next1;
|
|
if (xf_points[1].y > pos.y)
|
|
goto next1;
|
|
if (xf_points[2].y > pos.y)
|
|
goto next1;
|
|
if (xf_points[3].y > pos.y)
|
|
goto next1;
|
|
|
|
return false;
|
|
|
|
next1:
|
|
|
|
low_limit = pos.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 > pos.x)
|
|
goto next3;
|
|
if (xf_points[1].x > pos.x)
|
|
goto next3;
|
|
if (xf_points[2].x > pos.x)
|
|
goto next3;
|
|
if (xf_points[3].x > pos.x)
|
|
goto next3;
|
|
|
|
return false;
|
|
|
|
next3:
|
|
|
|
low_limit = pos.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] = {
|
|
pos,
|
|
Vector2(pos.x + size.x, pos.y),
|
|
Vector2(pos.x, pos.y + size.y),
|
|
Vector2(pos.x + size.x, pos.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 &v) const {
|
|
|
|
return Vector2(
|
|
tdotx(v),
|
|
tdoty(v));
|
|
}
|
|
|
|
Vector2 Transform2D::basis_xform_inv(const Vector2 &v) const {
|
|
|
|
return Vector2(
|
|
elements[0].dot(v),
|
|
elements[1].dot(v));
|
|
}
|
|
|
|
Vector2 Transform2D::xform(const Vector2 &v) const {
|
|
|
|
return Vector2(
|
|
tdotx(v),
|
|
tdoty(v)) +
|
|
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.pos);
|
|
|
|
Rect2 new_rect;
|
|
new_rect.pos = 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.pos),
|
|
xform_inv(Vector2(p_rect.pos.x, p_rect.pos.y + p_rect.size.y)),
|
|
xform_inv(Vector2(p_rect.pos.x + p_rect.size.x, p_rect.pos.y + p_rect.size.y)),
|
|
xform_inv(Vector2(p_rect.pos.x + p_rect.size.x, p_rect.pos.y))
|
|
};
|
|
|
|
Rect2 new_rect;
|
|
new_rect.pos = ends[0];
|
|
new_rect.expand_to(ends[1]);
|
|
new_rect.expand_to(ends[2]);
|
|
new_rect.expand_to(ends[3]);
|
|
|
|
return new_rect;
|
|
}
|
|
|
|
#endif
|