godot/core/math/math_2d.h
Rémi Verschelde 41e3592041
Merge pull request #13347 from Noshyaar/hang_in_there
Rect2: add function returning same rect with positive w and h
2017-12-09 18:08:09 +01:00

918 lines
24 KiB
C++

/*************************************************************************/
/* math_2d.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2017 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 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 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 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 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 = 1e20;
if (p_point.x < position.x) {
dist = MIN(dist, position.x - p_point.x);
}
if (p_point.y < position.y) {
dist = MIN(dist, position.y - p_point.y);
}
if (p_point.x >= (position.x + size.x)) {
dist = MIN(p_point.x - (position.x + size.x), dist);
}
if (p_point.y >= (position.y + size.y)) {
dist = MIN(p_point.y - (position.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.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.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