diff options
Diffstat (limited to 'core/math')
| -rw-r--r-- | core/math/camera_matrix.h | 2 | ||||
| -rw-r--r-- | core/math/delaunay.h | 2 | ||||
| -rw-r--r-- | core/math/geometry.h | 2 | ||||
| -rw-r--r-- | core/math/math_2d.h | 1002 | ||||
| -rw-r--r-- | core/math/math_defs.h | 59 | ||||
| -rw-r--r-- | core/math/math_funcs.h | 7 | ||||
| -rw-r--r-- | core/math/rect2.cpp | 240 | ||||
| -rw-r--r-- | core/math/rect2.h | 371 | ||||
| -rw-r--r-- | core/math/transform_2d.cpp (renamed from core/math/math_2d.cpp) | 284 | ||||
| -rw-r--r-- | core/math/transform_2d.h | 201 | ||||
| -rw-r--r-- | core/math/triangulate.h | 2 | ||||
| -rw-r--r-- | core/math/vector2.cpp | 250 | ||||
| -rw-r--r-- | core/math/vector2.h | 316 | ||||
| -rw-r--r-- | core/math/vector3.h | 6 |
14 files changed, 1440 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..75d9b8b311 --- /dev/null +++ b/core/math/vector2.cpp @@ -0,0 +1,250 @@ +/*************************************************************************/ +/* 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_b) const { + return p_b * (dot(p_b) / p_b.dot(p_b)); +} + +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..fbcdc80b60 --- /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_b) 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 diff --git a/core/math/vector3.h b/core/math/vector3.h index 433adf09ee..a719e3965d 100644 --- a/core/math/vector3.h +++ b/core/math/vector3.h @@ -109,6 +109,8 @@ struct Vector3 { _FORCE_INLINE_ real_t distance_to(const Vector3 &p_b) const; _FORCE_INLINE_ real_t distance_squared_to(const Vector3 &p_b) const; + _FORCE_INLINE_ Vector3 project(const Vector3 &p_b) const; + _FORCE_INLINE_ real_t angle_to(const Vector3 &p_b) const; _FORCE_INLINE_ Vector3 slide(const Vector3 &p_normal) const; @@ -238,6 +240,10 @@ real_t Vector3::distance_squared_to(const Vector3 &p_b) const { return (p_b - *this).length_squared(); } +Vector3 Vector3::project(const Vector3 &p_b) const { + return p_b * (dot(p_b) / p_b.dot(p_b)); +} + real_t Vector3::angle_to(const Vector3 &p_b) const { return Math::atan2(cross(p_b).length(), dot(p_b)); |