1002 lines
26 KiB
C++
1002 lines
26 KiB
C++
/*************************************************************************/
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/* math_2d.h */
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/*************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#ifndef MATH_2D_H
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#define MATH_2D_H
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#include "math_funcs.h"
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#include "ustring.h"
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/**
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@author Juan Linietsky <reduzio@gmail.com>
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*/
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enum Margin {
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MARGIN_LEFT,
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MARGIN_TOP,
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MARGIN_RIGHT,
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MARGIN_BOTTOM
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};
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enum Corner {
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CORNER_TOP_LEFT,
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CORNER_TOP_RIGHT,
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CORNER_BOTTOM_RIGHT,
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CORNER_BOTTOM_LEFT
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};
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enum Orientation {
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HORIZONTAL,
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VERTICAL
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};
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enum HAlign {
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HALIGN_LEFT,
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HALIGN_CENTER,
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HALIGN_RIGHT
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};
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enum VAlign {
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VALIGN_TOP,
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VALIGN_CENTER,
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VALIGN_BOTTOM
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};
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struct Vector2 {
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union {
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real_t x;
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real_t width;
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};
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union {
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real_t y;
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real_t height;
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};
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_FORCE_INLINE_ real_t &operator[](int p_idx) {
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return p_idx ? y : x;
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}
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_FORCE_INLINE_ const real_t &operator[](int p_idx) const {
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return p_idx ? y : x;
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}
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void normalize();
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Vector2 normalized() const;
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bool is_normalized() const;
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real_t length() const;
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real_t length_squared() const;
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real_t distance_to(const Vector2 &p_vector2) const;
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real_t distance_squared_to(const Vector2 &p_vector2) const;
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real_t angle_to(const Vector2 &p_vector2) const;
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real_t angle_to_point(const Vector2 &p_vector2) const;
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real_t dot(const Vector2 &p_other) const;
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real_t cross(const Vector2 &p_other) const;
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Vector2 project(const Vector2 &p_vec) const;
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Vector2 plane_project(real_t p_d, const Vector2 &p_vec) const;
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Vector2 clamped(real_t p_len) const;
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_FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_t);
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_FORCE_INLINE_ Vector2 linear_interpolate(const Vector2 &p_b, real_t p_t) const;
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_FORCE_INLINE_ Vector2 slerp(const Vector2 &p_b, real_t p_t) const;
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Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_t) const;
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Vector2 slide(const Vector2 &p_normal) const;
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Vector2 bounce(const Vector2 &p_normal) const;
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Vector2 reflect(const Vector2 &p_normal) const;
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Vector2 operator+(const Vector2 &p_v) const;
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void operator+=(const Vector2 &p_v);
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Vector2 operator-(const Vector2 &p_v) const;
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void operator-=(const Vector2 &p_v);
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Vector2 operator*(const Vector2 &p_v1) const;
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Vector2 operator*(const real_t &rvalue) const;
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void operator*=(const real_t &rvalue);
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void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }
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Vector2 operator/(const Vector2 &p_v1) const;
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Vector2 operator/(const real_t &rvalue) const;
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void operator/=(const real_t &rvalue);
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Vector2 operator-() const;
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bool operator==(const Vector2 &p_vec2) const;
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bool operator!=(const Vector2 &p_vec2) const;
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bool operator<(const Vector2 &p_vec2) const { return (x == p_vec2.x) ? (y < p_vec2.y) : (x < p_vec2.x); }
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bool operator<=(const Vector2 &p_vec2) const { return (x == p_vec2.x) ? (y <= p_vec2.y) : (x <= p_vec2.x); }
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real_t angle() const;
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void set_rotation(real_t p_radians) {
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x = Math::cos(p_radians);
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y = Math::sin(p_radians);
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}
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_FORCE_INLINE_ Vector2 abs() const {
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return Vector2(Math::abs(x), Math::abs(y));
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}
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Vector2 rotated(real_t p_by) const;
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Vector2 tangent() const {
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return Vector2(y, -x);
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}
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Vector2 floor() const;
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Vector2 ceil() const;
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Vector2 round() const;
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Vector2 snapped(const Vector2 &p_by) const;
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real_t aspect() const { return width / height; }
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operator String() const { return String::num(x) + ", " + String::num(y); }
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_FORCE_INLINE_ Vector2(real_t p_x, real_t p_y) {
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x = p_x;
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y = p_y;
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}
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_FORCE_INLINE_ Vector2() {
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x = 0;
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y = 0;
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}
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};
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_FORCE_INLINE_ Vector2 Vector2::plane_project(real_t p_d, const Vector2 &p_vec) const {
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return p_vec - *this * (dot(p_vec) - p_d);
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}
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_FORCE_INLINE_ Vector2 operator*(real_t p_scalar, const Vector2 &p_vec) {
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return p_vec * p_scalar;
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}
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_FORCE_INLINE_ Vector2 Vector2::operator+(const Vector2 &p_v) const {
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return Vector2(x + p_v.x, y + p_v.y);
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}
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_FORCE_INLINE_ void Vector2::operator+=(const Vector2 &p_v) {
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x += p_v.x;
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y += p_v.y;
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}
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_FORCE_INLINE_ Vector2 Vector2::operator-(const Vector2 &p_v) const {
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return Vector2(x - p_v.x, y - p_v.y);
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}
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_FORCE_INLINE_ void Vector2::operator-=(const Vector2 &p_v) {
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x -= p_v.x;
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y -= p_v.y;
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}
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_FORCE_INLINE_ Vector2 Vector2::operator*(const Vector2 &p_v1) const {
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return Vector2(x * p_v1.x, y * p_v1.y);
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};
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_FORCE_INLINE_ Vector2 Vector2::operator*(const real_t &rvalue) const {
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return Vector2(x * rvalue, y * rvalue);
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};
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_FORCE_INLINE_ void Vector2::operator*=(const real_t &rvalue) {
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x *= rvalue;
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y *= rvalue;
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};
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_FORCE_INLINE_ Vector2 Vector2::operator/(const Vector2 &p_v1) const {
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return Vector2(x / p_v1.x, y / p_v1.y);
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};
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_FORCE_INLINE_ Vector2 Vector2::operator/(const real_t &rvalue) const {
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return Vector2(x / rvalue, y / rvalue);
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};
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_FORCE_INLINE_ void Vector2::operator/=(const real_t &rvalue) {
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x /= rvalue;
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y /= rvalue;
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};
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_FORCE_INLINE_ Vector2 Vector2::operator-() const {
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return Vector2(-x, -y);
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}
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_FORCE_INLINE_ bool Vector2::operator==(const Vector2 &p_vec2) const {
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return x == p_vec2.x && y == p_vec2.y;
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}
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_FORCE_INLINE_ bool Vector2::operator!=(const Vector2 &p_vec2) const {
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return x != p_vec2.x || y != p_vec2.y;
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}
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Vector2 Vector2::linear_interpolate(const Vector2 &p_b, real_t p_t) const {
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Vector2 res = *this;
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res.x += (p_t * (p_b.x - x));
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res.y += (p_t * (p_b.y - y));
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return res;
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}
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Vector2 Vector2::slerp(const Vector2 &p_b, real_t p_t) const {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_V(is_normalized() == false, Vector2());
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#endif
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real_t theta = angle_to(p_b);
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return rotated(theta * p_t);
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}
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Vector2 Vector2::linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_t) {
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Vector2 res = p_a;
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res.x += (p_t * (p_b.x - p_a.x));
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res.y += (p_t * (p_b.y - p_a.y));
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return res;
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}
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typedef Vector2 Size2;
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typedef Vector2 Point2;
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struct Transform2D;
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struct Rect2 {
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Point2 position;
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Size2 size;
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const Vector2 &get_position() const { return position; }
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void set_position(const Vector2 &p_pos) { position = p_pos; }
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const Vector2 &get_size() const { return size; }
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void set_size(const Vector2 &p_size) { size = p_size; }
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real_t get_area() const { return size.width * size.height; }
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inline bool intersects(const Rect2 &p_rect) const {
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if (position.x >= (p_rect.position.x + p_rect.size.width))
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return false;
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if ((position.x + size.width) <= p_rect.position.x)
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return false;
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if (position.y >= (p_rect.position.y + p_rect.size.height))
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return false;
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if ((position.y + size.height) <= p_rect.position.y)
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return false;
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return true;
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}
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inline real_t distance_to(const Vector2 &p_point) const {
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real_t dist = 0.0;
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bool inside = true;
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if (p_point.x < position.x) {
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real_t d = position.x - p_point.x;
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dist = inside ? d : MIN(dist, d);
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inside = false;
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}
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if (p_point.y < position.y) {
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real_t d = position.y - p_point.y;
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dist = inside ? d : MIN(dist, d);
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inside = false;
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}
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if (p_point.x >= (position.x + size.x)) {
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real_t d = p_point.x - (position.x + size.x);
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dist = inside ? d : MIN(dist, d);
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inside = false;
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}
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if (p_point.y >= (position.y + size.y)) {
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real_t d = p_point.y - (position.y + size.y);
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dist = inside ? d : MIN(dist, d);
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inside = false;
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}
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if (inside)
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return 0;
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else
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return dist;
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}
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_FORCE_INLINE_ bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const;
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bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = NULL, Point2 *r_normal = NULL) const;
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inline bool encloses(const Rect2 &p_rect) const {
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return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
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((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
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((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
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}
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inline bool has_no_area() const {
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return (size.x <= 0 || size.y <= 0);
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}
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inline Rect2 clip(const Rect2 &p_rect) const { /// return a clipped rect
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Rect2 new_rect = p_rect;
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if (!intersects(new_rect))
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return Rect2();
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new_rect.position.x = MAX(p_rect.position.x, position.x);
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new_rect.position.y = MAX(p_rect.position.y, position.y);
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Point2 p_rect_end = p_rect.position + p_rect.size;
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Point2 end = position + size;
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new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x;
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new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y;
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return new_rect;
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}
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inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect
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Rect2 new_rect;
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new_rect.position.x = MIN(p_rect.position.x, position.x);
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new_rect.position.y = MIN(p_rect.position.y, position.y);
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new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
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new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
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new_rect.size = new_rect.size - new_rect.position; //make relative again
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return new_rect;
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};
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inline bool has_point(const Point2 &p_point) const {
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if (p_point.x < position.x)
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return false;
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if (p_point.y < position.y)
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return false;
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if (p_point.x >= (position.x + size.x))
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return false;
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if (p_point.y >= (position.y + size.y))
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return false;
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return true;
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}
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inline bool no_area() const { return (size.width <= 0 || size.height <= 0); }
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bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; }
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bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; }
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inline Rect2 grow(real_t p_by) const {
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Rect2 g = *this;
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g.position.x -= p_by;
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g.position.y -= p_by;
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g.size.width += p_by * 2;
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g.size.height += p_by * 2;
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return g;
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}
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inline Rect2 grow_margin(Margin p_margin, real_t p_amount) const {
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Rect2 g = *this;
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g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0,
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(MARGIN_TOP == p_margin) ? p_amount : 0,
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(MARGIN_RIGHT == p_margin) ? p_amount : 0,
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(MARGIN_BOTTOM == p_margin) ? p_amount : 0);
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return g;
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}
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inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const {
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Rect2 g = *this;
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g.position.x -= p_left;
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g.position.y -= p_top;
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g.size.width += p_left + p_right;
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g.size.height += p_top + p_bottom;
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return g;
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}
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inline Rect2 expand(const Vector2 &p_vector) const {
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Rect2 r = *this;
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r.expand_to(p_vector);
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return r;
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}
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inline void expand_to(const Vector2 &p_vector) { //in place function for speed
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Vector2 begin = position;
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Vector2 end = position + size;
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if (p_vector.x < begin.x)
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begin.x = p_vector.x;
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if (p_vector.y < begin.y)
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begin.y = p_vector.y;
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if (p_vector.x > end.x)
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end.x = p_vector.x;
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if (p_vector.y > end.y)
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end.y = p_vector.y;
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position = begin;
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size = end - begin;
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}
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inline Rect2 abs() const {
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return Rect2(Point2(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs());
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}
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operator String() const { return String(position) + ", " + String(size); }
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Rect2() {}
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Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) :
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position(Point2(p_x, p_y)),
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size(Size2(p_width, p_height)) {
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}
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Rect2(const Point2 &p_pos, const Size2 &p_size) :
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position(p_pos),
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size(p_size) {
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}
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};
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/* INTEGER STUFF */
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struct Point2i {
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union {
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int x;
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int width;
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};
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union {
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int y;
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int height;
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};
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_FORCE_INLINE_ int &operator[](int p_idx) {
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return p_idx ? y : x;
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}
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_FORCE_INLINE_ const int &operator[](int p_idx) const {
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return p_idx ? y : x;
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}
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Point2i operator+(const Point2i &p_v) const;
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void operator+=(const Point2i &p_v);
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Point2i operator-(const Point2i &p_v) const;
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void operator-=(const Point2i &p_v);
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Point2i operator*(const Point2i &p_v1) const;
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Point2i operator*(const int &rvalue) const;
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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]);
|
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return new_rect;
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}
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#endif
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