858 lines
21 KiB
C++
858 lines
21 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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/* http://www.godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2016 Juan Linietsky, Ariel Manzur. */
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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 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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float x;
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float width;
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};
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union {
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float y;
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float height;
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};
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_FORCE_INLINE_ float& operator[](int p_idx) {
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return p_idx?y:x;
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}
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_FORCE_INLINE_ const float& 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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float length() const;
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float length_squared() const;
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float distance_to(const Vector2& p_vector2) const;
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float distance_squared_to(const Vector2& p_vector2) const;
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float angle_to(const Vector2& p_vector2) const;
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float angle_to_point(const Vector2& p_vector2) const;
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float dot(const Vector2& p_other) const;
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float cross(const Vector2& p_other) const;
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Vector2 cross(real_t 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,float p_t);
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_FORCE_INLINE_ Vector2 linear_interpolate(const Vector2& p_b,float p_t) const;
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Vector2 cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const;
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Vector2 cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const;
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Vector2 slide(const Vector2& p_vec) const;
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Vector2 reflect(const Vector2& p_vec) 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 float &rvalue) const;
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void operator*=(const float &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 float &rvalue) const;
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void operator/=(const float &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(float p_radians) {
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x=Math::sin(p_radians);
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y=Math::cos(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(float 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 snapped(const Vector2& p_by) const;
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float get_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(float p_x,float p_y) { x=p_x; y=p_y; }
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_FORCE_INLINE_ Vector2() { x=0; y=0; }
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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*(float p_scalar, const Vector2& p_vec) {
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return p_vec*p_scalar;
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}
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Vector2 Vector2::linear_interpolate(const Vector2& p_b,float 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::linear_interpolate(const Vector2& p_a, const Vector2& p_b,float 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 Matrix32;
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struct Rect2 {
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Point2 pos;
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Size2 size;
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const Vector2& get_pos() const { return pos; }
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void set_pos(const Vector2& p_pos) { pos=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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float 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 ( pos.x >= (p_rect.pos.x + p_rect.size.width) )
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return false;
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if ( (pos.x+size.width) <= p_rect.pos.x )
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return false;
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if ( pos.y >= (p_rect.pos.y + p_rect.size.height) )
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return false;
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if ( (pos.y+size.height) <= p_rect.pos.y )
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return false;
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return true;
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}
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inline float distance_to(const Vector2& p_point) const {
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float dist = 1e20;
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if (p_point.x < pos.x) {
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dist=MIN(dist,pos.x-p_point.x);
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}
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if (p_point.y < pos.y) {
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dist=MIN(dist,pos.y-p_point.y);
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}
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if (p_point.x >= (pos.x+size.x) ) {
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dist=MIN(p_point.x-(pos.x+size.x),dist);
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}
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if (p_point.y >= (pos.y+size.y) ) {
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dist=MIN(p_point.y-(pos.y+size.y),dist);
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}
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if (dist==1e20)
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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 Matrix32& 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.pos.x>=pos.x) && (p_rect.pos.y>=pos.y) &&
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((p_rect.pos.x+p_rect.size.x)<(pos.x+size.x)) &&
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((p_rect.pos.y+p_rect.size.y)<(pos.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.pos.x = MAX( p_rect.pos.x , pos.x );
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new_rect.pos.y = MAX( p_rect.pos.y , pos.y );
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Point2 p_rect_end=p_rect.pos+p_rect.size;
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Point2 end=pos+size;
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new_rect.size.x=MIN(p_rect_end.x,end.x) - new_rect.pos.x;
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new_rect.size.y=MIN(p_rect_end.y,end.y) - new_rect.pos.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.pos.x=MIN( p_rect.pos.x , pos.x );
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new_rect.pos.y=MIN( p_rect.pos.y , pos.y );
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new_rect.size.x = MAX( p_rect.pos.x+p_rect.size.x , pos.x+size.x );
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new_rect.size.y = MAX( p_rect.pos.y+p_rect.size.y , pos.y+size.y );
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new_rect.size = new_rect.size - new_rect.pos; //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 < pos.x)
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return false;
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if (p_point.y < pos.y)
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return false;
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if (p_point.x >= (pos.x+size.x) )
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return false;
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if (p_point.y >= (pos.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 pos==p_rect.pos && size==p_rect.size; }
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bool operator!=(const Rect2& p_rect) const { return pos!=p_rect.pos || 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.pos.x-=p_by;
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g.pos.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 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=pos;
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Vector2 end=pos+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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pos=begin;
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size=end-begin;
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}
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operator String() const { return String(pos)+", "+String(size); }
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Rect2() {}
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Rect2( float p_x, float p_y, float p_width, float p_height) { pos=Point2(p_x,p_y); size=Size2( p_width, p_height ); }
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Rect2( const Point2& p_pos, const Size2& p_size ) { pos=p_pos; size=p_size; }
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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);
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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);
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Point2i operator-() const;
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bool operator<(const Point2i& p_vec2) const { return (x==p_vec2.x)?(y<p_vec2.y):(x<p_vec2.x); }
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bool operator>(const Point2i& p_vec2) const { return (x==p_vec2.x)?(y>p_vec2.y):(x>p_vec2.x); }
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bool operator==(const Point2i& p_vec2) const;
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bool operator!=(const Point2i& p_vec2) const;
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float get_aspect() const { return width/(float)height; }
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operator String() const { return String::num(x)+", "+String::num(y); }
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operator Vector2() const { return Vector2(x,y); }
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inline Point2i(const Vector2& p_vec2) { x=(int)p_vec2.x; y=(int)p_vec2.y; }
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inline Point2i(int p_x,int p_y) { x=p_x; y=p_y; }
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inline Point2i() { x=0; y=0; }
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};
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typedef Point2i Size2i;
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struct Rect2i {
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Point2i pos;
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Size2i size;
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const Point2i& get_pos() const { return pos; }
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void set_pos(const Point2i& p_pos) { pos=p_pos; }
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const Point2i& get_size() const { return size; }
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void set_size(const Point2i& p_size) { size=p_size; }
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int get_area() const { return size.width*size.height; }
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inline bool intersects(const Rect2i& p_rect) const {
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if ( pos.x > (p_rect.pos.x + p_rect.size.width) )
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return false;
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if ( (pos.x+size.width) < p_rect.pos.x )
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return false;
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if ( pos.y > (p_rect.pos.y + p_rect.size.height) )
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return false;
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if ( (pos.y+size.height) < p_rect.pos.y )
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return false;
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return true;
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}
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inline bool encloses(const Rect2i& p_rect) const {
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return (p_rect.pos.x>=pos.x) && (p_rect.pos.y>=pos.y) &&
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((p_rect.pos.x+p_rect.size.x)<(pos.x+size.x)) &&
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((p_rect.pos.y+p_rect.size.y)<(pos.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 Rect2i clip(const Rect2i& p_rect) const { /// return a clipped rect
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Rect2i new_rect=p_rect;
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if (!intersects( new_rect ))
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return Rect2i();
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new_rect.pos.x = MAX( p_rect.pos.x , pos.x );
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new_rect.pos.y = MAX( p_rect.pos.y , pos.y );
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Point2 p_rect_end=p_rect.pos+p_rect.size;
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Point2 end=pos+size;
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new_rect.size.x=(int)(MIN(p_rect_end.x,end.x) - new_rect.pos.x);
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new_rect.size.y=(int)(MIN(p_rect_end.y,end.y) - new_rect.pos.y);
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return new_rect;
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}
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inline Rect2i merge(const Rect2i& p_rect) const { ///< return a merged rect
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Rect2i new_rect;
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new_rect.pos.x=MIN( p_rect.pos.x , pos.x );
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new_rect.pos.y=MIN( p_rect.pos.y , pos.y );
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new_rect.size.x = MAX( p_rect.pos.x+p_rect.size.x , pos.x+size.x );
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new_rect.size.y = MAX( p_rect.pos.y+p_rect.size.y , pos.y+size.y );
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new_rect.size = new_rect.size - new_rect.pos; //make relative again
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return new_rect;
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};
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bool has_point(const Point2& p_point) const {
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if (p_point.x < pos.x)
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return false;
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if (p_point.y < pos.y)
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return false;
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if (p_point.x >= (pos.x+size.x) )
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return false;
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if (p_point.y >= (pos.y+size.y) )
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return false;
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return true;
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}
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bool no_area() { return (size.width<=0 || size.height<=0 ); }
|
|
|
|
bool operator==(const Rect2i& p_rect) const { return pos==p_rect.pos && size==p_rect.size; }
|
|
bool operator!=(const Rect2i& p_rect) const { return pos!=p_rect.pos || size!=p_rect.size; }
|
|
|
|
Rect2i grow(int p_by) const {
|
|
|
|
Rect2i g=*this;
|
|
g.pos.x-=p_by;
|
|
g.pos.y-=p_by;
|
|
g.size.width+=p_by*2;
|
|
g.size.height+=p_by*2;
|
|
return g;
|
|
}
|
|
|
|
inline void expand_to(const Point2i& p_vector) {
|
|
|
|
Point2i begin=pos;
|
|
Point2i end=pos+size;
|
|
|
|
if (p_vector.x<begin.x)
|
|
begin.x=p_vector.x;
|
|
if (p_vector.y<begin.y)
|
|
begin.y=p_vector.y;
|
|
|
|
if (p_vector.x>end.x)
|
|
end.x=p_vector.x;
|
|
if (p_vector.y>end.y)
|
|
end.y=p_vector.y;
|
|
|
|
pos=begin;
|
|
size=end-begin;
|
|
}
|
|
|
|
|
|
operator String() const { return String(pos)+", "+String(size); }
|
|
|
|
operator Rect2() const { return Rect2(pos,size); }
|
|
Rect2i(const Rect2& p_r2) { pos=p_r2.pos; size=p_r2.size; }
|
|
Rect2i() {}
|
|
Rect2i( int p_x, int p_y, int p_width, int p_height) { pos=Point2(p_x,p_y); size=Size2( p_width, p_height ); }
|
|
Rect2i( const Point2& p_pos, const Size2& p_size ) { pos=p_pos; size=p_size; }
|
|
};
|
|
|
|
|
|
|
|
struct Matrix32 {
|
|
|
|
|
|
Vector2 elements[3];
|
|
|
|
|
|
_FORCE_INLINE_ float tdotx(const Vector2& v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
|
|
_FORCE_INLINE_ float 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();
|
|
Matrix32 inverse() const;
|
|
|
|
void affine_invert();
|
|
Matrix32 affine_inverse() const;
|
|
|
|
void set_rotation(real_t p_phi);
|
|
real_t get_rotation() const;
|
|
_FORCE_INLINE_ void set_rotation_and_scale(real_t p_phi,const Size2& p_scale);
|
|
void rotate(real_t p_phi);
|
|
|
|
void scale(const Vector2& p_scale);
|
|
void scale_basis(const Vector2& p_scale);
|
|
void translate( real_t p_tx, real_t p_ty);
|
|
void translate( const Vector2& p_translation );
|
|
|
|
float basis_determinant() const;
|
|
|
|
Vector2 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; }
|
|
|
|
Matrix32 scaled(const Vector2& p_scale) const;
|
|
Matrix32 basis_scaled(const Vector2& p_scale) const;
|
|
Matrix32 translated(const Vector2& p_offset) const;
|
|
Matrix32 rotated(float p_phi) const;
|
|
|
|
Matrix32 untranslated() const;
|
|
|
|
|
|
void orthonormalize();
|
|
Matrix32 orthonormalized() const;
|
|
|
|
bool operator==(const Matrix32& p_transform) const;
|
|
bool operator!=(const Matrix32& p_transform) const;
|
|
|
|
void operator*=(const Matrix32& p_transform);
|
|
Matrix32 operator*(const Matrix32& p_transform) const;
|
|
|
|
Matrix32 interpolate_with(const Matrix32& p_transform, float p_c) const;
|
|
|
|
_FORCE_INLINE_ Vector2 basis_xform(const Vector2& p_vec) const;
|
|
_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2& p_vec) const;
|
|
_FORCE_INLINE_ Vector2 xform(const Vector2& p_vec) const;
|
|
_FORCE_INLINE_ Vector2 xform_inv(const Vector2& p_vec) const;
|
|
_FORCE_INLINE_ Rect2 xform(const Rect2& p_vec) const;
|
|
_FORCE_INLINE_ Rect2 xform_inv(const Rect2& p_vec) const;
|
|
|
|
|
|
operator String() const;
|
|
|
|
|
|
Matrix32(real_t p_rot, const Vector2& p_pos);
|
|
Matrix32() { elements[0][0]=1.0; elements[1][1]=1.0; }
|
|
|
|
};
|
|
|
|
bool Rect2::intersects_transformed(const Matrix32& p_xform, const Rect2& p_rect) const {
|
|
|
|
//SAT intersection between local and transformed rect2
|
|
|
|
Vector2 xf_points[4]={
|
|
p_xform.xform(p_rect.pos),
|
|
p_xform.xform(Vector2(p_rect.pos.x+p_rect.size.x,p_rect.pos.y)),
|
|
p_xform.xform(Vector2(p_rect.pos.x,p_rect.pos.y+p_rect.size.y)),
|
|
p_xform.xform(Vector2(p_rect.pos.x+p_rect.size.x,p_rect.pos.y+p_rect.size.y)),
|
|
};
|
|
|
|
real_t low_limit;
|
|
|
|
//base rect2 first (faster)
|
|
|
|
if (xf_points[0].y>pos.y)
|
|
goto next1;
|
|
if (xf_points[1].y>pos.y)
|
|
goto next1;
|
|
if (xf_points[2].y>pos.y)
|
|
goto next1;
|
|
if (xf_points[3].y>pos.y)
|
|
goto next1;
|
|
|
|
return false;
|
|
|
|
next1:
|
|
|
|
low_limit=pos.y+size.y;
|
|
|
|
if (xf_points[0].y<low_limit)
|
|
goto next2;
|
|
if (xf_points[1].y<low_limit)
|
|
goto next2;
|
|
if (xf_points[2].y<low_limit)
|
|
goto next2;
|
|
if (xf_points[3].y<low_limit)
|
|
goto next2;
|
|
|
|
return false;
|
|
|
|
next2:
|
|
|
|
if (xf_points[0].x>pos.x)
|
|
goto next3;
|
|
if (xf_points[1].x>pos.x)
|
|
goto next3;
|
|
if (xf_points[2].x>pos.x)
|
|
goto next3;
|
|
if (xf_points[3].x>pos.x)
|
|
goto next3;
|
|
|
|
return false;
|
|
|
|
next3:
|
|
|
|
low_limit=pos.x+size.x;
|
|
|
|
if (xf_points[0].x<low_limit)
|
|
goto next4;
|
|
if (xf_points[1].x<low_limit)
|
|
goto next4;
|
|
if (xf_points[2].x<low_limit)
|
|
goto next4;
|
|
if (xf_points[3].x<low_limit)
|
|
goto next4;
|
|
|
|
return false;
|
|
|
|
next4:
|
|
|
|
Vector2 xf_points2[4]={
|
|
pos,
|
|
Vector2(pos.x+size.x,pos.y),
|
|
Vector2(pos.x,pos.y+size.y),
|
|
Vector2(pos.x+size.x,pos.y+size.y),
|
|
};
|
|
|
|
real_t maxa=p_xform.elements[0].dot(xf_points2[0]);
|
|
real_t mina=maxa;
|
|
|
|
real_t dp = p_xform.elements[0].dot(xf_points2[1]);
|
|
maxa=MAX(dp,maxa);
|
|
mina=MIN(dp,mina);
|
|
|
|
dp = p_xform.elements[0].dot(xf_points2[2]);
|
|
maxa=MAX(dp,maxa);
|
|
mina=MIN(dp,mina);
|
|
|
|
dp = p_xform.elements[0].dot(xf_points2[3]);
|
|
maxa=MAX(dp,maxa);
|
|
mina=MIN(dp,mina);
|
|
|
|
real_t maxb=p_xform.elements[0].dot(xf_points[0]);
|
|
real_t minb=maxb;
|
|
|
|
dp = p_xform.elements[0].dot(xf_points[1]);
|
|
maxb=MAX(dp,maxb);
|
|
minb=MIN(dp,minb);
|
|
|
|
dp = p_xform.elements[0].dot(xf_points[2]);
|
|
maxb=MAX(dp,maxb);
|
|
minb=MIN(dp,minb);
|
|
|
|
dp = p_xform.elements[0].dot(xf_points[3]);
|
|
maxb=MAX(dp,maxb);
|
|
minb=MIN(dp,minb);
|
|
|
|
|
|
if ( mina > maxb )
|
|
return false;
|
|
if ( minb > maxa )
|
|
return false;
|
|
|
|
maxa=p_xform.elements[1].dot(xf_points2[0]);
|
|
mina=maxa;
|
|
|
|
dp = p_xform.elements[1].dot(xf_points2[1]);
|
|
maxa=MAX(dp,maxa);
|
|
mina=MIN(dp,mina);
|
|
|
|
dp = p_xform.elements[1].dot(xf_points2[2]);
|
|
maxa=MAX(dp,maxa);
|
|
mina=MIN(dp,mina);
|
|
|
|
dp = p_xform.elements[1].dot(xf_points2[3]);
|
|
maxa=MAX(dp,maxa);
|
|
mina=MIN(dp,mina);
|
|
|
|
maxb=p_xform.elements[1].dot(xf_points[0]);
|
|
minb=maxb;
|
|
|
|
dp = p_xform.elements[1].dot(xf_points[1]);
|
|
maxb=MAX(dp,maxb);
|
|
minb=MIN(dp,minb);
|
|
|
|
dp = p_xform.elements[1].dot(xf_points[2]);
|
|
maxb=MAX(dp,maxb);
|
|
minb=MIN(dp,minb);
|
|
|
|
dp = p_xform.elements[1].dot(xf_points[3]);
|
|
maxb=MAX(dp,maxb);
|
|
minb=MIN(dp,minb);
|
|
|
|
|
|
if ( mina > maxb )
|
|
return false;
|
|
if ( minb > maxa )
|
|
return false;
|
|
|
|
|
|
return true;
|
|
|
|
}
|
|
|
|
Vector2 Matrix32::basis_xform(const Vector2& v) const {
|
|
|
|
return Vector2(
|
|
tdotx(v),
|
|
tdoty(v)
|
|
);
|
|
}
|
|
|
|
Vector2 Matrix32::basis_xform_inv(const Vector2& v) const{
|
|
|
|
return Vector2(
|
|
elements[0].dot(v),
|
|
elements[1].dot(v)
|
|
);
|
|
}
|
|
|
|
Vector2 Matrix32::xform(const Vector2& v) const {
|
|
|
|
return Vector2(
|
|
tdotx(v),
|
|
tdoty(v)
|
|
) + elements[2];
|
|
}
|
|
Vector2 Matrix32::xform_inv(const Vector2& p_vec) const {
|
|
|
|
Vector2 v = p_vec - elements[2];
|
|
|
|
return Vector2(
|
|
elements[0].dot(v),
|
|
elements[1].dot(v)
|
|
);
|
|
|
|
}
|
|
Rect2 Matrix32::xform(const Rect2& p_rect) const {
|
|
|
|
Vector2 x=elements[0]*p_rect.size.x;
|
|
Vector2 y=elements[1]*p_rect.size.y;
|
|
Vector2 pos = xform( p_rect.pos );
|
|
|
|
Rect2 new_rect;
|
|
new_rect.pos=pos;
|
|
new_rect.expand_to( pos+x );
|
|
new_rect.expand_to( pos+y );
|
|
new_rect.expand_to( pos+x+y );
|
|
return new_rect;
|
|
}
|
|
|
|
void Matrix32::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[0][1]=-Math::sin(p_rot)*p_scale.x;
|
|
elements[1][0]=Math::sin(p_rot)*p_scale.y;
|
|
|
|
}
|
|
|
|
Rect2 Matrix32::xform_inv(const Rect2& p_rect) const {
|
|
|
|
Vector2 ends[4]={
|
|
xform_inv( p_rect.pos ),
|
|
xform_inv( Vector2(p_rect.pos.x,p_rect.pos.y+p_rect.size.y ) ),
|
|
xform_inv( Vector2(p_rect.pos.x+p_rect.size.x,p_rect.pos.y+p_rect.size.y ) ),
|
|
xform_inv( Vector2(p_rect.pos.x+p_rect.size.x,p_rect.pos.y ) )
|
|
};
|
|
|
|
Rect2 new_rect;
|
|
new_rect.pos=ends[0];
|
|
new_rect.expand_to(ends[1]);
|
|
new_rect.expand_to(ends[2]);
|
|
new_rect.expand_to(ends[3]);
|
|
|
|
return new_rect;
|
|
}
|
|
|
|
|
|
#endif
|