f271591ac2
This is the follow up for the 2D changes mentioned in PR #6865. It fixes various mistakes regarding the order of matrix indices, order of transformation operations, usage of atan2 function and ensures that the sense of rotation is compatible with a left-handed coordinate system with Y-axis pointing down (which flips the sense of rotations along the z-axis). Also replaced float with real_t, and tried to make use of Matrix32 methods rather than accessing its elements directly. Affected code in the Godot code base is also fixed in this commit. The user code using functions involving angles such as atan2, angle_to, get_rotation, set_rotation will need to be updated to conform with the new behavior. Furthermore, the sign of the rotation angles in existing 2D scene files need to be flipped as well.
872 lines
22 KiB
C++
872 lines
22 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) 2007-2017 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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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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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 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,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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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 cubic_interpolate_soft(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_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 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 snapped(const Vector2& p_by) const;
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real_t 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(real_t p_x,real_t 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*(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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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::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 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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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 ( 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 real_t distance_to(const Vector2& p_point) const {
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real_t 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( real_t p_x, real_t p_y, real_t p_width, real_t p_height) { pos=Point2(p_x,p_y); size=Size2( p_width, p_height ); }
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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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real_t get_aspect() const { return width/(real_t)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
|
|
|
|
return new_rect;
|
|
};
|
|
bool has_point(const Point2& p_point) const {
|
|
if (p_point.x < pos.x)
|
|
return false;
|
|
if (p_point.y < pos.y)
|
|
return false;
|
|
|
|
if (p_point.x >= (pos.x+size.x) )
|
|
return false;
|
|
if (p_point.y >= (pos.y+size.y) )
|
|
return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
bool no_area() { return (size.width<=0 || size.height<=0 ); }
|
|
|
|
bool operator==(const Rect2i& p_rect) const { return pos==p_rect.pos && size==p_rect.size; }
|
|
bool operator!=(const Rect2i& p_rect) const { return pos!=p_rect.pos || size!=p_rect.size; }
|
|
|
|
Rect2i grow(int p_by) const {
|
|
|
|
Rect2i g=*this;
|
|
g.pos.x-=p_by;
|
|
g.pos.y-=p_by;
|
|
g.size.width+=p_by*2;
|
|
g.size.height+=p_by*2;
|
|
return g;
|
|
}
|
|
|
|
inline void expand_to(const Point2i& p_vector) {
|
|
|
|
Point2i begin=pos;
|
|
Point2i end=pos+size;
|
|
|
|
if (p_vector.x<begin.x)
|
|
begin.x=p_vector.x;
|
|
if (p_vector.y<begin.y)
|
|
begin.y=p_vector.y;
|
|
|
|
if (p_vector.x>end.x)
|
|
end.x=p_vector.x;
|
|
if (p_vector.y>end.y)
|
|
end.y=p_vector.y;
|
|
|
|
pos=begin;
|
|
size=end-begin;
|
|
}
|
|
|
|
|
|
operator String() const { return String(pos)+", "+String(size); }
|
|
|
|
operator Rect2() const { return Rect2(pos,size); }
|
|
Rect2i(const Rect2& p_r2) { pos=p_r2.pos; size=p_r2.size; }
|
|
Rect2i() {}
|
|
Rect2i( int p_x, int p_y, int p_width, int p_height) { pos=Point2(p_x,p_y); size=Size2( p_width, p_height ); }
|
|
Rect2i( const Point2& p_pos, const Size2& p_size ) { pos=p_pos; size=p_size; }
|
|
};
|
|
|
|
|
|
|
|
struct Matrix32 {
|
|
// Warning #1: basis of Matrix32 is stored differently from Matrix3. 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();
|
|
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 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; }
|
|
|
|
Matrix32 scaled(const Size2& p_scale) const;
|
|
Matrix32 basis_scaled(const Size2& p_scale) const;
|
|
Matrix32 translated(const Vector2& p_offset) const;
|
|
Matrix32 rotated(real_t 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, real_t p_c) const;
|
|
|
|
_FORCE_INLINE_ Vector2 basis_xform(const Vector2& p_vec) const;
|
|
_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2& p_vec) const;
|
|
_FORCE_INLINE_ Vector2 xform(const Vector2& p_vec) const;
|
|
_FORCE_INLINE_ Vector2 xform_inv(const Vector2& p_vec) const;
|
|
_FORCE_INLINE_ Rect2 xform(const Rect2& p_vec) const;
|
|
_FORCE_INLINE_ Rect2 xform_inv(const Rect2& p_vec) const;
|
|
|
|
operator String() const;
|
|
|
|
Matrix32(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;
|
|
}
|
|
|
|
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[1][0]=-Math::sin(p_rot)*p_scale.y;
|
|
elements[0][1]=Math::sin(p_rot)*p_scale.x;
|
|
|
|
}
|
|
|
|
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
|