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+/*************************************************************************/
+/* math_2d.h */
+/*************************************************************************/
+/* This file is part of: */
+/* GODOT ENGINE */
+/* http://www.godotengine.org */
+/*************************************************************************/
+/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
+/* */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the */
+/* "Software"), to deal in the Software without restriction, including */
+/* without limitation the rights to use, copy, modify, merge, publish, */
+/* distribute, sublicense, and/or sell copies of the Software, and to */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions: */
+/* */
+/* The above copyright notice and this permission notice shall be */
+/* included in all copies or substantial portions of the Software. */
+/* */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
+/*************************************************************************/
+#ifndef MATH_2D_H
+#define MATH_2D_H
+
+#include "math_funcs.h"
+#include "ustring.h"
+/**
+ @author Juan Linietsky <reduzio@gmail.com>
+*/
+enum Margin {
+
+ MARGIN_LEFT,
+ MARGIN_TOP,
+ MARGIN_RIGHT,
+ MARGIN_BOTTOM
+};
+
+enum Orientation {
+
+ HORIZONTAL,
+ VERTICAL
+};
+
+enum HAlign {
+
+ HALIGN_LEFT,
+ HALIGN_CENTER,
+ HALIGN_RIGHT
+};
+
+enum VAlign {
+
+ VALIGN_TOP,
+ VALIGN_CENTER,
+ VALIGN_BOTTOM
+};
+
+struct Vector2 {
+
+ union {
+ float x;
+ float width;
+ };
+ union {
+ float y;
+ float height;
+ };
+
+
+ _FORCE_INLINE_ float& operator[](int p_idx) {
+ return p_idx?y:x;
+ }
+ _FORCE_INLINE_ const float& operator[](int p_idx) const {
+ return p_idx?y:x;
+ }
+
+ void normalize();
+ Vector2 normalized() const;
+
+ float length() const;
+ float length_squared() const;
+
+ float distance_to(const Vector2& p_vector2) const;
+ float distance_squared_to(const Vector2& p_vector2) const;
+ float angle_to(const Vector2& p_vector2) const;
+
+ float dot(const Vector2& p_other) const;
+ float cross(const Vector2& p_other) const;
+ Vector2 cross(real_t p_other) const;
+ Vector2 project(const Vector2& p_vec) const;
+
+ Vector2 plane_project(real_t p_d, const Vector2& p_vec) const;
+
+ Vector2 clamped(real_t p_len) const;
+
+ _FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2& p_a, const Vector2& p_b,float p_t);
+ _FORCE_INLINE_ Vector2 linear_interpolate(const Vector2& p_b,float p_t) const;
+ Vector2 cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const;
+ Vector2 cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const;
+
+
+ Vector2 operator+(const Vector2& p_v) const;
+ void operator+=(const Vector2& p_v);
+ Vector2 operator-(const Vector2& p_v) const;
+ void operator-=(const Vector2& p_v);
+ Vector2 operator*(const Vector2 &p_v1) const;
+
+ Vector2 operator*(const float &rvalue) const;
+ void operator*=(const float &rvalue);
+ void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }
+
+ Vector2 operator/(const Vector2 &p_v1) const;
+
+ Vector2 operator/(const float &rvalue) const;
+
+ void operator/=(const float &rvalue);
+
+ Vector2 operator-() const;
+
+ bool operator==(const Vector2& p_vec2) const;
+ bool operator!=(const Vector2& p_vec2) const;
+
+ bool operator<(const Vector2& p_vec2) const { return (x==p_vec2.x)?(y<p_vec2.y):(x<p_vec2.x); }
+ bool operator<=(const Vector2& p_vec2) const { return (x==p_vec2.x)?(y<=p_vec2.y):(x<=p_vec2.x); }
+
+ real_t atan2() const;
+
+ void set_rotation(float p_radians) {
+
+ x=Math::sin(p_radians);
+ y=Math::cos(p_radians);
+ }
+
+ _FORCE_INLINE_ Vector2 abs() const {
+
+ return Vector2( Math::abs(x), Math::abs(y) );
+ }
+
+ Vector2 rotated(float p_by) const;
+ Vector2 tangent() const {
+
+ return Vector2(y,-x);
+ }
+
+ Vector2 floor() const;
+ Vector2 snapped(const Vector2& p_by) const;
+ float get_aspect() const { return width/height; }
+
+
+ operator String() const { return String::num(x)+","+String::num(y); }
+
+ inline Vector2(float p_x,float p_y) { x=p_x; y=p_y; }
+ inline Vector2() { x=0; y=0; }
+};
+
+_FORCE_INLINE_ Vector2 Vector2::plane_project(real_t p_d, const Vector2& p_vec) const {
+
+ return p_vec - *this * ( dot(p_vec) -p_d);
+}
+
+
+_FORCE_INLINE_ Vector2 operator*(float p_scalar, const Vector2& p_vec) {
+
+ return p_vec*p_scalar;
+}
+
+Vector2 Vector2::linear_interpolate(const Vector2& p_b,float p_t) const {
+
+ Vector2 res=*this;
+
+ res.x+= (p_t * (p_b.x-x));
+ res.y+= (p_t * (p_b.y-y));
+
+ return res;
+
+}
+
+Vector2 Vector2::linear_interpolate(const Vector2& p_a, const Vector2& p_b,float p_t) {
+
+ Vector2 res=p_a;
+
+ res.x+= (p_t * (p_b.x-p_a.x));
+ res.y+= (p_t * (p_b.y-p_a.y));
+
+ return res;
+}
+
+typedef Vector2 Size2;
+typedef Vector2 Point2;
+
+
+struct Rect2 {
+
+ Point2 pos;
+ Size2 size;
+
+ const Vector2& get_pos() const { return pos; }
+ void set_pos(const Vector2& p_pos) { pos=p_pos; }
+ const Vector2& get_size() const { return size; }
+ void set_size(const Vector2& p_size) { size=p_size; }
+
+ float get_area() const { return size.width*size.height; }
+
+ inline bool intersects(const Rect2& p_rect) const {
+ if ( pos.x > (p_rect.pos.x + p_rect.size.width) )
+ return false;
+ if ( (pos.x+size.width) < p_rect.pos.x )
+ return false;
+ if ( pos.y > (p_rect.pos.y + p_rect.size.height) )
+ return false;
+ if ( (pos.y+size.height) < p_rect.pos.y )
+ return false;
+
+ return true;
+ }
+
+ bool intersects_segment(const Point2& p_from, const Point2& p_to, Point2* r_pos=NULL, Point2* r_normal=NULL) const;
+
+ inline bool encloses(const Rect2& p_rect) const {
+
+ return (p_rect.pos.x>=pos.x) && (p_rect.pos.y>=pos.y) &&
+ ((p_rect.pos.x+p_rect.size.x)<(pos.x+size.x)) &&
+ ((p_rect.pos.y+p_rect.size.y)<(pos.y+size.y));
+
+ }
+
+ inline bool has_no_area() const {
+
+ return (size.x<=0 || size.y<=0);
+
+ }
+ inline Rect2 clip(const Rect2& p_rect) const { /// return a clipped rect
+
+ Rect2 new_rect=p_rect;
+
+ if (!intersects( new_rect ))
+ return Rect2();
+
+ new_rect.pos.x = MAX( p_rect.pos.x , pos.x );
+ new_rect.pos.y = MAX( p_rect.pos.y , pos.y );
+
+ Point2 p_rect_end=p_rect.pos+p_rect.size;
+ Point2 end=pos+size;
+
+ new_rect.size.x=MIN(p_rect_end.x,end.x) - new_rect.pos.x;
+ new_rect.size.y=MIN(p_rect_end.y,end.y) - new_rect.pos.y;
+
+ return new_rect;
+ }
+
+ inline Rect2 merge(const Rect2& p_rect) const { ///< return a merged rect
+
+ Rect2 new_rect;
+
+ new_rect.pos.x=MIN( p_rect.pos.x , pos.x );
+ new_rect.pos.y=MIN( p_rect.pos.y , pos.y );
+
+
+ new_rect.size.x = MAX( p_rect.pos.x+p_rect.size.x , pos.x+size.x );
+ new_rect.size.y = MAX( p_rect.pos.y+p_rect.size.y , pos.y+size.y );
+
+ 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() const { return (size.width<=0 || size.height<=0 ); }
+
+ bool operator==(const Rect2& p_rect) const { return pos==p_rect.pos && size==p_rect.size; }
+ bool operator!=(const Rect2& p_rect) const { return pos!=p_rect.pos || size!=p_rect.size; }
+
+ Rect2 grow(real_t p_by) const {
+
+ Rect2 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 Rect2 expand(const Vector2& p_vector) const {
+
+ Rect2 r = *this;
+ r.expand_to(p_vector);
+ return r;
+ }
+
+ inline void expand_to(const Vector2& p_vector) { //in place function for speed
+
+ Vector2 begin=pos;
+ Vector2 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); }
+
+ Rect2() {}
+ 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 ); }
+ Rect2( const Point2& p_pos, const Size2& p_size ) { pos=p_pos; size=p_size; }
+};
+
+
+/* INTEGER STUFF */
+
+struct Point2i {
+
+ union {
+ int x;
+ int width;
+ };
+ union {
+ int y;
+ int height;
+ };
+
+
+ _FORCE_INLINE_ int& operator[](int p_idx) {
+ return p_idx?y:x;
+ }
+ _FORCE_INLINE_ const int& operator[](int p_idx) const {
+ return p_idx?y:x;
+ }
+
+ Point2i operator+(const Point2i& p_v) const;
+ void operator+=(const Point2i& p_v);
+ Point2i operator-(const Point2i& p_v) const;
+ void operator-=(const Point2i& p_v);
+ Point2i operator*(const Point2i &p_v1) const;
+
+ Point2i operator*(const int &rvalue) const;
+ void operator*=(const int &rvalue);
+
+ Point2i operator/(const Point2i &p_v1) const;
+
+ Point2i operator/(const int &rvalue) const;
+
+ void operator/=(const int &rvalue);
+
+ Point2i operator-() const;
+ bool operator<(const Point2i& p_vec2) const { return (x==p_vec2.x)?(y<p_vec2.y):(x<p_vec2.x); }
+ bool operator>(const Point2i& p_vec2) const { return (x==p_vec2.x)?(y>p_vec2.y):(x>p_vec2.x); }
+
+ bool operator==(const Point2i& p_vec2) const;
+ bool operator!=(const Point2i& p_vec2) const;
+
+ float get_aspect() const { return width/(float)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 pos;
+ Size2i size;
+
+ const Point2i& get_pos() const { return pos; }
+ void set_pos(const Point2i& p_pos) { pos=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 ( pos.x > (p_rect.pos.x + p_rect.size.width) )
+ return false;
+ if ( (pos.x+size.width) < p_rect.pos.x )
+ return false;
+ if ( pos.y > (p_rect.pos.y + p_rect.size.height) )
+ return false;
+ if ( (pos.y+size.height) < p_rect.pos.y )
+ return false;
+
+ return true;
+ }
+
+ inline bool encloses(const Rect2i& p_rect) const {
+
+ return (p_rect.pos.x>=pos.x) && (p_rect.pos.y>=pos.y) &&
+ ((p_rect.pos.x+p_rect.size.x)<(pos.x+size.x)) &&
+ ((p_rect.pos.y+p_rect.size.y)<(pos.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.pos.x = MAX( p_rect.pos.x , pos.x );
+ new_rect.pos.y = MAX( p_rect.pos.y , pos.y );
+
+ Point2 p_rect_end=p_rect.pos+p_rect.size;
+ Point2 end=pos+size;
+
+ new_rect.size.x=(int)(MIN(p_rect_end.x,end.x) - new_rect.pos.x);
+ new_rect.size.y=(int)(MIN(p_rect_end.y,end.y) - new_rect.pos.y);
+
+ return new_rect;
+ }
+
+ inline Rect2i merge(const Rect2i& p_rect) const { ///< return a merged rect
+
+ Rect2i new_rect;
+
+ new_rect.pos.x=MIN( p_rect.pos.x , pos.x );
+ new_rect.pos.y=MIN( p_rect.pos.y , pos.y );
+
+
+ new_rect.size.x = MAX( p_rect.pos.x+p_rect.size.x , pos.x+size.x );
+ new_rect.size.y = MAX( p_rect.pos.y+p_rect.size.y , pos.y+size.y );
+
+ new_rect.size = new_rect.size - new_rect.pos; //make relative again
+
+ return new_rect;
+ };
+ bool has_point(const Point2& p_point) {
+ 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 {
+
+
+ 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 );
+ 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; }
+
+};
+
+
+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
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