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-rw-r--r--core/math/math_2d.cpp597
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diff --git a/core/math/math_2d.cpp b/core/math/math_2d.cpp
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+/*************************************************************************/
+/* math_2d.cpp */
+/*************************************************************************/
+/* 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. */
+/*************************************************************************/
+#include "math_2d.h"
+
+
+real_t Vector2::atan2() const {
+
+ return Math::atan2(x,y);
+}
+
+float Vector2::length() const {
+
+ return Math::sqrt( x*x + y*y );
+}
+
+float Vector2::length_squared() const {
+
+ return x*x + y*y;
+}
+
+void Vector2::normalize() {
+
+ float l = x*x + y*y;
+ if (l!=0) {
+
+ l=Math::sqrt(l);
+ x/=l;
+ y/=l;
+ }
+}
+
+Vector2 Vector2::normalized() const {
+
+ Vector2 v=*this;
+ v.normalize();
+ return v;
+}
+
+float Vector2::distance_to(const Vector2& p_vector2) const {
+
+ return Math::sqrt( (x-p_vector2.x)*(x-p_vector2.x) + (y-p_vector2.y)*(y-p_vector2.y));
+}
+
+float Vector2::distance_squared_to(const Vector2& p_vector2) const {
+
+ return (x-p_vector2.x)*(x-p_vector2.x) + (y-p_vector2.y)*(y-p_vector2.y);
+}
+
+float Vector2::angle_to(const Vector2& p_vector2) const {
+
+ return Math::atan2( x-p_vector2.x, y - p_vector2.y );
+}
+
+float Vector2::dot(const Vector2& p_other) const {
+
+ return x*p_other.x + y*p_other.y;
+}
+
+float Vector2::cross(const Vector2& p_other) const {
+
+ return x*p_other.y - y*p_other.x;
+}
+
+Vector2 Vector2::cross(real_t p_other) const {
+
+ return Vector2(p_other*y,-p_other*x);
+}
+
+
+Vector2 Vector2::operator+(const Vector2& p_v) const {
+
+ return Vector2(x+p_v.x,y+p_v.y);
+}
+void Vector2::operator+=(const Vector2& p_v) {
+
+ x+=p_v.x; y+=p_v.y;
+}
+Vector2 Vector2::operator-(const Vector2& p_v) const {
+
+ return Vector2(x-p_v.x,y-p_v.y);
+}
+void Vector2::operator-=(const Vector2& p_v) {
+
+ x-=p_v.x; y-=p_v.y;
+}
+
+Vector2 Vector2::operator*(const Vector2 &p_v1) const {
+
+ return Vector2(x * p_v1.x, y * p_v1.y);
+};
+
+Vector2 Vector2::operator*(const float &rvalue) const {
+
+ return Vector2(x * rvalue, y * rvalue);
+};
+void Vector2::operator*=(const float &rvalue) {
+
+ x *= rvalue; y *= rvalue;
+};
+
+Vector2 Vector2::operator/(const Vector2 &p_v1) const {
+
+ return Vector2(x / p_v1.x, y / p_v1.y);
+};
+
+Vector2 Vector2::operator/(const float &rvalue) const {
+
+ return Vector2(x / rvalue, y / rvalue);
+};
+
+void Vector2::operator/=(const float &rvalue) {
+
+ x /= rvalue; y /= rvalue;
+};
+
+Vector2 Vector2::operator-() const {
+
+ return Vector2(-x,-y);
+}
+
+bool Vector2::operator==(const Vector2& p_vec2) const {
+
+ return x==p_vec2.x && y==p_vec2.y;
+}
+bool Vector2::operator!=(const Vector2& p_vec2) const {
+
+ return x!=p_vec2.x || y!=p_vec2.y;
+}
+Vector2 Vector2::floor() const {
+
+ return Vector2( Math::floor(x), Math::floor(y) );
+}
+
+Vector2 Vector2::rotated(float p_by) const {
+
+ Vector2 v;
+ v.set_rotation(atan2()+p_by);
+ v*=length();
+ return v;
+}
+
+Vector2 Vector2::project(const Vector2& p_vec) const {
+
+ Vector2 v1=p_vec;
+ Vector2 v2=*this;
+ return v2 * ( v1.dot(v2) / v2.dot(v2));
+}
+
+Vector2 Vector2::snapped(const Vector2& p_by) const {
+
+ return Vector2(
+ Math::stepify(x,p_by.x),
+ Math::stepify(y,p_by.y)
+ );
+}
+
+Vector2 Vector2::clamped(real_t p_len) const {
+
+ return *this;
+ real_t l = length();
+ Vector2 v = *this;
+ if (l>0 && p_len<l) {
+
+ v/=l;
+ v*=p_len;
+ }
+
+ return v;
+}
+
+Vector2 Vector2::cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const {
+#if 0
+ k[0] = ((*this) (vi[0] + 1, vi[1], vi[2])) - ((*this) (vi[0],
+ vi[1],vi[2])); //fk = a0
+ k[1] = (((*this) (vi[0] + 1, vi[1], vi[2])) - ((*this) ((int) (v(0) -
+ 1), vi[1],vi[2])))*0.5; //dk = a1
+ k[2] = (((*this) ((int) (v(0) + 2), vi[1], vi[2])) - ((*this) (vi[0],
+ vi[1],vi[2])))*0.5; //dk+1
+ k[3] = k[0]*3 - k[1]*2 - k[2];//a2
+ k[4] = k[1] + k[2] - k[0]*2;//a3
+
+ //ip = a3(t-tk)³ + a2(t-tk)² + a1(t-tk) + a0
+ //
+ //a3 = dk + dk+1 - Dk
+ //a2 = 3Dk - 2dk - dk+1
+ //a1 = dk
+ //a0 = fk
+ //
+ //dk = (fk+1 - fk-1)*0.5
+ //Dk = (fk+1 - fk)
+
+ float dk =
+#endif
+
+ return Vector2();
+}
+
+Vector2 Vector2::cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const {
+
+
+
+ float mu = p_t;
+ float mu2 = mu*mu;
+
+ Vector2 a0 = p_post_b - p_b - p_pre_a + *this;
+ Vector2 a1 = p_pre_a - *this - a0;
+ Vector2 a2 = p_b - p_pre_a;
+ Vector2 a3 = *this;
+
+ return ( a0*mu*mu2 + a1*mu2 + a2*mu + a3 );
+
+ /*
+ float t = p_t;
+ real_t t2 = t*t;
+ real_t t3 = t2*t;
+
+ real_t a = 2.0*t3- 3.0*t2 + 1;
+ real_t b = -2.0*t3+ 3.0*t2;
+ real_t c = t3- 2.0*t2 + t;
+ real_t d = t3- t2;
+
+ Vector2 p_a=*this;
+
+ return Vector2(
+ (a * p_a.x) + (b *p_b.x) + (c * p_pre_a.x) + (d * p_post_b.x),
+ (a * p_a.y) + (b *p_b.y) + (c * p_pre_a.y) + (d * p_post_b.y)
+ );
+*/
+
+}
+
+
+bool Rect2::intersects_segment(const Point2& p_from, const Point2& p_to, Point2* r_pos,Point2* r_normal) const {
+
+ real_t min=0,max=1;
+ int axis=0;
+ float sign=0;
+
+ for(int i=0;i<2;i++) {
+ real_t seg_from=p_from[i];
+ real_t seg_to=p_to[i];
+ real_t box_begin=pos[i];
+ real_t box_end=box_begin+size[i];
+ real_t cmin,cmax;
+ float csign;
+
+ if (seg_from < seg_to) {
+
+ if (seg_from > box_end || seg_to < box_begin)
+ return false;
+ real_t length=seg_to-seg_from;
+ cmin = (seg_from < box_begin)?((box_begin - seg_from)/length):0;
+ cmax = (seg_to > box_end)?((box_end - seg_from)/length):1;
+ csign=-1.0;
+
+ } else {
+
+ if (seg_to > box_end || seg_from < box_begin)
+ return false;
+ real_t length=seg_to-seg_from;
+ cmin = (seg_from > box_end)?(box_end - seg_from)/length:0;
+ cmax = (seg_to < box_begin)?(box_begin - seg_from)/length:1;
+ csign=1.0;
+ }
+
+ if (cmin > min) {
+ min = cmin;
+ axis=i;
+ sign=csign;
+ }
+ if (cmax < max)
+ max = cmax;
+ if (max < min)
+ return false;
+ }
+
+
+ Vector2 rel=p_to-p_from;
+
+ if (r_normal) {
+ Vector2 normal;
+ normal[axis]=sign;
+ *r_normal=normal;
+ }
+
+ if (r_pos)
+ *r_pos=p_from+rel*min;
+
+ return true;
+}
+
+/* Point2i */
+
+Point2i Point2i::operator+(const Point2i& p_v) const {
+
+ return Point2i(x+p_v.x,y+p_v.y);
+}
+void Point2i::operator+=(const Point2i& p_v) {
+
+ x+=p_v.x; y+=p_v.y;
+}
+Point2i Point2i::operator-(const Point2i& p_v) const {
+
+ return Point2i(x-p_v.x,y-p_v.y);
+}
+void Point2i::operator-=(const Point2i& p_v) {
+
+ x-=p_v.x; y-=p_v.y;
+}
+
+Point2i Point2i::operator*(const Point2i &p_v1) const {
+
+ return Point2i(x * p_v1.x, y * p_v1.y);
+};
+
+Point2i Point2i::operator*(const int &rvalue) const {
+
+ return Point2i(x * rvalue, y * rvalue);
+};
+void Point2i::operator*=(const int &rvalue) {
+
+ x *= rvalue; y *= rvalue;
+};
+
+Point2i Point2i::operator/(const Point2i &p_v1) const {
+
+ return Point2i(x / p_v1.x, y / p_v1.y);
+};
+
+Point2i Point2i::operator/(const int &rvalue) const {
+
+ return Point2i(x / rvalue, y / rvalue);
+};
+
+void Point2i::operator/=(const int &rvalue) {
+
+ x /= rvalue; y /= rvalue;
+};
+
+Point2i Point2i::operator-() const {
+
+ return Point2i(-x,-y);
+}
+
+bool Point2i::operator==(const Point2i& p_vec2) const {
+
+ return x==p_vec2.x && y==p_vec2.y;
+}
+bool Point2i::operator!=(const Point2i& p_vec2) const {
+
+ return x!=p_vec2.x || y!=p_vec2.y;
+}
+
+void Matrix32::invert() {
+
+ SWAP(elements[0][1],elements[1][0]);
+ elements[2] = basis_xform(-elements[2]);
+}
+
+Matrix32 Matrix32::inverse() const {
+
+ Matrix32 inv=*this;
+ inv.invert();
+ return inv;
+
+}
+
+void Matrix32::affine_invert() {
+
+ float det = elements[0][0]*elements[1][1] - elements[1][0]*elements[0][1];
+ ERR_FAIL_COND(det==0);
+ float idet = 1.0 / det;
+
+ SWAP( elements[0][0],elements[1][1] );
+ elements[0]*=Vector2(idet,-idet);
+ elements[1]*=Vector2(-idet,idet);
+
+ elements[2] = basis_xform(-elements[2]);
+
+}
+
+Matrix32 Matrix32::affine_inverse() const {
+
+ Matrix32 inv=*this;
+ inv.affine_invert();
+ return inv;
+}
+
+void Matrix32::rotate(real_t p_phi) {
+
+ Matrix32 rot(p_phi,Vector2());
+ *this *= rot;
+}
+
+real_t Matrix32::get_rotation() const {
+
+ return Math::atan2(elements[1].x,elements[1].y);
+}
+
+void Matrix32::set_rotation(real_t p_rot) {
+
+ real_t cr = Math::cos(p_rot);
+ real_t sr = Math::sin(p_rot);
+ elements[0][0]=cr;
+ elements[1][1]=cr;
+ elements[0][1]=-sr;
+ elements[1][0]=sr;
+}
+
+Matrix32::Matrix32(real_t p_rot, const Vector2& p_pos) {
+
+ real_t cr = Math::cos(p_rot);
+ real_t sr = Math::sin(p_rot);
+ elements[0][0]=cr;
+ elements[1][1]=cr;
+ elements[0][1]=-sr;
+ elements[1][0]=sr;
+ elements[2]=p_pos;
+}
+
+Vector2 Matrix32::get_scale() const {
+
+ return Vector2( elements[0].length(), elements[1].length() );
+}
+
+void Matrix32::scale(const Vector2& p_scale) {
+
+ elements[0]*=p_scale;
+ elements[1]*=p_scale;
+ elements[2]*=p_scale;
+}
+void Matrix32::scale_basis(const Vector2& p_scale) {
+
+ elements[0]*=p_scale;
+ elements[1]*=p_scale;
+
+}
+void Matrix32::translate( real_t p_tx, real_t p_ty) {
+
+ translate(Vector2(p_tx,p_ty));
+}
+void Matrix32::translate( const Vector2& p_translation ) {
+
+ elements[2]+=basis_xform(p_translation);
+}
+
+
+void Matrix32::orthonormalize() {
+
+ // Gram-Schmidt Process
+
+ Vector2 x=elements[0];
+ Vector2 y=elements[1];
+
+ x.normalize();
+ y = (y-x*(x.dot(y)));
+ y.normalize();
+
+ elements[0]=x;
+ elements[1]=y;
+}
+Matrix32 Matrix32::orthonormalized() const {
+
+ Matrix32 on=*this;
+ on.orthonormalize();
+ return on;
+
+}
+
+bool Matrix32::operator==(const Matrix32& p_transform) const {
+
+ for(int i=0;i<3;i++) {
+ if (elements[i]!=p_transform.elements[i])
+ return false;
+ }
+
+ return true;
+}
+
+bool Matrix32::operator!=(const Matrix32& p_transform) const {
+
+ for(int i=0;i<3;i++) {
+ if (elements[i]!=p_transform.elements[i])
+ return true;
+ }
+
+ return false;
+
+}
+
+void Matrix32::operator*=(const Matrix32& p_transform) {
+
+ elements[2] = xform(p_transform.elements[2]);
+
+ float x0,x1,y0,y1;
+/*
+ x0 = p_transform.tdotx(elements[0]);
+ x1 = p_transform.tdoty(elements[0]);
+ y0 = p_transform.tdotx(elements[1]);
+ y1 = p_transform.tdoty(elements[1]);*/
+
+ x0 = tdotx(p_transform.elements[0]);
+ x1 = tdoty(p_transform.elements[0]);
+ y0 = tdotx(p_transform.elements[1]);
+ y1 = tdoty(p_transform.elements[1]);
+
+ elements[0][0]=x0;
+ elements[0][1]=x1;
+ elements[1][0]=y0;
+ elements[1][1]=y1;
+}
+
+
+Matrix32 Matrix32::operator*(const Matrix32& p_transform) const {
+
+ Matrix32 t = *this;
+ t*=p_transform;
+ return t;
+
+}
+
+Matrix32 Matrix32::scaled(const Vector2& p_scale) const {
+
+ Matrix32 copy=*this;
+ copy.scale(p_scale);
+ return copy;
+
+}
+
+Matrix32 Matrix32::basis_scaled(const Vector2& p_scale) const {
+
+ Matrix32 copy=*this;
+ copy.scale_basis(p_scale);
+ return copy;
+
+}
+
+Matrix32 Matrix32::untranslated() const {
+
+ Matrix32 copy=*this;
+ copy.elements[2]=Vector2();
+ return copy;
+}
+
+Matrix32 Matrix32::translated(const Vector2& p_offset) const {
+
+ Matrix32 copy=*this;
+ copy.translate(p_offset);
+ return copy;
+
+}
+
+Matrix32 Matrix32::rotated(float p_phi) const {
+
+ Matrix32 copy=*this;
+ copy.rotate(p_phi);
+ return copy;
+
+}
+
+
+Matrix32 Matrix32::interpolate_with(const Matrix32& p_transform, float p_c) const {
+
+
+ return Matrix32();
+}
+
+Matrix32::operator String() const {
+
+ return String(String()+elements[0]+", "+elements[1]+", "+elements[2]);
+}
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