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.
660 lines
14 KiB
C++
660 lines
14 KiB
C++
/*************************************************************************/
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/* math_2d.cpp */
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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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#include "math_2d.h"
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real_t Vector2::angle() const {
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return Math::atan2(y,x);
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}
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real_t Vector2::length() const {
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return Math::sqrt( x*x + y*y );
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}
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real_t Vector2::length_squared() const {
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return x*x + y*y;
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}
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void Vector2::normalize() {
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real_t l = x*x + y*y;
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if (l!=0) {
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l=Math::sqrt(l);
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x/=l;
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y/=l;
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}
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}
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Vector2 Vector2::normalized() const {
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Vector2 v=*this;
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v.normalize();
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return v;
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}
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real_t Vector2::distance_to(const Vector2& p_vector2) const {
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return Math::sqrt( (x-p_vector2.x)*(x-p_vector2.x) + (y-p_vector2.y)*(y-p_vector2.y));
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}
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real_t Vector2::distance_squared_to(const Vector2& p_vector2) const {
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return (x-p_vector2.x)*(x-p_vector2.x) + (y-p_vector2.y)*(y-p_vector2.y);
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}
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real_t Vector2::angle_to(const Vector2& p_vector2) const {
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return Math::atan2( cross(p_vector2), dot(p_vector2) );
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}
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real_t Vector2::angle_to_point(const Vector2& p_vector2) const {
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return Math::atan2( y - p_vector2.y, x-p_vector2.x );
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}
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real_t Vector2::dot(const Vector2& p_other) const {
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return x*p_other.x + y*p_other.y;
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}
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real_t Vector2::cross(const Vector2& p_other) const {
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return x*p_other.y - y*p_other.x;
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}
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Vector2 Vector2::cross(real_t p_other) const {
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return Vector2(p_other*y,-p_other*x);
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}
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Vector2 Vector2::operator+(const Vector2& p_v) const {
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return Vector2(x+p_v.x,y+p_v.y);
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}
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void Vector2::operator+=(const Vector2& p_v) {
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x+=p_v.x; y+=p_v.y;
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}
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Vector2 Vector2::operator-(const Vector2& p_v) const {
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return Vector2(x-p_v.x,y-p_v.y);
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}
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void Vector2::operator-=(const Vector2& p_v) {
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x-=p_v.x; y-=p_v.y;
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}
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Vector2 Vector2::operator*(const Vector2 &p_v1) const {
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return Vector2(x * p_v1.x, y * p_v1.y);
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};
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Vector2 Vector2::operator*(const real_t &rvalue) const {
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return Vector2(x * rvalue, y * rvalue);
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};
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void Vector2::operator*=(const real_t &rvalue) {
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x *= rvalue; y *= rvalue;
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};
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Vector2 Vector2::operator/(const Vector2 &p_v1) const {
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return Vector2(x / p_v1.x, y / p_v1.y);
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};
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Vector2 Vector2::operator/(const real_t &rvalue) const {
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return Vector2(x / rvalue, y / rvalue);
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};
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void Vector2::operator/=(const real_t &rvalue) {
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x /= rvalue; y /= rvalue;
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};
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Vector2 Vector2::operator-() const {
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return Vector2(-x,-y);
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}
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bool Vector2::operator==(const Vector2& p_vec2) const {
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return x==p_vec2.x && y==p_vec2.y;
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}
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bool Vector2::operator!=(const Vector2& p_vec2) const {
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return x!=p_vec2.x || y!=p_vec2.y;
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}
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Vector2 Vector2::floor() const {
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return Vector2( Math::floor(x), Math::floor(y) );
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}
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Vector2 Vector2::rotated(real_t p_by) const {
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Vector2 v;
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v.set_rotation(angle()+p_by);
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v*=length();
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return v;
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}
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Vector2 Vector2::project(const Vector2& p_vec) const {
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Vector2 v1=p_vec;
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Vector2 v2=*this;
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return v2 * ( v1.dot(v2) / v2.dot(v2));
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}
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Vector2 Vector2::snapped(const Vector2& p_by) const {
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return Vector2(
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Math::stepify(x,p_by.x),
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Math::stepify(y,p_by.y)
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);
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}
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Vector2 Vector2::clamped(real_t p_len) const {
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real_t l = length();
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Vector2 v = *this;
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if (l>0 && p_len<l) {
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v/=l;
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v*=p_len;
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}
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return v;
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}
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Vector2 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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#if 0
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k[0] = ((*this) (vi[0] + 1, vi[1], vi[2])) - ((*this) (vi[0],
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vi[1],vi[2])); //fk = a0
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k[1] = (((*this) (vi[0] + 1, vi[1], vi[2])) - ((*this) ((int) (v(0) -
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1), vi[1],vi[2])))*0.5; //dk = a1
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k[2] = (((*this) ((int) (v(0) + 2), vi[1], vi[2])) - ((*this) (vi[0],
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vi[1],vi[2])))*0.5; //dk+1
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k[3] = k[0]*3 - k[1]*2 - k[2];//a2
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k[4] = k[1] + k[2] - k[0]*2;//a3
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//ip = a3(t-tk)³ + a2(t-tk)² + a1(t-tk) + a0
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//
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//a3 = dk + dk+1 - Dk
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//a2 = 3Dk - 2dk - dk+1
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//a1 = dk
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//a0 = fk
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//
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//dk = (fk+1 - fk-1)*0.5
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//Dk = (fk+1 - fk)
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real_t dk =
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#endif
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return Vector2();
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}
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Vector2 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 p0=p_pre_a;
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Vector2 p1=*this;
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Vector2 p2=p_b;
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Vector2 p3=p_post_b;
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real_t t = p_t;
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real_t t2 = t * t;
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real_t t3 = t2 * t;
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Vector2 out;
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out = 0.5f * ( ( p1 * 2.0f) +
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( -p0 + p2 ) * t +
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( 2.0f * p0 - 5.0f * p1 + 4 * p2 - p3 ) * t2 +
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( -p0 + 3.0f * p1 - 3.0f * p2 + p3 ) * t3 );
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return out;
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/*
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real_t mu = p_t;
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real_t mu2 = mu*mu;
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Vector2 a0 = p_post_b - p_b - p_pre_a + *this;
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Vector2 a1 = p_pre_a - *this - a0;
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Vector2 a2 = p_b - p_pre_a;
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Vector2 a3 = *this;
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return ( a0*mu*mu2 + a1*mu2 + a2*mu + a3 );
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*/
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/*
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real_t t = p_t;
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real_t t2 = t*t;
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real_t t3 = t2*t;
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real_t a = 2.0*t3- 3.0*t2 + 1;
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real_t b = -2.0*t3+ 3.0*t2;
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real_t c = t3- 2.0*t2 + t;
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real_t d = t3- t2;
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Vector2 p_a=*this;
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return Vector2(
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(a * p_a.x) + (b *p_b.x) + (c * p_pre_a.x) + (d * p_post_b.x),
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(a * p_a.y) + (b *p_b.y) + (c * p_pre_a.y) + (d * p_post_b.y)
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);
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*/
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}
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Vector2 Vector2::slide(const Vector2& p_vec) const {
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return p_vec - *this * this->dot(p_vec);
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}
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Vector2 Vector2::reflect(const Vector2& p_vec) const {
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return p_vec - *this * this->dot(p_vec) * 2.0;
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}
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bool Rect2::intersects_segment(const Point2& p_from, const Point2& p_to, Point2* r_pos,Point2* r_normal) const {
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real_t min=0,max=1;
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int axis=0;
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real_t sign=0;
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for(int i=0;i<2;i++) {
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real_t seg_from=p_from[i];
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real_t seg_to=p_to[i];
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real_t box_begin=pos[i];
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real_t box_end=box_begin+size[i];
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real_t cmin,cmax;
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real_t csign;
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if (seg_from < seg_to) {
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if (seg_from > box_end || seg_to < box_begin)
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return false;
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real_t length=seg_to-seg_from;
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cmin = (seg_from < box_begin)?((box_begin - seg_from)/length):0;
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cmax = (seg_to > box_end)?((box_end - seg_from)/length):1;
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csign=-1.0;
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} else {
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if (seg_to > box_end || seg_from < box_begin)
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return false;
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real_t length=seg_to-seg_from;
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cmin = (seg_from > box_end)?(box_end - seg_from)/length:0;
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cmax = (seg_to < box_begin)?(box_begin - seg_from)/length:1;
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csign=1.0;
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}
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if (cmin > min) {
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min = cmin;
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axis=i;
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sign=csign;
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}
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if (cmax < max)
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max = cmax;
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if (max < min)
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return false;
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}
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Vector2 rel=p_to-p_from;
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if (r_normal) {
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Vector2 normal;
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normal[axis]=sign;
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*r_normal=normal;
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}
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if (r_pos)
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*r_pos=p_from+rel*min;
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return true;
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}
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/* Point2i */
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Point2i Point2i::operator+(const Point2i& p_v) const {
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return Point2i(x+p_v.x,y+p_v.y);
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}
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void Point2i::operator+=(const Point2i& p_v) {
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x+=p_v.x; y+=p_v.y;
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}
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Point2i Point2i::operator-(const Point2i& p_v) const {
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return Point2i(x-p_v.x,y-p_v.y);
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}
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void Point2i::operator-=(const Point2i& p_v) {
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x-=p_v.x; y-=p_v.y;
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}
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Point2i Point2i::operator*(const Point2i &p_v1) const {
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return Point2i(x * p_v1.x, y * p_v1.y);
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};
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Point2i Point2i::operator*(const int &rvalue) const {
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return Point2i(x * rvalue, y * rvalue);
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};
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void Point2i::operator*=(const int &rvalue) {
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x *= rvalue; y *= rvalue;
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};
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Point2i Point2i::operator/(const Point2i &p_v1) const {
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return Point2i(x / p_v1.x, y / p_v1.y);
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};
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Point2i Point2i::operator/(const int &rvalue) const {
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return Point2i(x / rvalue, y / rvalue);
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};
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void Point2i::operator/=(const int &rvalue) {
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x /= rvalue; y /= rvalue;
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};
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Point2i Point2i::operator-() const {
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return Point2i(-x,-y);
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}
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bool Point2i::operator==(const Point2i& p_vec2) const {
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return x==p_vec2.x && y==p_vec2.y;
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}
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bool Point2i::operator!=(const Point2i& p_vec2) const {
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return x!=p_vec2.x || y!=p_vec2.y;
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}
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void Matrix32::invert() {
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// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
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// Matrix32::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
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SWAP(elements[0][1],elements[1][0]);
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elements[2] = basis_xform(-elements[2]);
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}
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Matrix32 Matrix32::inverse() const {
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Matrix32 inv=*this;
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inv.invert();
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return inv;
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}
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void Matrix32::affine_invert() {
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real_t det = basis_determinant();
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ERR_FAIL_COND(det==0);
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real_t idet = 1.0 / det;
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SWAP( elements[0][0],elements[1][1] );
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elements[0]*=Vector2(idet,-idet);
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elements[1]*=Vector2(-idet,idet);
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elements[2] = basis_xform(-elements[2]);
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}
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Matrix32 Matrix32::affine_inverse() const {
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Matrix32 inv=*this;
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inv.affine_invert();
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return inv;
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}
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void Matrix32::rotate(real_t p_phi) {
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*this = Matrix32(p_phi,Vector2()) * (*this);
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}
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real_t Matrix32::get_rotation() const {
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real_t det = basis_determinant();
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Matrix32 m = orthonormalized();
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if (det < 0) {
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m.scale_basis(Size2(-1,-1));
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}
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return Math::atan2(m[0].y,m[0].x);
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}
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void Matrix32::set_rotation(real_t p_rot) {
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real_t cr = Math::cos(p_rot);
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real_t sr = Math::sin(p_rot);
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elements[0][0]=cr;
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elements[0][1]=sr;
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elements[1][0]=-sr;
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elements[1][1]=cr;
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}
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Matrix32::Matrix32(real_t p_rot, const Vector2& p_pos) {
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real_t cr = Math::cos(p_rot);
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real_t sr = Math::sin(p_rot);
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elements[0][0]=cr;
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elements[0][1]=sr;
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elements[1][0]=-sr;
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elements[1][1]=cr;
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elements[2]=p_pos;
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}
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Size2 Matrix32::get_scale() const {
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real_t det_sign = basis_determinant() > 0 ? 1 : -1;
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return det_sign * Size2( elements[0].length(), elements[1].length() );
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}
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void Matrix32::scale(const Size2& p_scale) {
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scale_basis(p_scale);
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elements[2]*=p_scale;
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}
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void Matrix32::scale_basis(const Size2& p_scale) {
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elements[0][0]*=p_scale.x;
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elements[0][1]*=p_scale.y;
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elements[1][0]*=p_scale.x;
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elements[1][1]*=p_scale.y;
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}
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void Matrix32::translate( real_t p_tx, real_t p_ty) {
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translate(Vector2(p_tx,p_ty));
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}
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void Matrix32::translate( const Vector2& p_translation ) {
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elements[2]+=basis_xform(p_translation);
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}
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void Matrix32::orthonormalize() {
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// Gram-Schmidt Process
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Vector2 x=elements[0];
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Vector2 y=elements[1];
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x.normalize();
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y = (y-x*(x.dot(y)));
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y.normalize();
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|
|
|
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]);
|
|
|
|
real_t x0,x1,y0,y1;
|
|
|
|
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 Size2& p_scale) const {
|
|
|
|
Matrix32 copy=*this;
|
|
copy.scale(p_scale);
|
|
return copy;
|
|
|
|
}
|
|
|
|
Matrix32 Matrix32::basis_scaled(const Size2& 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(real_t p_phi) const {
|
|
|
|
Matrix32 copy=*this;
|
|
copy.rotate(p_phi);
|
|
return copy;
|
|
|
|
}
|
|
|
|
real_t Matrix32::basis_determinant() const {
|
|
|
|
return elements[0].x * elements[1].y - elements[0].y * elements[1].x;
|
|
}
|
|
|
|
Matrix32 Matrix32::interpolate_with(const Matrix32& p_transform, real_t p_c) const {
|
|
|
|
//extract parameters
|
|
Vector2 p1 = get_origin();
|
|
Vector2 p2 = p_transform.get_origin();
|
|
|
|
real_t r1 = get_rotation();
|
|
real_t r2 = p_transform.get_rotation();
|
|
|
|
Size2 s1 = get_scale();
|
|
Size2 s2 = p_transform.get_scale();
|
|
|
|
//slerp rotation
|
|
Vector2 v1(Math::cos(r1), Math::sin(r1));
|
|
Vector2 v2(Math::cos(r2), Math::sin(r2));
|
|
|
|
real_t dot = v1.dot(v2);
|
|
|
|
dot = (dot < -1.0) ? -1.0 : ((dot > 1.0) ? 1.0 : dot); //clamp dot to [-1,1]
|
|
|
|
Vector2 v;
|
|
|
|
if (dot > 0.9995) {
|
|
v = Vector2::linear_interpolate(v1, v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues
|
|
} else {
|
|
real_t angle = p_c*Math::acos(dot);
|
|
Vector2 v3 = (v2 - v1*dot).normalized();
|
|
v = v1*Math::cos(angle) + v3*Math::sin(angle);
|
|
}
|
|
|
|
//construct matrix
|
|
Matrix32 res(Math::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_c));
|
|
res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c));
|
|
return res;
|
|
}
|
|
|
|
Matrix32::operator String() const {
|
|
|
|
return String(String()+elements[0]+", "+elements[1]+", "+elements[2]);
|
|
}
|