656 lines
14 KiB
C++
656 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) 2007-2016 Juan Linietsky, Ariel Manzur. */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#include "math_2d.h"
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real_t Vector2::angle() const {
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return Math::atan2(x,y);
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}
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float Vector2::length() const {
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return Math::sqrt( x*x + y*y );
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}
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float 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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float 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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float 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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float 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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float Vector2::angle_to(const Vector2& p_vector2) const {
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return Math::atan2( tangent().dot(p_vector2), dot(p_vector2) );
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}
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float Vector2::angle_to_point(const Vector2& p_vector2) const {
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return Math::atan2( x-p_vector2.x, y - p_vector2.y );
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}
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float 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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float 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 float &rvalue) const {
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return Vector2(x * rvalue, y * rvalue);
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};
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void Vector2::operator*=(const float &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 float &rvalue) const {
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return Vector2(x / rvalue, y / rvalue);
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};
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void Vector2::operator/=(const float &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(float 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,float 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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float 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,float 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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float t = p_t;
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float t2 = t * t;
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float 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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float mu = p_t;
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float 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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float 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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float 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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float 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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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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float det = elements[0][0]*elements[1][1] - elements[1][0]*elements[0][1];
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ERR_FAIL_COND(det==0);
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float 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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Matrix32 rot(p_phi,Vector2());
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*this *= rot;
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}
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real_t Matrix32::get_rotation() const {
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return Math::atan2(elements[1].x,elements[1].y);
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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[1][1]=cr;
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elements[0][1]=-sr;
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elements[1][0]=sr;
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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[1][1]=cr;
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elements[0][1]=-sr;
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elements[1][0]=sr;
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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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return 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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elements[0]*=p_scale;
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elements[1]*=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]*=p_scale;
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elements[1]*=p_scale;
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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;
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elements[1]=y;
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}
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Matrix32 Matrix32::orthonormalized() const {
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Matrix32 on=*this;
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on.orthonormalize();
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return on;
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}
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bool Matrix32::operator==(const Matrix32& p_transform) const {
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for(int i=0;i<3;i++) {
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if (elements[i]!=p_transform.elements[i])
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return false;
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}
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return true;
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}
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bool Matrix32::operator!=(const Matrix32& p_transform) const {
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for(int i=0;i<3;i++) {
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if (elements[i]!=p_transform.elements[i])
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return true;
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}
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return false;
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}
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void Matrix32::operator*=(const Matrix32& p_transform) {
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elements[2] = xform(p_transform.elements[2]);
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float x0,x1,y0,y1;
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x0 = tdotx(p_transform.elements[0]);
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x1 = tdoty(p_transform.elements[0]);
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y0 = tdotx(p_transform.elements[1]);
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y1 = tdoty(p_transform.elements[1]);
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elements[0][0]=x0;
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elements[0][1]=x1;
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elements[1][0]=y0;
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elements[1][1]=y1;
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}
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Matrix32 Matrix32::operator*(const Matrix32& p_transform) const {
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Matrix32 t = *this;
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t*=p_transform;
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return t;
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}
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Matrix32 Matrix32::scaled(const Size2& p_scale) const {
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Matrix32 copy=*this;
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copy.scale(p_scale);
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return copy;
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|
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}
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Matrix32 Matrix32::basis_scaled(const Size2& p_scale) const {
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|
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Matrix32 copy=*this;
|
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copy.scale_basis(p_scale);
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return copy;
|
|
|
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}
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|
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Matrix32 Matrix32::untranslated() const {
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|
|
|
Matrix32 copy=*this;
|
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copy.elements[2]=Vector2();
|
|
return copy;
|
|
}
|
|
|
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Matrix32 Matrix32::translated(const Vector2& p_offset) const {
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|
|
|
Matrix32 copy=*this;
|
|
copy.translate(p_offset);
|
|
return copy;
|
|
|
|
}
|
|
|
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Matrix32 Matrix32::rotated(float p_phi) const {
|
|
|
|
Matrix32 copy=*this;
|
|
copy.rotate(p_phi);
|
|
return copy;
|
|
|
|
}
|
|
|
|
float 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, float 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]);
|
|
}
|