97d510531a
When performing polar decomposition in 2D as B = R.S, where R is rotation (with determinant +1) and S is scaling, use the convention that reflections are absorbed into S through a reflection around y axis. In 3D, this is done by using a reflection along all three axes, but since the dimensionality is even in 2D, one axis needs to be chosen. Fixes Matrix32::get_rotation and Matrix32::get_scale (which weren't properly fixed in #7445).
648 lines
15 KiB
C++
648 lines
15 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;
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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;
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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;
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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;
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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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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 = 0.5 * ((p1 * 2.0) +
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(-p0 + p2) * t +
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(2.0 * p0 - 5.0 * p1 + 4 * p2 - p3) * t2 +
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(-p0 + 3.0 * p1 - 3.0 * 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;
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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;
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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;
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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;
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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 Transform2D::invert() {
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// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
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// Transform2D::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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Transform2D Transform2D::inverse() const {
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Transform2D inv = *this;
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inv.invert();
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return inv;
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}
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void Transform2D::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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Transform2D Transform2D::affine_inverse() const {
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Transform2D inv = *this;
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inv.affine_invert();
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return inv;
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}
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void Transform2D::rotate(real_t p_phi) {
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*this = Transform2D(p_phi, Vector2()) * (*this);
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}
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real_t Transform2D::get_rotation() const {
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real_t det = basis_determinant();
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Transform2D m = orthonormalized();
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if (det < 0) {
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m.scale_basis(Size2(1, -1)); // convention to separate rotation and reflection for 2D is to absorb a flip along y into scaling.
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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 Transform2D::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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Transform2D::Transform2D(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 Transform2D::get_scale() const {
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real_t det_sign = basis_determinant() > 0 ? 1 : -1;
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return Size2(elements[0].length(), det_sign * elements[1].length());
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}
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void Transform2D::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 Transform2D::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 Transform2D::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 Transform2D::translate(const Vector2 &p_translation) {
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elements[2] += basis_xform(p_translation);
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}
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void Transform2D::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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Transform2D Transform2D::orthonormalized() const {
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Transform2D on = *this;
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on.orthonormalize();
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return on;
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}
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bool Transform2D::operator==(const Transform2D &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 Transform2D::operator!=(const Transform2D &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 Transform2D::operator*=(const Transform2D &p_transform) {
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elements[2] = xform(p_transform.elements[2]);
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real_t 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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|
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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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|
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Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
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|
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Transform2D t = *this;
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t *= p_transform;
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return t;
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|
}
|
|
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Transform2D Transform2D::scaled(const Size2 &p_scale) const {
|
|
|
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Transform2D copy = *this;
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|
copy.scale(p_scale);
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|
return copy;
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|
}
|
|
|
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Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
|
|
|
|
Transform2D copy = *this;
|
|
copy.scale_basis(p_scale);
|
|
return copy;
|
|
}
|
|
|
|
Transform2D Transform2D::untranslated() const {
|
|
|
|
Transform2D copy = *this;
|
|
copy.elements[2] = Vector2();
|
|
return copy;
|
|
}
|
|
|
|
Transform2D Transform2D::translated(const Vector2 &p_offset) const {
|
|
|
|
Transform2D copy = *this;
|
|
copy.translate(p_offset);
|
|
return copy;
|
|
}
|
|
|
|
Transform2D Transform2D::rotated(real_t p_phi) const {
|
|
|
|
Transform2D copy = *this;
|
|
copy.rotate(p_phi);
|
|
return copy;
|
|
}
|
|
|
|
real_t Transform2D::basis_determinant() const {
|
|
|
|
return elements[0].x * elements[1].y - elements[0].y * elements[1].x;
|
|
}
|
|
|
|
Transform2D Transform2D::interpolate_with(const Transform2D &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
|
|
Transform2D 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;
|
|
}
|
|
|
|
Transform2D::operator String() const {
|
|
|
|
return String(String() + elements[0] + ", " + elements[1] + ", " + elements[2]);
|
|
}
|