mirror of https://github.com/ArduPilot/ardupilot
466 lines
16 KiB
C++
466 lines
16 KiB
C++
/*
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* vector3.cpp
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* Copyright (C) Andrew Tridgell 2012
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*
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* This file is free software: you can redistribute it and/or modify it
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* under the terms of the GNU General Public License as published by the
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* Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This file is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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* See the GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#pragma GCC optimize("O2")
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#include "AP_Math.h"
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template <typename T>
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float Vector2<T>::length_squared() const
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{
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return (float)(x*x + y*y);
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}
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template <typename T>
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float Vector2<T>::length(void) const
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{
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return norm(x, y);
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}
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// dot product
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template <typename T>
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T Vector2<T>::operator *(const Vector2<T> &v) const
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{
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return x*v.x + y*v.y;
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}
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// cross product
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template <typename T>
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T Vector2<T>::operator %(const Vector2<T> &v) const
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{
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return x*v.y - y*v.x;
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}
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template <typename T>
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Vector2<T> &Vector2<T>::operator *=(const T num)
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{
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x*=num; y*=num;
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return *this;
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}
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template <typename T>
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Vector2<T> &Vector2<T>::operator /=(const T num)
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{
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x /= num; y /= num;
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return *this;
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}
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template <typename T>
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Vector2<T> &Vector2<T>::operator -=(const Vector2<T> &v)
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{
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x -= v.x; y -= v.y;
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return *this;
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}
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template <typename T>
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bool Vector2<T>::is_nan(void) const
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{
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return isnan(x) || isnan(y);
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}
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template <typename T>
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bool Vector2<T>::is_inf(void) const
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{
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return isinf(x) || isinf(y);
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}
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template <typename T>
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Vector2<T> &Vector2<T>::operator +=(const Vector2<T> &v)
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{
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x+=v.x; y+=v.y;
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return *this;
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}
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template <typename T>
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Vector2<T> Vector2<T>::operator /(const T num) const
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{
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return Vector2<T>(x/num, y/num);
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}
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template <typename T>
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Vector2<T> Vector2<T>::operator *(const T num) const
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{
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return Vector2<T>(x*num, y*num);
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}
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template <typename T>
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Vector2<T> Vector2<T>::operator -(const Vector2<T> &v) const
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{
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return Vector2<T>(x-v.x, y-v.y);
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}
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template <typename T>
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Vector2<T> Vector2<T>::operator +(const Vector2<T> &v) const
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{
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return Vector2<T>(x+v.x, y+v.y);
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}
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template <typename T>
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Vector2<T> Vector2<T>::operator -(void) const
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{
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return Vector2<T>(-x,-y);
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}
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template <typename T>
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bool Vector2<T>::operator ==(const Vector2<T> &v) const
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{
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return (is_equal(x,v.x) && is_equal(y,v.y));
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}
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template <typename T>
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bool Vector2<T>::operator !=(const Vector2<T> &v) const
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{
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return (!is_equal(x,v.x) || !is_equal(y,v.y));
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}
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template <typename T>
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float Vector2<T>::angle(const Vector2<T> &v2) const
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{
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const float len = this->length() * v2.length();
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if (len <= 0) {
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return 0.0f;
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}
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const float cosv = ((*this)*v2) / len;
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if (cosv >= 1) {
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return 0.0f;
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}
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if (cosv <= -1) {
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return M_PI;
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}
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return acosf(cosv);
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}
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template <typename T>
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float Vector2<T>::angle(void) const
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{
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return M_PI_2 + atan2f(-x, y);
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}
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// find the intersection between two line segments
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// returns true if they intersect, false if they do not
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// the point of intersection is returned in the intersection argument
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template <typename T>
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bool Vector2<T>::segment_intersection(const Vector2<T>& seg1_start, const Vector2<T>& seg1_end, const Vector2<T>& seg2_start, const Vector2<T>& seg2_end, Vector2<T>& intersection)
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{
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// implementation borrowed from http://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect
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const Vector2<T> r1 = seg1_end - seg1_start;
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const Vector2<T> r2 = seg2_end - seg2_start;
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const Vector2<T> ss2_ss1 = seg2_start - seg1_start;
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const float r1xr2 = r1 % r2;
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const float q_pxr = ss2_ss1 % r1;
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if (fabsf(r1xr2) < FLT_EPSILON) {
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// either collinear or parallel and non-intersecting
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return false;
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} else {
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// t = (q - p) * s / (r * s)
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// u = (q - p) * r / (r * s)
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const float t = (ss2_ss1 % r2) / r1xr2;
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const float u = q_pxr / r1xr2;
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if ((u >= 0) && (u <= 1) && (t >= 0) && (t <= 1)) {
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// lines intersect
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// t can be any non-negative value because (p, p + r) is a ray
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// u must be between 0 and 1 because (q, q + s) is a line segment
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intersection = seg1_start + (r1*t);
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return true;
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} else {
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// non-parallel and non-intersecting
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return false;
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}
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}
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}
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// find the intersection between a line segment and a circle
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// returns true if they intersect and intersection argument is updated with intersection closest to seg_start
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// solution adapted from http://stackoverflow.com/questions/1073336/circle-line-segment-collision-detection-algorithm
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template <typename T>
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bool Vector2<T>::circle_segment_intersection(const Vector2<T>& seg_start, const Vector2<T>& seg_end, const Vector2<T>& circle_center, float radius, Vector2<T>& intersection)
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{
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// calculate segment start and end as offsets from circle's center
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const Vector2f seg_start_local = seg_start - circle_center;
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// calculate vector from start to end
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const Vector2f seg_end_minus_start = seg_end - seg_start;
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const float a = sq(seg_end_minus_start.x) + sq(seg_end_minus_start.y);
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const float b = 2 * ((seg_end_minus_start.x * seg_start_local.x) + (seg_end_minus_start.y * seg_start_local.y));
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const float c = sq(seg_start_local.x) + sq(seg_start_local.y) - sq(radius);
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const float delta = sq(b) - (4.0f * a * c);
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// check for invalid data
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if (::is_zero(a)) {
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return false;
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}
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if (isnan(a) || isnan(b) || isnan(c) || isnan(delta)) {
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return false;
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}
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// check for invalid delta (i.e. discriminant)
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if (delta < 0.0f) {
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return false;
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}
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const float delta_sqrt = sqrtf(delta);
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const float t1 = (-b + delta_sqrt) / (2.0f * a);
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const float t2 = (-b - delta_sqrt) / (2.0f * a);
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// Three hit cases:
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// -o-> --|--> | | --|->
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// Impale(t1 hit,t2 hit), Poke(t1 hit,t2>1), ExitWound(t1<0, t2 hit),
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// Three miss cases:
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// -> o o -> | -> |
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// FallShort (t1>1,t2>1), Past (t1<0,t2<0), CompletelyInside(t1<0, t2>1)
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// intersection = new Vector3(E.x + t1 * d.x, secondPoint.y, E.y + t1 * d.y);
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// intersection.x = seg_start.x + t1 * seg_end_minus_start.x;
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// intersection.y = seg_start.y + t1 * seg_end_minus_start.y;
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if ((t1 >= 0.0f) && (t1 <= 1.0f)) {
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// t1 is the intersection, and it is closer than t2 (since t1 uses -b - discriminant)
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// Impale, Poke
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intersection = seg_start + (seg_end_minus_start * t1);
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return true;
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}
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// here t1 did not intersect so we are either started inside the sphere or completely past it
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if ((t2 >= 0.0f) && (t2 <= 1.0f)) {
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// ExitWound
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intersection = seg_start + (seg_end_minus_start * t2);
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return true;
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}
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// no intersection: FallShort, Past or CompletelyInside
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return false;
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}
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// normalizes this vector
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template <typename T>
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void Vector2<T>::normalize()
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{
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*this /= length();
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}
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// returns the normalized vector
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template <typename T>
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Vector2<T> Vector2<T>::normalized() const
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{
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return *this/length();
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}
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// reflects this vector about n
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template <typename T>
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void Vector2<T>::reflect(const Vector2<T> &n)
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{
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const Vector2<T> orig(*this);
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project(n);
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*this = *this*2 - orig;
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}
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// projects this vector onto v
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template <typename T>
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void Vector2<T>::project(const Vector2<T> &v)
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{
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*this= v * (*this * v)/(v*v);
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}
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// returns this vector projected onto v
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template <typename T>
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Vector2<T> Vector2<T>::projected(const Vector2<T> &v)
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{
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return v * (*this * v)/(v*v);
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}
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// extrapolate position given bearing (in degrees) and distance
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template <typename T>
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void Vector2<T>::offset_bearing(float bearing, float distance)
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{
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x += cosf(radians(bearing)) * distance;
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y += sinf(radians(bearing)) * distance;
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}
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// given a position pos_delta and a velocity v1 produce a vector
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// perpendicular to v1 maximising distance from p1
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template <typename T>
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Vector2<T> Vector2<T>::perpendicular(const Vector2<T> &pos_delta, const Vector2<T> &v1)
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{
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const Vector2<T> perpendicular1 = Vector2<T>(-v1[1], v1[0]);
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const Vector2<T> perpendicular2 = Vector2<T>(v1[1], -v1[0]);
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const T d1 = perpendicular1 * pos_delta;
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const T d2 = perpendicular2 * pos_delta;
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if (d1 > d2) {
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return perpendicular1;
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}
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return perpendicular2;
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}
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/*
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* Returns the point closest to p on the line segment (v,w).
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*
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* Comments and implementation taken from
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* http://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment
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*/
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template <typename T>
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Vector2<T> Vector2<T>::closest_point(const Vector2<T> &p, const Vector2<T> &v, const Vector2<T> &w)
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{
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// length squared of line segment
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const float l2 = (v - w).length_squared();
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if (l2 < FLT_EPSILON) {
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// v == w case
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return v;
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}
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// Consider the line extending the segment, parameterized as v + t (w - v).
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// We find projection of point p onto the line.
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// It falls where t = [(p-v) . (w-v)] / |w-v|^2
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// We clamp t from [0,1] to handle points outside the segment vw.
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const float t = ((p - v) * (w - v)) / l2;
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if (t <= 0) {
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return v;
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} else if (t >= 1) {
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return w;
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} else {
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return v + (w - v)*t;
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}
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}
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/*
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* Returns the point closest to p on the line segment (0,w).
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*
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* this is a simplification of closest point with a general segment, with v=(0,0)
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*/
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template <typename T>
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Vector2<T> Vector2<T>::closest_point(const Vector2<T> &p, const Vector2<T> &w)
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{
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// length squared of line segment
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const float l2 = w.length_squared();
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if (l2 < FLT_EPSILON) {
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// v == w case
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return w;
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}
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const float t = (p * w) / l2;
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if (t <= 0) {
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return Vector2<T>(0,0);
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} else if (t >= 1) {
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return w;
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} else {
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return w*t;
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}
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}
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// closest distance between a line segment and a point
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// https://stackoverflow.com/questions/2824478/shortest-distance-between-two-line-segments
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template <typename T>
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float Vector2<T>::closest_distance_between_line_and_point_squared(const Vector2<T> &w1,
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const Vector2<T> &w2,
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const Vector2<T> &p)
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{
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return closest_distance_between_radial_and_point_squared(w2-w1, p-w1);
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}
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// w1 and w2 define a line segment
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// p is a point
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// returns the closest distance between the line segment and the point
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template <typename T>
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float Vector2<T>::closest_distance_between_line_and_point(const Vector2<T> &w1,
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const Vector2<T> &w2,
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const Vector2<T> &p)
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{
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return sqrtf(closest_distance_between_line_and_point_squared(w1, w2, p));
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}
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// a1->a2 and b2->v2 define two line segments
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// returns the square of the closest distance between the two line segments
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// see https://stackoverflow.com/questions/2824478/shortest-distance-between-two-line-segments
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template <typename T>
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float Vector2<T>::closest_distance_between_lines_squared(const Vector2<T> &a1,
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const Vector2<T> &a2,
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const Vector2<T> &b1,
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const Vector2<T> &b2)
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{
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const float dist1 = Vector2<T>::closest_distance_between_line_and_point_squared(b1,b2,a1);
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const float dist2 = Vector2<T>::closest_distance_between_line_and_point_squared(b1,b2,a2);
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const float dist3 = Vector2<T>::closest_distance_between_line_and_point_squared(a1,a2,b1);
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const float dist4 = Vector2<T>::closest_distance_between_line_and_point_squared(a1,a2,b2);
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const float m1 = MIN(dist1,dist2);
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const float m2 = MIN(dist3,dist4);
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return MIN(m1,m2);
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}
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// w defines a line segment from the origin
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// p is a point
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// returns the square of the closest distance between the radial and the point
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template <typename T>
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float Vector2<T>::closest_distance_between_radial_and_point_squared(const Vector2<T> &w,
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const Vector2<T> &p)
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{
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const Vector2<T> closest = closest_point(p, w);
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return (closest - p).length_squared();
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}
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// w defines a line segment from the origin
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// p is a point
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// returns the closest distance between the radial and the point
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template <typename T>
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float Vector2<T>::closest_distance_between_radial_and_point(const Vector2<T> &w,
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const Vector2<T> &p)
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{
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return sqrtf(closest_distance_between_radial_and_point_squared(w,p));
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}
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// only define for float
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template float Vector2<float>::length_squared(void) const;
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template float Vector2<float>::length(void) const;
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template Vector2<float> Vector2<float>::normalized() const;
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template void Vector2<float>::normalize();
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template float Vector2<float>::operator *(const Vector2<float> &v) const;
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template float Vector2<float>::operator %(const Vector2<float> &v) const;
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template Vector2<float> &Vector2<float>::operator *=(const float num);
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template Vector2<float> &Vector2<float>::operator /=(const float num);
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template Vector2<float> &Vector2<float>::operator -=(const Vector2<float> &v);
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template Vector2<float> &Vector2<float>::operator +=(const Vector2<float> &v);
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template Vector2<float> Vector2<float>::operator /(const float num) const;
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template Vector2<float> Vector2<float>::operator *(const float num) const;
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template Vector2<float> Vector2<float>::operator +(const Vector2<float> &v) const;
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template Vector2<float> Vector2<float>::operator -(const Vector2<float> &v) const;
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template Vector2<float> Vector2<float>::operator -(void) const;
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template bool Vector2<float>::operator ==(const Vector2<float> &v) const;
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template bool Vector2<float>::operator !=(const Vector2<float> &v) const;
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template bool Vector2<float>::is_nan(void) const;
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template bool Vector2<float>::is_inf(void) const;
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template float Vector2<float>::angle(const Vector2<float> &v) const;
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template float Vector2<float>::angle(void) const;
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template void Vector2<float>::offset_bearing(float bearing, float distance);
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template bool Vector2<float>::segment_intersection(const Vector2<float>& seg1_start, const Vector2<float>& seg1_end, const Vector2<float>& seg2_start, const Vector2<float>& seg2_end, Vector2<float>& intersection);
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template bool Vector2<float>::circle_segment_intersection(const Vector2<float>& seg_start, const Vector2<float>& seg_end, const Vector2<float>& circle_center, float radius, Vector2<float>& intersection);
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template Vector2<float> Vector2<float>::perpendicular(const Vector2<float> &pos_delta, const Vector2<float> &v1);
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template Vector2<float> Vector2<float>::closest_point(const Vector2<float> &p, const Vector2<float> &v, const Vector2<float> &w);
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template float Vector2<float>::closest_distance_between_radial_and_point_squared(const Vector2<float> &w, const Vector2<float> &p);
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template float Vector2<float>::closest_distance_between_radial_and_point(const Vector2<float> &w, const Vector2<float> &p);
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template float Vector2<float>::closest_distance_between_line_and_point(const Vector2<float> &w1, const Vector2<float> &w2, const Vector2<float> &p);
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template float Vector2<float>::closest_distance_between_line_and_point_squared(const Vector2<float> &w1, const Vector2<float> &w2, const Vector2<float> &p);
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template float Vector2<float>::closest_distance_between_lines_squared(const Vector2<float> &a1,const Vector2<float> &a2,const Vector2<float> &b1,const Vector2<float> &b2);
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template Vector2<float> Vector2<float>::projected(const Vector2<float> &v);
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template void Vector2<float>::reflect(const Vector2<float> &n);
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template bool Vector2<long>::operator ==(const Vector2<long> &v) const;
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// define for int
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template bool Vector2<int>::operator ==(const Vector2<int> &v) const;
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template bool Vector2<int>::operator !=(const Vector2<int> &v) const;
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