mirror of https://github.com/ArduPilot/ardupilot
414 lines
12 KiB
C++
414 lines
12 KiB
C++
/*
|
|
This program is free software: you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation, either version 3 of the License, or
|
|
(at your option) any later version.
|
|
|
|
This program is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with this program. If not, see <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
// Copyright 2010 Michael Smith, all rights reserved.
|
|
|
|
// Derived closely from:
|
|
/****************************************
|
|
* 3D Vector Classes
|
|
* By Bill Perone (billperone@yahoo.com)
|
|
* Original: 9-16-2002
|
|
* Revised: 19-11-2003
|
|
* 11-12-2003
|
|
* 18-12-2003
|
|
* 06-06-2004
|
|
*
|
|
* Copyright 2003, This code is provided "as is" and you can use it freely as long as
|
|
* credit is given to Bill Perone in the application it is used in
|
|
*
|
|
* Notes:
|
|
* if a*b = 0 then a & b are orthogonal
|
|
* a%b = -b%a
|
|
* a*(b%c) = (a%b)*c
|
|
* a%b = a(cast to matrix)*b
|
|
* (a%b).length() = area of parallelogram formed by a & b
|
|
* (a%b).length() = a.length()*b.length() * sin(angle between a & b)
|
|
* (a%b).length() = 0 if angle between a & b = 0 or a.length() = 0 or b.length() = 0
|
|
* a * (b%c) = volume of parallelpiped formed by a, b, c
|
|
* vector triple product: a%(b%c) = b*(a*c) - c*(a*b)
|
|
* scalar triple product: a*(b%c) = c*(a%b) = b*(c%a)
|
|
* vector quadruple product: (a%b)*(c%d) = (a*c)*(b*d) - (a*d)*(b*c)
|
|
* if a is unit vector along b then a%b = -b%a = -b(cast to matrix)*a = 0
|
|
* vectors a1...an are linearly dependent if there exists a vector of scalars (b) where a1*b1 + ... + an*bn = 0
|
|
* or if the matrix (A) * b = 0
|
|
*
|
|
****************************************/
|
|
#pragma once
|
|
|
|
#ifndef MATH_CHECK_INDEXES
|
|
#define MATH_CHECK_INDEXES 0
|
|
#endif
|
|
|
|
#include <cmath>
|
|
#include <float.h>
|
|
#include <string.h>
|
|
#if MATH_CHECK_INDEXES
|
|
#include <assert.h>
|
|
#endif
|
|
|
|
#include "rotations.h"
|
|
|
|
#include "ftype.h"
|
|
|
|
template <typename T>
|
|
class Matrix3;
|
|
|
|
template <typename T>
|
|
class Vector2;
|
|
|
|
template <typename T>
|
|
class Vector3
|
|
{
|
|
|
|
public:
|
|
T x, y, z;
|
|
|
|
// trivial ctor
|
|
constexpr Vector3()
|
|
: x(0)
|
|
, y(0)
|
|
, z(0) {}
|
|
|
|
// setting ctor
|
|
constexpr Vector3(const T x0, const T y0, const T z0)
|
|
: x(x0)
|
|
, y(y0)
|
|
, z(z0) {}
|
|
|
|
//Create a Vector3 from a Vector2 with z
|
|
constexpr Vector3(const Vector2<T> &v0, const T z0)
|
|
: x(v0.x)
|
|
, y(v0.y)
|
|
, z(z0) {}
|
|
|
|
// test for equality
|
|
bool operator ==(const Vector3<T> &v) const;
|
|
|
|
// test for inequality
|
|
bool operator !=(const Vector3<T> &v) const;
|
|
|
|
// negation
|
|
Vector3<T> operator -(void) const;
|
|
|
|
// addition
|
|
Vector3<T> operator +(const Vector3<T> &v) const;
|
|
|
|
// subtraction
|
|
Vector3<T> operator -(const Vector3<T> &v) const;
|
|
|
|
// uniform scaling
|
|
Vector3<T> operator *(const T num) const;
|
|
|
|
// uniform scaling
|
|
Vector3<T> operator /(const T num) const;
|
|
|
|
// addition
|
|
Vector3<T> &operator +=(const Vector3<T> &v);
|
|
|
|
// subtraction
|
|
Vector3<T> &operator -=(const Vector3<T> &v);
|
|
|
|
// uniform scaling
|
|
Vector3<T> &operator *=(const T num);
|
|
|
|
// uniform scaling
|
|
Vector3<T> &operator /=(const T num);
|
|
|
|
// non-uniform scaling
|
|
Vector3<T> &operator *=(const Vector3<T> &v) {
|
|
x *= v.x; y *= v.y; z *= v.z;
|
|
return *this;
|
|
}
|
|
|
|
// allow a vector3 to be used as an array, 0 indexed
|
|
T & operator[](uint8_t i) {
|
|
T *_v = &x;
|
|
#if MATH_CHECK_INDEXES
|
|
assert(i >= 0 && i < 3);
|
|
#endif
|
|
return _v[i];
|
|
}
|
|
|
|
const T & operator[](uint8_t i) const {
|
|
const T *_v = &x;
|
|
#if MATH_CHECK_INDEXES
|
|
assert(i >= 0 && i < 3);
|
|
#endif
|
|
return _v[i];
|
|
}
|
|
|
|
// dot product
|
|
T operator *(const Vector3<T> &v) const;
|
|
|
|
// dot product for Lua
|
|
T dot(const Vector3<T> &v) const {
|
|
return *this * v;
|
|
}
|
|
|
|
// multiply a row vector by a matrix, to give a row vector
|
|
Vector3<T> row_times_mat(const Matrix3<T> &m) const;
|
|
|
|
// multiply a column vector by a row vector, returning a 3x3 matrix
|
|
Matrix3<T> mul_rowcol(const Vector3<T> &v) const;
|
|
|
|
// cross product
|
|
Vector3<T> operator %(const Vector3<T> &v) const;
|
|
|
|
// cross product for Lua
|
|
Vector3<T> cross(const Vector3<T> &v) const {
|
|
return *this % v;
|
|
}
|
|
|
|
// scale a vector3
|
|
Vector3<T> scale(const T v) const {
|
|
return *this * v;
|
|
}
|
|
|
|
// computes the angle between this vector and another vector
|
|
T angle(const Vector3<T> &v2) const;
|
|
|
|
// check if any elements are NAN
|
|
bool is_nan(void) const WARN_IF_UNUSED;
|
|
|
|
// check if any elements are infinity
|
|
bool is_inf(void) const WARN_IF_UNUSED;
|
|
|
|
// check if all elements are zero
|
|
bool is_zero(void) const WARN_IF_UNUSED {
|
|
return x == 0 && y == 0 && z == 0;
|
|
}
|
|
|
|
|
|
// rotate by a standard rotation
|
|
void rotate(enum Rotation rotation);
|
|
void rotate_inverse(enum Rotation rotation);
|
|
|
|
// rotate vector by angle in radians in xy plane leaving z untouched
|
|
void rotate_xy(T rotation_rad);
|
|
|
|
// return xy components of a vector3 as a vector2.
|
|
// this returns a reference to the original vector3 xy data
|
|
const Vector2<T> &xy() const {
|
|
return *(const Vector2<T> *)this;
|
|
}
|
|
Vector2<T> &xy() {
|
|
return *(Vector2<T> *)this;
|
|
}
|
|
|
|
// gets the length of this vector squared
|
|
T length_squared() const
|
|
{
|
|
return (T)(*this * *this);
|
|
}
|
|
|
|
// gets the length of this vector
|
|
T length(void) const;
|
|
|
|
// limit xy component vector to a given length. returns true if vector was limited
|
|
bool limit_length_xy(T max_length);
|
|
|
|
// normalizes this vector
|
|
void normalize()
|
|
{
|
|
*this /= length();
|
|
}
|
|
|
|
// zero the vector
|
|
void zero()
|
|
{
|
|
x = y = z = 0;
|
|
}
|
|
|
|
// returns the normalized version of this vector
|
|
Vector3<T> normalized() const
|
|
{
|
|
return *this/length();
|
|
}
|
|
|
|
// reflects this vector about n
|
|
void reflect(const Vector3<T> &n)
|
|
{
|
|
Vector3<T> orig(*this);
|
|
project(n);
|
|
*this = *this*2 - orig;
|
|
}
|
|
|
|
// projects this vector onto v
|
|
void project(const Vector3<T> &v)
|
|
{
|
|
*this= v * (*this * v)/(v*v);
|
|
}
|
|
|
|
// returns this vector projected onto v
|
|
Vector3<T> projected(const Vector3<T> &v) const
|
|
{
|
|
return v * (*this * v)/(v*v);
|
|
}
|
|
|
|
// distance from the tip of this vector to another vector squared (so as to avoid the sqrt calculation)
|
|
T distance_squared(const Vector3<T> &v) const {
|
|
const T dist_x = x-v.x;
|
|
const T dist_y = y-v.y;
|
|
const T dist_z = z-v.z;
|
|
return (dist_x*dist_x + dist_y*dist_y + dist_z*dist_z);
|
|
}
|
|
|
|
// distance from the tip of this vector to a line segment specified by two vectors
|
|
T distance_to_segment(const Vector3<T> &seg_start, const Vector3<T> &seg_end) const;
|
|
|
|
// extrapolate position given bearing and pitch (in degrees) and distance
|
|
void offset_bearing(T bearing, T pitch, T distance);
|
|
|
|
/*
|
|
conversion to/from double
|
|
*/
|
|
Vector3<float> tofloat() const {
|
|
return Vector3<float>{float(x),float(y),float(z)};
|
|
}
|
|
Vector3<double> todouble() const {
|
|
return Vector3<double>{x,y,z};
|
|
}
|
|
|
|
// convert from right-front-up to front-right-down
|
|
// or ENU to NED
|
|
Vector3<T> rfu_to_frd() const {
|
|
return Vector3<T>{y,x,-z};
|
|
}
|
|
|
|
// given a position p1 and a velocity v1 produce a vector
|
|
// perpendicular to v1 maximising distance from p1. If p1 is the
|
|
// zero vector the return from the function will always be the
|
|
// zero vector - that should be checked for.
|
|
static Vector3<T> perpendicular(const Vector3<T> &p1, const Vector3<T> &v1)
|
|
{
|
|
const T d = p1 * v1;
|
|
if (::is_zero(d)) {
|
|
return p1;
|
|
}
|
|
const Vector3<T> parallel = (v1 * d) / v1.length_squared();
|
|
Vector3<T> perpendicular = p1 - parallel;
|
|
|
|
return perpendicular;
|
|
}
|
|
|
|
// Shortest distance between point(p) to a point contained in the line segment defined by w1,w2
|
|
static T closest_distance_between_line_and_point(const Vector3<T> &w1, const Vector3<T> &w2, const Vector3<T> &p);
|
|
|
|
// Point in the line segment defined by w1,w2 which is closest to point(p)
|
|
static Vector3<T> point_on_line_closest_to_other_point(const Vector3<T> &w1, const Vector3<T> &w2, const Vector3<T> &p);
|
|
|
|
// This implementation is borrowed from: http://geomalgorithms.com/a07-_distance.html
|
|
// INPUT: 4 points corresponding to start and end of two line segments
|
|
|
|
// OUTPUT: closest point on segment 2, from segment 1, gets passed on reference as "closest_point"
|
|
static void segment_to_segment_closest_point(const Vector3<T>& seg1_start, const Vector3<T>& seg1_end, const Vector3<T>& seg2_start, const Vector3<T>& seg2_end, Vector3<T>& closest_point);
|
|
|
|
// Returns true if the passed 3D segment passes through a plane defined by plane normal, and a point on the plane
|
|
static bool segment_plane_intersect(const Vector3<T>& seg_start, const Vector3<T>& seg_end, const Vector3<T>& plane_normal, const Vector3<T>& plane_point);
|
|
};
|
|
|
|
// check if all elements are zero
|
|
template<> inline bool Vector3<float>::is_zero(void) const {
|
|
return ::is_zero(x) && ::is_zero(y) && ::is_zero(z);
|
|
}
|
|
|
|
template<> inline bool Vector3<double>::is_zero(void) const {
|
|
return ::is_zero(x) && ::is_zero(y) && ::is_zero(z);
|
|
}
|
|
|
|
// The creation of temporary vector objects as return types creates a significant overhead in certain hot
|
|
// code paths. This allows callers to select the inline versions where profiling shows a significant benefit
|
|
#if defined(AP_INLINE_VECTOR_OPS) && !defined(HAL_DEBUG_BUILD)
|
|
|
|
// vector cross product
|
|
template <typename T>
|
|
inline Vector3<T> Vector3<T>::operator %(const Vector3<T> &v) const
|
|
{
|
|
return Vector3<T>(y*v.z - z*v.y, z*v.x - x*v.z, x*v.y - y*v.x);
|
|
}
|
|
|
|
// dot product
|
|
template <typename T>
|
|
inline T Vector3<T>::operator *(const Vector3<T> &v) const
|
|
{
|
|
return x*v.x + y*v.y + z*v.z;
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> &Vector3<T>::operator *=(const T num)
|
|
{
|
|
x*=num; y*=num; z*=num;
|
|
return *this;
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> &Vector3<T>::operator /=(const T num)
|
|
{
|
|
x /= num; y /= num; z /= num;
|
|
return *this;
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> &Vector3<T>::operator -=(const Vector3<T> &v)
|
|
{
|
|
x -= v.x; y -= v.y; z -= v.z;
|
|
return *this;
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> &Vector3<T>::operator +=(const Vector3<T> &v)
|
|
{
|
|
x+=v.x; y+=v.y; z+=v.z;
|
|
return *this;
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> Vector3<T>::operator /(const T num) const
|
|
{
|
|
return Vector3<T>(x/num, y/num, z/num);
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> Vector3<T>::operator *(const T num) const
|
|
{
|
|
return Vector3<T>(x*num, y*num, z*num);
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> Vector3<T>::operator -(const Vector3<T> &v) const
|
|
{
|
|
return Vector3<T>(x-v.x, y-v.y, z-v.z);
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> Vector3<T>::operator +(const Vector3<T> &v) const
|
|
{
|
|
return Vector3<T>(x+v.x, y+v.y, z+v.z);
|
|
}
|
|
|
|
template <typename T>
|
|
inline Vector3<T> Vector3<T>::operator -(void) const
|
|
{
|
|
return Vector3<T>(-x,-y,-z);
|
|
}
|
|
#endif
|
|
|
|
typedef Vector3<int16_t> Vector3i;
|
|
typedef Vector3<uint16_t> Vector3ui;
|
|
typedef Vector3<int32_t> Vector3l;
|
|
typedef Vector3<uint32_t> Vector3ul;
|
|
typedef Vector3<float> Vector3f;
|
|
typedef Vector3<double> Vector3d;
|