ardupilot/libraries/AP_Math/vector3.cpp

633 lines
17 KiB
C++

/*
* vector3.cpp
* Copyright (C) Andrew Tridgell 2012
*
* This file 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 file 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/>.
*/
#pragma GCC optimize("O2")
#include "AP_Math.h"
#include <AP_InternalError/AP_InternalError.h>
// rotate a vector by a standard rotation, attempting
// to use the minimum number of floating point operations
template <typename T>
void Vector3<T>::rotate(enum Rotation rotation)
{
T tmp;
switch (rotation) {
case ROTATION_NONE:
return;
case ROTATION_YAW_45: {
tmp = HALF_SQRT_2*(float)(x - y);
y = HALF_SQRT_2*(float)(x + y);
x = tmp;
return;
}
case ROTATION_YAW_90: {
tmp = x; x = -y; y = tmp;
return;
}
case ROTATION_YAW_135: {
tmp = -HALF_SQRT_2*(float)(x + y);
y = HALF_SQRT_2*(float)(x - y);
x = tmp;
return;
}
case ROTATION_YAW_180:
x = -x; y = -y;
return;
case ROTATION_YAW_225: {
tmp = HALF_SQRT_2*(float)(y - x);
y = -HALF_SQRT_2*(float)(x + y);
x = tmp;
return;
}
case ROTATION_YAW_270: {
tmp = x; x = y; y = -tmp;
return;
}
case ROTATION_YAW_315: {
tmp = HALF_SQRT_2*(float)(x + y);
y = HALF_SQRT_2*(float)(y - x);
x = tmp;
return;
}
case ROTATION_ROLL_180: {
y = -y; z = -z;
return;
}
case ROTATION_ROLL_180_YAW_45: {
tmp = HALF_SQRT_2*(float)(x + y);
y = HALF_SQRT_2*(float)(x - y);
x = tmp; z = -z;
return;
}
case ROTATION_ROLL_180_YAW_90: {
tmp = x; x = y; y = tmp; z = -z;
return;
}
case ROTATION_ROLL_180_YAW_135: {
tmp = HALF_SQRT_2*(float)(y - x);
y = HALF_SQRT_2*(float)(y + x);
x = tmp; z = -z;
return;
}
case ROTATION_PITCH_180: {
x = -x; z = -z;
return;
}
case ROTATION_ROLL_180_YAW_225: {
tmp = -HALF_SQRT_2*(float)(x + y);
y = HALF_SQRT_2*(float)(y - x);
x = tmp; z = -z;
return;
}
case ROTATION_ROLL_180_YAW_270: {
tmp = x; x = -y; y = -tmp; z = -z;
return;
}
case ROTATION_ROLL_180_YAW_315: {
tmp = HALF_SQRT_2*(float)(x - y);
y = -HALF_SQRT_2*(float)(x + y);
x = tmp; z = -z;
return;
}
case ROTATION_ROLL_90: {
tmp = z; z = y; y = -tmp;
return;
}
case ROTATION_ROLL_90_YAW_45: {
tmp = z; z = y; y = -tmp;
tmp = HALF_SQRT_2*(float)(x - y);
y = HALF_SQRT_2*(float)(x + y);
x = tmp;
return;
}
case ROTATION_ROLL_90_YAW_90: {
tmp = z; z = y; y = -tmp;
tmp = x; x = -y; y = tmp;
return;
}
case ROTATION_ROLL_90_YAW_135: {
tmp = z; z = y; y = -tmp;
tmp = -HALF_SQRT_2*(float)(x + y);
y = HALF_SQRT_2*(float)(x - y);
x = tmp;
return;
}
case ROTATION_ROLL_270: {
tmp = z; z = -y; y = tmp;
return;
}
case ROTATION_ROLL_270_YAW_45: {
tmp = z; z = -y; y = tmp;
tmp = HALF_SQRT_2*(float)(x - y);
y = HALF_SQRT_2*(float)(x + y);
x = tmp;
return;
}
case ROTATION_ROLL_270_YAW_90: {
tmp = z; z = -y; y = tmp;
tmp = x; x = -y; y = tmp;
return;
}
case ROTATION_ROLL_270_YAW_135: {
tmp = z; z = -y; y = tmp;
tmp = -HALF_SQRT_2*(float)(x + y);
y = HALF_SQRT_2*(float)(x - y);
x = tmp;
return;
}
case ROTATION_PITCH_90: {
tmp = z; z = -x; x = tmp;
return;
}
case ROTATION_PITCH_270: {
tmp = z; z = x; x = -tmp;
return;
}
case ROTATION_PITCH_180_YAW_90: {
z = -z;
tmp = -x; x = -y; y = tmp;
return;
}
case ROTATION_PITCH_180_YAW_270: {
x = -x; z = -z;
tmp = x; x = y; y = -tmp;
return;
}
case ROTATION_ROLL_90_PITCH_90: {
tmp = z; z = y; y = -tmp;
tmp = z; z = -x; x = tmp;
return;
}
case ROTATION_ROLL_180_PITCH_90: {
y = -y; z = -z;
tmp = z; z = -x; x = tmp;
return;
}
case ROTATION_ROLL_270_PITCH_90: {
tmp = z; z = -y; y = tmp;
tmp = z; z = -x; x = tmp;
return;
}
case ROTATION_ROLL_90_PITCH_180: {
tmp = z; z = y; y = -tmp;
x = -x; z = -z;
return;
}
case ROTATION_ROLL_270_PITCH_180: {
tmp = z; z = -y; y = tmp;
x = -x; z = -z;
return;
}
case ROTATION_ROLL_90_PITCH_270: {
tmp = z; z = y; y = -tmp;
tmp = z; z = x; x = -tmp;
return;
}
case ROTATION_ROLL_180_PITCH_270: {
y = -y; z = -z;
tmp = z; z = x; x = -tmp;
return;
}
case ROTATION_ROLL_270_PITCH_270: {
tmp = z; z = -y; y = tmp;
tmp = z; z = x; x = -tmp;
return;
}
case ROTATION_ROLL_90_PITCH_180_YAW_90: {
tmp = z; z = y; y = -tmp;
x = -x; z = -z;
tmp = x; x = -y; y = tmp;
return;
}
case ROTATION_ROLL_90_YAW_270: {
tmp = z; z = y; y = -tmp;
tmp = x; x = y; y = -tmp;
return;
}
case ROTATION_ROLL_90_PITCH_68_YAW_293: {
float tmpx = x;
float tmpy = y;
float tmpz = z;
x = 0.143039f * tmpx + 0.368776f * tmpy + -0.918446f * tmpz;
y = -0.332133f * tmpx + -0.856289f * tmpy + -0.395546f * tmpz;
z = -0.932324f * tmpx + 0.361625f * tmpy + 0.000000f * tmpz;
return;
}
case ROTATION_PITCH_315: {
tmp = HALF_SQRT_2*(float)(x - z);
z = HALF_SQRT_2*(float)(x + z);
x = tmp;
return;
}
case ROTATION_ROLL_90_PITCH_315: {
tmp = z; z = y; y = -tmp;
tmp = HALF_SQRT_2*(float)(x - z);
z = HALF_SQRT_2*(float)(x + z);
x = tmp;
return;
}
case ROTATION_PITCH_7: {
const float sin_pitch = 0.12186934340514748f; // sinf(pitch);
const float cos_pitch = 0.992546151641322f; // cosf(pitch);
float tmpx = x;
float tmpz = z;
x = cos_pitch * tmpx + sin_pitch * tmpz;
z = -sin_pitch * tmpx + cos_pitch * tmpz;
return;
}
case ROTATION_CUSTOM:
// Error: caller must perform custom rotations via matrix multiplication
INTERNAL_ERROR(AP_InternalError::error_t::flow_of_control);
return;
case ROTATION_MAX:
break;
}
// rotation invalid
INTERNAL_ERROR(AP_InternalError::error_t::bad_rotation);
}
template <typename T>
void Vector3<T>::rotate_inverse(enum Rotation rotation)
{
Vector3<T> x_vec(1.0f,0.0f,0.0f);
Vector3<T> y_vec(0.0f,1.0f,0.0f);
Vector3<T> z_vec(0.0f,0.0f,1.0f);
x_vec.rotate(rotation);
y_vec.rotate(rotation);
z_vec.rotate(rotation);
Matrix3<T> M(
x_vec.x, y_vec.x, z_vec.x,
x_vec.y, y_vec.y, z_vec.y,
x_vec.z, y_vec.z, z_vec.z
);
(*this) = M.mul_transpose(*this);
}
// rotate vector by angle in radians in xy plane leaving z untouched
template <typename T>
void Vector3<T>::rotate_xy(float angle_rad)
{
const float cs = cosf(angle_rad);
const float sn = sinf(angle_rad);
float rx = x * cs - y * sn;
float ry = x * sn + y * cs;
x = rx;
y = ry;
}
// vector cross product
template <typename T>
Vector3<T> Vector3<T>::operator %(const Vector3<T> &v) const
{
Vector3<T> temp(y*v.z - z*v.y, z*v.x - x*v.z, x*v.y - y*v.x);
return temp;
}
// dot product
template <typename T>
T Vector3<T>::operator *(const Vector3<T> &v) const
{
return x*v.x + y*v.y + z*v.z;
}
template <typename T>
float Vector3<T>::length(void) const
{
return norm(x, y, z);
}
// limit xy component vector to a given length. returns true if vector was limited
template <typename T>
bool Vector3<T>::limit_length_xy(float max_length)
{
const float length_xy = norm(x, y);
if ((length_xy > max_length) && is_positive(length_xy)) {
x *= (max_length / length_xy);
y *= (max_length / length_xy);
return true;
}
return false;
}
template <typename T>
Vector3<T> &Vector3<T>::operator *=(const T num)
{
x*=num; y*=num; z*=num;
return *this;
}
template <typename T>
Vector3<T> &Vector3<T>::operator /=(const T num)
{
x /= num; y /= num; z /= num;
return *this;
}
template <typename T>
Vector3<T> &Vector3<T>::operator -=(const Vector3<T> &v)
{
x -= v.x; y -= v.y; z -= v.z;
return *this;
}
template <typename T>
bool Vector3<T>::is_nan(void) const
{
return isnan(x) || isnan(y) || isnan(z);
}
template <typename T>
bool Vector3<T>::is_inf(void) const
{
return isinf(x) || isinf(y) || isinf(z);
}
template <typename T>
Vector3<T> &Vector3<T>::operator +=(const Vector3<T> &v)
{
x+=v.x; y+=v.y; z+=v.z;
return *this;
}
template <typename T>
Vector3<T> Vector3<T>::operator /(const T num) const
{
return Vector3<T>(x/num, y/num, z/num);
}
template <typename T>
Vector3<T> Vector3<T>::operator *(const T num) const
{
return Vector3<T>(x*num, y*num, z*num);
}
template <typename T>
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>
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>
Vector3<T> Vector3<T>::operator -(void) const
{
return Vector3<T>(-x,-y,-z);
}
template <typename T>
bool Vector3<T>::operator ==(const Vector3<T> &v) const
{
return (is_equal(x,v.x) && is_equal(y,v.y) && is_equal(z,v.z));
}
template <typename T>
bool Vector3<T>::operator !=(const Vector3<T> &v) const
{
return (!is_equal(x,v.x) || !is_equal(y,v.y) || !is_equal(z,v.z));
}
template <typename T>
float Vector3<T>::angle(const Vector3<T> &v2) const
{
const float len = this->length() * v2.length();
if (len <= 0) {
return 0.0f;
}
const float cosv = ((*this)*v2) / len;
if (fabsf(cosv) >= 1) {
return 0.0f;
}
return acosf(cosv);
}
// multiplication of transpose by a vector
template <typename T>
Vector3<T> Vector3<T>::operator *(const Matrix3<T> &m) const
{
return Vector3<T>(*this * m.colx(),
*this * m.coly(),
*this * m.colz());
}
// multiply a column vector by a row vector, returning a 3x3 matrix
template <typename T>
Matrix3<T> Vector3<T>::mul_rowcol(const Vector3<T> &v2) const
{
const Vector3<T> v1 = *this;
return Matrix3<T>(v1.x * v2.x, v1.x * v2.y, v1.x * v2.z,
v1.y * v2.x, v1.y * v2.y, v1.y * v2.z,
v1.z * v2.x, v1.z * v2.y, v1.z * v2.z);
}
// extrapolate position given bearing and pitch (in degrees) and distance
template <typename T>
void Vector3<T>::offset_bearing(float bearing, float pitch, float distance)
{
y += cosf(radians(pitch)) * sinf(radians(bearing)) * distance;
x += cosf(radians(pitch)) * cosf(radians(bearing)) * distance;
z += sinf(radians(pitch)) * distance;
}
// distance from the tip of this vector to a line segment specified by two vectors
template <typename T>
float Vector3<T>::distance_to_segment(const Vector3<T> &seg_start, const Vector3<T> &seg_end) const
{
// triangle side lengths
const float a = (*this-seg_start).length();
const float b = (seg_start-seg_end).length();
const float c = (seg_end-*this).length();
// protect against divide by zero later
if (::is_zero(b)) {
return 0.0f;
}
// semiperimeter of triangle
const float s = (a+b+c) * 0.5f;
float area_squared = s*(s-a)*(s-b)*(s-c);
// area must be constrained above 0 because a triangle could have 3 points could be on a line and float rounding could push this under 0
if (area_squared < 0.0f) {
area_squared = 0.0f;
}
const float area = safe_sqrt(area_squared);
return 2.0f*area/b;
}
// Shortest distance between point(p) to a point contained in the line segment defined by w1,w2
template <typename T>
float Vector3<T>::closest_distance_between_line_and_point(const Vector3<T> &w1, const Vector3<T> &w2, const Vector3<T> &p)
{
const Vector3<T> nearest = point_on_line_closest_to_other_point(w1, w2, p);
const float dist = (nearest - p).length();
return dist;
}
// Point in the line segment defined by w1,w2 which is closest to point(p)
// this is based on the explanation given here: www.fundza.com/vectors/point2line/index.html
template <typename T>
Vector3<T> Vector3<T>::point_on_line_closest_to_other_point(const Vector3<T> &w1, const Vector3<T> &w2, const Vector3<T> &p)
{
const Vector3<T> line_vec = w2-w1;
const Vector3<T> p_vec = p - w1;
const float line_vec_len = line_vec.length();
// protection against divide by zero
if(::is_zero(line_vec_len)) {
return {0.0f, 0.0f, 0.0f};
}
const float scale = 1/line_vec_len;
const Vector3<T> unit_vec = line_vec * scale;
const Vector3<T> scaled_p_vec = p_vec * scale;
float dot_product = unit_vec * scaled_p_vec;
dot_product = constrain_float(dot_product,0.0f,1.0f);
const Vector3<T> closest_point = line_vec * dot_product;
return (closest_point + w1);
}
// Closest point between two line segments
// 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"
template <typename T>
void Vector3<T>::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)
{
// direction vectors
const Vector3<T> line1 = seg1_end - seg1_start;
const Vector3<T> line2 = seg2_end - seg2_start;
const Vector3<T> diff = seg1_start - seg2_start;
const float a = line1*line1;
const float b = line1*line2;
const float c = line2*line2;
const float d = line1*diff;
const float e = line2*diff;
const float discriminant = (a*c) - (b*b);
float sN, sD = discriminant; // default sD = D >= 0
float tc, tN, tD = discriminant; // tc = tN / tD, default tD = D >= 0
if (discriminant < FLT_EPSILON) {
sN = 0.0; // force using point seg1_start on line 1
sD = 1.0; // to prevent possible division by 0.0 later
tN = e;
tD = c;
} else {
// get the closest points on the infinite lines
sN = (b*e - c*d);
tN = (a*e - b*d);
if (sN < 0.0) {
// sc < 0 => the s=0 edge is visible
sN = 0.0;
tN = e;
tD = c;
} else if (sN > sD) {
// sc > 1 => the s=1 edge is visible
sN = sD;
tN = e + b;
tD = c;
}
}
if (tN < 0.0) {
// tc < 0 => the t=0 edge is visible
tN = 0.0;
// recompute sc for this edge
if (-d < 0.0) {
sN = 0.0;
} else if (-d > a) {
sN = sD;
} else {
sN = -d;
sD = a;
}
} else if (tN > tD) {
// tc > 1 => the t=1 edge is visible
tN = tD;
// recompute sc for this edge
if ((-d + b) < 0.0) {
sN = 0;
} else if ((-d + b) > a) {
sN = sD;
} else {
sN = (-d + b);
sD = a;
}
}
// finally do the division to get tc
tc = (fabsf(tN) < FLT_EPSILON ? 0.0 : tN / tD);
// closest point on seg2
closest_point = seg2_start + line2*tc;
}
// Returns true if the passed 3D segment passes through a plane defined by plane normal, and a point on the plane
template <typename T>
bool Vector3<T>::segment_plane_intersect(const Vector3<T>& seg_start, const Vector3<T>& seg_end, const Vector3<T>& plane_normal, const Vector3<T>& plane_point)
{
Vector3<T> u = seg_end - seg_start;
Vector3<T> w = seg_start - plane_point;
float D = plane_normal * u;
float N = -(plane_normal * w);
if (fabsf(D) < FLT_EPSILON) {
if (::is_zero(N)) {
// segment lies in this plane
return true;
} else {
// does not intersect
return false;
}
}
const float sI = N / D;
if (sI < 0 || sI > 1) {
// does not intersect
return false;
}
// intersects at unique point
return true;
}
// return xy components of a vector3
template <typename T>
Vector2<T> Vector3<T>::xy()
{
return Vector2<T>{x,y};
}
// define for float and double
template class Vector3<float>;
template class Vector3<double>;
// define needed ops for Vector3l
template Vector3<int32_t> &Vector3<int32_t>::operator +=(const Vector3<int32_t> &v);