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ardupilot/libraries/AP_Math/vector3.cpp

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/*
* 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);
}
// 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);
}
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);
}
// 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
// this is based on the explanation given here: www.fundza.com/vectors/point2line/index.html
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> 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;
}
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> nearest = line_vec * dot_product;
const float dist = (nearest - p_vec).length();
return dist;
}
// define for float
template void Vector3<float>::rotate(enum Rotation);
template void Vector3<float>::rotate_inverse(enum Rotation);
template float Vector3<float>::length(void) const;
template Vector3<float> Vector3<float>::operator %(const Vector3<float> &v) const;
template float Vector3<float>::operator *(const Vector3<float> &v) const;
template Vector3<float> Vector3<float>::operator *(const Matrix3<float> &m) const;
template Matrix3<float> Vector3<float>::mul_rowcol(const Vector3<float> &v) const;
template Vector3<float> &Vector3<float>::operator *=(const float num);
template Vector3<float> &Vector3<float>::operator /=(const float num);
template Vector3<float> &Vector3<float>::operator -=(const Vector3<float> &v);
template Vector3<float> &Vector3<float>::operator +=(const Vector3<float> &v);
template Vector3<float> Vector3<float>::operator /(const float num) const;
template Vector3<float> Vector3<float>::operator *(const float num) const;
template Vector3<float> Vector3<float>::operator +(const Vector3<float> &v) const;
template Vector3<float> Vector3<float>::operator -(const Vector3<float> &v) const;
template Vector3<float> Vector3<float>::operator -(void) const;
template bool Vector3<float>::operator ==(const Vector3<float> &v) const;
template bool Vector3<float>::operator !=(const Vector3<float> &v) const;
template bool Vector3<float>::is_nan(void) const;
template bool Vector3<float>::is_inf(void) const;
template float Vector3<float>::angle(const Vector3<float> &v) const;
template float Vector3<float>::distance_to_segment(const Vector3<float> &seg_start, const Vector3<float> &seg_end) const;
template float Vector3<float>::closest_distance_between_line_and_point(const Vector3<float> &w1, const Vector3<float> &w2, const Vector3<float> &p);
// define needed ops for Vector3l
template Vector3<int32_t> &Vector3<int32_t>::operator +=(const Vector3<int32_t> &v);
template void Vector3<double>::rotate(enum Rotation);
template void Vector3<double>::rotate_inverse(enum Rotation);
template float Vector3<double>::length(void) const;
template Vector3<double> Vector3<double>::operator %(const Vector3<double> &v) const;
template double Vector3<double>::operator *(const Vector3<double> &v) const;
template Vector3<double> Vector3<double>::operator *(const Matrix3<double> &m) const;
template Matrix3<double> Vector3<double>::mul_rowcol(const Vector3<double> &v) const;
template Vector3<double> &Vector3<double>::operator *=(const double num);
template Vector3<double> &Vector3<double>::operator /=(const double num);
template Vector3<double> &Vector3<double>::operator -=(const Vector3<double> &v);
template Vector3<double> &Vector3<double>::operator +=(const Vector3<double> &v);
template Vector3<double> Vector3<double>::operator /(const double num) const;
template Vector3<double> Vector3<double>::operator *(const double num) const;
template Vector3<double> Vector3<double>::operator +(const Vector3<double> &v) const;
template Vector3<double> Vector3<double>::operator -(const Vector3<double> &v) const;
template Vector3<double> Vector3<double>::operator -(void) const;
template bool Vector3<double>::operator ==(const Vector3<double> &v) const;
template bool Vector3<double>::operator !=(const Vector3<double> &v) const;
template bool Vector3<double>::is_nan(void) const;
template bool Vector3<double>::is_inf(void) const;
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