vector3.cpp

Go to the documentation of this file.

/*
 * 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("O3")

#include "AP_Math.h"

#define HALF_SQRT_2 0.70710678118654757f

// 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:
    case ROTATION_MAX:
        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_CUSTOM: // no-op; caller should perform custom rotations via matrix multiplication
        return;
    }
}

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
{
    float len = this->length() * v2.length();
    if (len <= 0) {
        return 0.0f;
    }
    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
    float a = (*this-seg_start).length();
    float b = (seg_start-seg_end).length();
    float c = (seg_end-*this).length();

    // protect against divide by zero later
    if (fabsf(b) < FLT_EPSILON) {
        return 0.0f;
    }

    // semiperimeter of triangle
    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;
    }
    float area = safe_sqrt(area_squared);
    return 2.0f*area/b;
}

// 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;

// 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;