Vector3.hh

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/*
 * Copyright (C) 2014 Open Source Robotics Foundation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
*/
#ifndef _IGNITION_VECTOR3_HH_
#define _IGNITION_VECTOR3_HH_

#include <iostream>
#include <fstream>
#include <cmath>
#include <algorithm>

#include <ignition/math/Helpers.hh>
#include <ignition/math/IndexException.hh>

namespace ignition
{
  namespace math
  {
    template<typename T>
    class Vector3
    {
      public: static const Vector3 Zero;

      public: static const Vector3 One;

      public: static const Vector3 UnitX;

      public: static const Vector3 UnitY;

      public: static const Vector3 UnitZ;

      public: Vector3()
      {
        this->data[0] = 0;
        this->data[1] = 0;
        this->data[2] = 0;
      }

      public: Vector3(const T &_x, const T &_y, const T &_z)
      {
        this->data[0] = _x;
        this->data[1] = _y;
        this->data[2] = _z;
      }

      public: Vector3(const Vector3<T> &_v)
      {
        this->data[0] = _v[0];
        this->data[1] = _v[1];
        this->data[2] = _v[2];
      }

      public: virtual ~Vector3() {}

      public: T Sum() const
      {
        return this->data[0] + this->data[1] + this->data[2];
      }

      public: T Distance(const Vector3<T> &_pt) const
      {
        return sqrt((this->data[0]-_pt[0])*(this->data[0]-_pt[0]) +
                    (this->data[1]-_pt[1])*(this->data[1]-_pt[1]) +
                    (this->data[2]-_pt[2])*(this->data[2]-_pt[2]));
      }

      public: T Distance(T _x, T _y, T _z) const
      {
        return this->Distance(Vector3(_x, _y, _z));
      }

      public: T Length() const
      {
        return sqrt(this->data[0] * this->data[0] +
                    this->data[1] * this->data[1] +
                    this->data[2] * this->data[2]);
      }

      public: T SquaredLength() const
      {
        return this->data[0] * this->data[0] +
               this->data[1] * this->data[1] +
               this->data[2] * this->data[2];
      }

      public: Vector3 Normalize()
      {
        T d = sqrt(this->data[0] * this->data[0] +
                   this->data[1] * this->data[1] +
                   this->data[2] * this->data[2]);

        if (!equal<T>(d, static_cast<T>(0.0)))
        {
          this->data[0] /= d;
          this->data[1] /= d;
          this->data[2] /= d;
        }

        return *this;
      }

      public: Vector3 Round()
      {
        this->data[0] = nearbyint(this->data[0]);
        this->data[1] = nearbyint(this->data[1]);
        this->data[2] = nearbyint(this->data[2]);
        return *this;
      }

      public: Vector3 Rounded() const
      {
        Vector3<T> result = *this;
        result.Round();
        return result;
      }

      public: inline void Set(T _x = 0, T _y = 0, T _z = 0)
      {
        this->data[0] = _x;
        this->data[1] = _y;
        this->data[2] = _z;
      }

      public: Vector3 Cross(const Vector3<T> &_v) const
      {
        return Vector3(this->data[1] * _v[2] - this->data[2] * _v[1],
                       this->data[2] * _v[0] - this->data[0] * _v[2],
                       this->data[0] * _v[1] - this->data[1] * _v[0]);
      }

      public: T Dot(const Vector3<T> &_v) const
      {
        return this->data[0] * _v[0] +
               this->data[1] * _v[1] +
               this->data[2] * _v[2];
      }

      public: Vector3 Abs() const
      {
        return Vector3(std::abs(this->data[0]),
                       std::abs(this->data[1]),
                       std::abs(this->data[2]));
      }

      public: Vector3 Perpendicular() const
      {
        static const T sqrZero = 1e-06 * 1e-06;

        Vector3<T> perp = this->Cross(Vector3(1, 0, 0));

        // Check the length of the vector
        if (perp.SquaredLength() < sqrZero)
        {
          perp = this->Cross(Vector3(0, 1, 0));
        }

        return perp;
      }

      public: static Vector3 Normal(const Vector3<T> &_v1,
                  const Vector3<T> &_v2, const Vector3<T> &_v3)
      {
        Vector3<T> a = _v2 - _v1;
        Vector3<T> b = _v3 - _v1;
        Vector3<T> n = a.Cross(b);
        return n;
      }

      public: T DistToLine(const Vector3<T> &_pt1, const Vector3 &_pt2)
      {
        T d = ((*this) - _pt1).Cross((*this) - _pt2).Length();
        d = d / (_pt2 - _pt1).Length();
        return d;
      }

      public: void Max(const Vector3<T> &_v)
      {
        if (_v[0] > this->data[0])
          this->data[0] = _v[0];
        if (_v[1] > this->data[1])
          this->data[1] = _v[1];
        if (_v[2] > this->data[2])
          this->data[2] = _v[2];
      }

      public: void Min(const Vector3<T> &_v)
      {
        if (_v[0] < this->data[0])
          this->data[0] = _v[0];
        if (_v[1] < this->data[1])
          this->data[1] = _v[1];
        if (_v[2] < this->data[2])
          this->data[2] = _v[2];
      }

      public: T Max() const
      {
        return std::max(std::max(this->data[0], this->data[1]), this->data[2]);
      }

      public: T Min() const
      {
        return std::min(std::min(this->data[0], this->data[1]), this->data[2]);
      }

      public: Vector3 &operator=(const Vector3<T> &_v)
      {
        this->data[0] = _v[0];
        this->data[1] = _v[1];
        this->data[2] = _v[2];

        return *this;
      }

      public: Vector3 &operator=(T _v)
      {
        this->data[0] = _v;
        this->data[1] = _v;
        this->data[2] = _v;

        return *this;
      }

      public: Vector3 operator+(const Vector3<T> &_v) const
      {
        return Vector3(this->data[0] + _v[0],
                       this->data[1] + _v[1],
                       this->data[2] + _v[2]);
      }

      public: const Vector3 &operator+=(const Vector3<T> &_v)
      {
        this->data[0] += _v[0];
        this->data[1] += _v[1];
        this->data[2] += _v[2];

        return *this;
      }

      public: inline Vector3 operator-() const
      {
        return Vector3(-this->data[0], -this->data[1], -this->data[2]);
      }

      public: inline Vector3<T> operator-(const Vector3<T> &_pt) const
      {
        return Vector3(this->data[0] - _pt[0],
                       this->data[1] - _pt[1],
                       this->data[2] - _pt[2]);
      }

      public: const Vector3<T> &operator-=(const Vector3<T> &_pt)
      {
        this->data[0] -= _pt[0];
        this->data[1] -= _pt[1];
        this->data[2] -= _pt[2];

        return *this;
      }

      public: const Vector3<T> operator/(const Vector3<T> &_pt) const
      {
        return Vector3(this->data[0] / _pt[0],
                       this->data[1] / _pt[1],
                       this->data[2] / _pt[2]);
      }

      public: const Vector3<T> &operator/=(const Vector3<T> &_pt)
      {
        this->data[0] /= _pt[0];
        this->data[1] /= _pt[1];
        this->data[2] /= _pt[2];

        return *this;
      }

      public: const Vector3<T> operator/(T _v) const
      {
        return Vector3(this->data[0] / _v,
                       this->data[1] / _v,
                       this->data[2] / _v);
      }

      public: const Vector3<T> &operator/=(T _v)
      {
        this->data[0] /= _v;
        this->data[1] /= _v;
        this->data[2] /= _v;

        return *this;
      }

      public: Vector3<T> operator*(const Vector3<T> &_p) const
      {
        return Vector3(this->data[0] * _p[0],
                       this->data[1] * _p[1],
                       this->data[2] * _p[2]);
      }

      public: const Vector3<T> &operator*=(const Vector3<T> &_v)
      {
        this->data[0] *= _v[0];
        this->data[1] *= _v[1];
        this->data[2] *= _v[2];

        return *this;
      }

      public: inline Vector3<T> operator*(T _s) const
      {
        return Vector3<T>(this->data[0] * _s,
                          this->data[1] * _s,
                          this->data[2] * _s);
      }

      public: friend inline Vector3<T> operator*(T _s, const Vector3<T> &_v)
      {
        return Vector3<T>(_v.X() * _s, _v.Y() * _s, _v.Z() * _s);
      }

      public: const Vector3<T> &operator*=(T _v)
      {
        this->data[0] *= _v;
        this->data[1] *= _v;
        this->data[2] *= _v;

        return *this;
      }

      public: bool operator==(const Vector3<T> &_v) const
      {
        return equal<T>(this->data[0], _v[0], static_cast<T>(0.001)) &&
               equal<T>(this->data[1], _v[1], static_cast<T>(0.001)) &&
               equal<T>(this->data[2], _v[2], static_cast<T>(0.001));
      }

      public: bool operator!=(const Vector3<T> &_v) const
      {
        return !(*this == _v);
      }

      public: bool IsFinite() const
      {
        // std::isfinite works with floating point values,
        // need to explicit cast to avoid ambiguity in vc++.
        return std::isfinite(static_cast<double>(this->data[0])) &&
               std::isfinite(static_cast<double>(this->data[1])) &&
               std::isfinite(static_cast<double>(this->data[2]));
      }

      public: inline void Correct()
      {
        // std::isfinite works with floating point values,
        // need to explicit cast to avoid ambiguity in vc++.
        if (!std::isfinite(static_cast<double>(this->data[0])))
          this->data[0] = 0;
        if (!std::isfinite(static_cast<double>(this->data[1])))
          this->data[1] = 0;
        if (!std::isfinite(static_cast<double>(this->data[2])))
          this->data[2] = 0;
      }

      public: T operator[](size_t _index) const
      {
        if (_index > 2)
          throw IndexException();
        return this->data[_index];
      }

      public: void Round(int _precision)
      {
        this->data[0] = precision(this->data[0], _precision);
        this->data[1] = precision(this->data[1], _precision);
        this->data[2] = precision(this->data[2], _precision);
      }

      public: bool Equal(const Vector3<T> &_v) const
      {
        return equal<T>(this->data[0], _v[0]) &&
               equal<T>(this->data[1], _v[1]) &&
               equal<T>(this->data[2], _v[2]);
      }

      public: inline T X() const
      {
        return this->data[0];
      }

      public: inline T Y() const
      {
        return this->data[1];
      }

      public: inline T Z() const
      {
        return this->data[2];
      }

      public: inline T &X()
      {
        return this->data[0];
      }

      public: inline T &Y()
      {
        return this->data[1];
      }

      public: inline T &Z()
      {
        return this->data[2];
      }

      public: inline void X(const T &_v)
      {
        this->data[0] = _v;
      }

      public: inline void Y(const T &_v)
      {
        this->data[1] = _v;
      }

      public: inline void Z(const T &_v)
      {
        this->data[2] = _v;
      }

      public: friend std::ostream &operator<<(
                  std::ostream &_out, const ignition::math::Vector3<T> &_pt)
      {
        _out << precision(_pt[0], 6) << " " << precision(_pt[1], 6) << " "
          << precision(_pt[2], 6);
        return _out;
      }

      public: friend std::istream &operator>>(
                  std::istream &_in, ignition::math::Vector3<T> &_pt)
      {
        // Skip white spaces
        _in.setf(std::ios_base::skipws);
        T x, y, z;
        _in >> x >> y >> z;
        _pt.Set(x, y, z);
        return _in;
      }

      private: T data[3];
    };

    template<typename T> const Vector3<T> Vector3<T>::Zero(0, 0, 0);
    template<typename T> const Vector3<T> Vector3<T>::One(1, 1, 1);
    template<typename T> const Vector3<T> Vector3<T>::UnitX(1, 0, 0);
    template<typename T> const Vector3<T> Vector3<T>::UnitY(0, 1, 0);
    template<typename T> const Vector3<T> Vector3<T>::UnitZ(0, 0, 1);

    typedef Vector3<int> Vector3i;
    typedef Vector3<double> Vector3d;
    typedef Vector3<float> Vector3f;
  }
}
#endif