Plane.hh

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/*
 * Copyright (C) 2012 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 GZ_MATH_PLANE_HH_
#define GZ_MATH_PLANE_HH_
 
#include <gz/math/AxisAlignedBox.hh>
#include <gz/math/Vector2.hh>
#include <gz/math/Vector3.hh>
#include <gz/math/config.hh>
#include <gz/math/Line2.hh>
#include <gz/math/Quaternion.hh>
#include <optional>
 
namespace gz::math
{
  // Inline bracket to help doxygen filtering.
  inline namespace GZ_MATH_VERSION_NAMESPACE {
  //
  template<typename T>
  class Plane
  {
    public: enum PlaneSide
    {
      NEGATIVE_SIDE = 0,
 
      POSITIVE_SIDE = 1,
 
      NO_SIDE = 2,
 
      BOTH_SIDE = 3
    };
 
    public: Plane()
    : d(0.0)
    {
    }
 
    public: explicit Plane(const Vector3<T> &_normal, T _offset = 0.0)
    : normal(_normal), d(_offset)
    {
    }
 
    public: Plane(const Vector3<T> &_normal, const Vector2<T> &_size,
                  T _offset)
    {
      this->Set(_normal, _size, _offset);
    }
 
    public: void Set(const Vector3<T> &_normal, T _offset)
    {
      this->normal = _normal;
      this->d = _offset;
    }
 
    public: void Set(const Vector3<T> &_normal, const Vector2<T> &_size,
                     T _offset)
    {
      this->normal = _normal;
      this->size = _size;
      this->d = _offset;
    }
 
    public: T Distance(const Vector3<T> &_point) const
    {
      return this->normal.Dot(_point) - this->d;
    }
 
    public: std::optional<Vector3<T>> Intersection(
      const Vector3<T> &_point,
      const Vector3<T> &_gradient,
      const double &_tolerance = 1e-6) const
    {
      if (std::abs(this->Normal().Dot(_gradient)) < _tolerance)
      {
        return std::nullopt;
      }
      auto constant = this->Offset() - this->Normal().Dot(_point);
      auto param = constant / this->Normal().Dot(_gradient);
      auto intersection = _point + _gradient*param;
 
      if (this->Size() == Vector2<T>(0, 0))
        return intersection;
 
      // Check if the point is within the size bounds
      // To do this we create a Quaternion using Angle, Axis constructor and
      // rotate the Y and X axis the same amount as the normal.
      auto dotProduct = Vector3<T>::UnitZ.Dot(this->Normal());
      auto angle = acos(dotProduct / this->Normal().Length());
      auto axis = Vector3<T>::UnitZ.Cross(this->Normal().Normalized());
      Quaternion<T> rotation(axis, angle);
 
      Vector3<T> rotatedXAxis = rotation * Vector3<T>::UnitX;
      Vector3<T> rotatedYAxis = rotation * Vector3<T>::UnitY;
 
      auto xBasis = rotatedXAxis.Dot(intersection);
      auto yBasis = rotatedYAxis.Dot(intersection);
 
      if (std::abs(xBasis) < this->Size().X() / 2 &&
          std::abs(yBasis) < this->Size().Y() / 2)
      {
        return intersection;
      }
      return std::nullopt;
    }
 
    public: PlaneSide Side(const Vector3<T> &_point) const
    {
      T dist = this->Distance(_point);
 
      if (dist < 0.0)
        return NEGATIVE_SIDE;
 
      if (dist > 0.0)
        return POSITIVE_SIDE;
 
      return NO_SIDE;
    }
 
    public: PlaneSide Side(const math::AxisAlignedBox &_box) const
    {
      double dist = this->Distance(_box.Center());
      double maxAbsDist = this->normal.AbsDot(_box.Size()/2.0);
 
      if (dist < -maxAbsDist)
        return NEGATIVE_SIDE;
 
      if (dist > maxAbsDist)
        return POSITIVE_SIDE;
 
      return BOTH_SIDE;
    }
 
    public: T Distance(const Vector3<T> &_origin,
                       const Vector3<T> &_dir) const
    {
      T denom = this->normal.Dot(_dir);
 
      if (std::abs(denom) < 1e-3)
      {
        // parallel
        return 0;
      }
      else
      {
        T nom = _origin.Dot(this->normal) - this->d;
        T t = -(nom/denom);
        return t;
      }
    }
 
    public: inline const Vector2<T> &Size() const
    {
      return this->size;
    }
 
    public: inline Vector2<T> &Size()
    {
      return this->size;
    }
 
    public: inline const Vector3<T> &Normal() const
    {
      return this->normal;
    }
 
    public: inline Vector3<T> &Normal()
    {
      return this->normal;
    }
 
    public: inline T Offset() const
    {
      return this->d;
    }
 
    private: Vector3<T> normal;
 
    private: Vector2<T> size;
 
    private: T d;
  };
 
  typedef Plane<int> Planei;
  typedef Plane<double> Planed;
  typedef Plane<float> Planef;
  }  // namespace GZ_MATH_VERSION_NAMESPACE
}  // namespace gz::math
#endif  // GZ_MATH_PLANE_HH_