Triangle3.hh

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/*
 * Copyright (C) 2016 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_TRIANGLE3_HH_
#define GZ_MATH_TRIANGLE3_HH_
 
#include <gz/math/Helpers.hh>
#include <gz/math/Line3.hh>
#include <gz/math/Plane.hh>
#include <gz/math/Vector3.hh>
#include <gz/math/config.hh>
 
namespace gz::math
{
  // Inline bracket to help doxygen filtering.
  inline namespace GZ_MATH_VERSION_NAMESPACE {
  //
  template<typename T>
  class Triangle3
  {
    public: Triangle3() = default;
 
    public: Triangle3(const Vector3<T> &_pt1,
                      const Vector3<T> &_pt2,
                      const Vector3<T> &_pt3)
    {
      this->Set(_pt1, _pt2, _pt3);
    }
 
    public: void Set(const unsigned int _index, const Vector3<T> &_pt)
    {
      this->pts[clamp(_index, 0u, 2u)] = _pt;
    }
 
    public: void Set(const Vector3<T> &_pt1,
                     const Vector3<T> &_pt2,
                     const Vector3<T> &_pt3)
    {
      this->pts[0] = _pt1;
      this->pts[1] = _pt2;
      this->pts[2] = _pt3;
    }
 
    public: bool Valid() const
    {
      T a = this->Side(0).Length();
      T b = this->Side(1).Length();
      T c = this->Side(2).Length();
      return (a+b) > c && (b+c) > a && (c+a) > b;
    }
 
    public: Line3<T> Side(const unsigned int _index) const
    {
      if (_index == 0)
        return Line3<T>(this->pts[0], this->pts[1]);
      else if (_index == 1)
        return Line3<T>(this->pts[1], this->pts[2]);
      else
        return Line3<T>(this->pts[2], this->pts[0]);
    }
 
    public: bool Contains(const Line3<T> &_line) const
    {
      return this->Contains(_line[0]) && this->Contains(_line[1]);
    }
 
    public: bool Contains(const Vector3<T> &_pt) const
    {
      // Make sure the point is on the same plane as the triangle
      if (Planed(this->Normal()).Side(Vector3d(_pt[0], _pt[1], _pt[2]))
        == Planed::NO_SIDE)
      {
        Vector3<T> v0 = this->pts[2] - this->pts[0];
        Vector3<T> v1 = this->pts[1] - this->pts[0];
        Vector3<T> v2 = _pt - this->pts[0];
 
        double dot00 = v0.Dot(v0);
        double dot01 = v0.Dot(v1);
        double dot02 = v0.Dot(v2);
        double dot11 = v1.Dot(v1);
        double dot12 = v1.Dot(v2);
 
        // Compute barycentric coordinates
        double invDenom = 1.0 / (dot00 * dot11 - dot01 * dot01);
        double u = (dot11 * dot02 - dot01 * dot12) * invDenom;
        double v = (dot00 * dot12 - dot01 * dot02) * invDenom;
 
        // Check if point is in triangle
        return (u >= 0) && (v >= 0) && (u + v <= 1);
      }
      return false;
    }
 
    public: Vector3d Normal() const
    {
      return math::Vector3d::Normal(
        Vector3d(this->pts[0][0], this->pts[0][1], this->pts[0][2]),
        Vector3d(this->pts[1][0], this->pts[1][1], this->pts[1][2]),
        Vector3d(this->pts[2][0], this->pts[2][1], this->pts[2][2]));
    }
 
    public: bool Intersects(
      const Line3<T> &_line, Vector3<T> &_ipt1) const
    {
      // Triangle normal
      Vector3d norm = this->Normal();
 
      // Ray direction to intersect with triangle
      Vector3<T> dir = (_line[1] - _line[0]).Normalize();
 
      double denom = norm.Dot(Vector3d(dir[0], dir[1], dir[2]));
 
      // Handle the case when the line is not co-planar with the triangle
      if (!math::equal(denom, 0.0))
      {
        // Distance from line start to triangle intersection
        Vector3<T> diff = _line[0] - this->pts[0];
        double intersection =
          -norm.Dot(Vector3d(diff[0], diff[1], diff[2])) / denom;
 
        // Make sure the ray intersects the triangle
        if (intersection < 1.0 || intersection > _line.Length())
          return false;
 
        // Return point of intersection
        _ipt1 = _line[0] + (dir * intersection);
 
        return true;
      }
      // Line co-planar with triangle
      else
      {
        // If the line is completely inside the triangle
        if (this->Contains(_line))
        {
          _ipt1 = _line[0];
          return true;
        }
        // If the line intersects the first side
        else if (_line.Intersect(this->Side(0), _ipt1))
        {
          return true;
        }
        // If the line intersects the second side
        else if (_line.Intersect(this->Side(1), _ipt1))
        {
          return true;
        }
        // If the line intersects the third side
        else if (_line.Intersect(this->Side(2), _ipt1))
        {
          return true;
        }
      }
 
      return false;
    }
 
    public: T Perimeter() const
    {
      return this->Side(0).Length() + this->Side(1).Length() +
             this->Side(2).Length();
    }
 
    public: double Area() const
    {
      double s = this->Perimeter() / 2.0;
      T a = this->Side(0).Length();
      T b = this->Side(1).Length();
      T c = this->Side(2).Length();
 
      // Heron's formula
      // http://en.wikipedia.org/wiki/Heron%27s_formula
      return sqrt(s * (s-a) * (s-b) * (s-c));
    }
 
    public: Vector3<T> operator[](const size_t _index) const
    {
      return this->pts[clamp(_index, GZ_ZERO_SIZE_T, GZ_TWO_SIZE_T)];
    }
 
    private: Vector3<T> pts[3];
  };
 
  typedef Triangle3<int> Triangle3i;
 
  typedef Triangle3<double> Triangle3d;
 
  typedef Triangle3<float> Triangle3f;
  }  // namespace GZ_MATH_VERSION_NAMESPACE
}  // namespace gz::math
#endif  // GZ_MATH_TRIANGLE3_HH_