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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_MATH_TRIANGLE_HH_
#define IGNITION_MATH_TRIANGLE_HH_
#include <set>
#include <ignition/math/Helpers.hh>
#include <ignition/math/Line2.hh>
#include <ignition/math/Vector2.hh>
#include <ignition/math/config.hh>
namespace ignition
{
namespace math
{
inline namespace IGNITION_MATH_VERSION_NAMESPACE
{
/// \class Triangle Triangle.hh ignition/math/Triangle.hh
/// \brief Triangle class and related functions.
template<typename T>
class Triangle
{
/// \brief Default constructor
public: Triangle() = default;
/// \brief Constructor
/// \param[in] _pt1 First point that defines the triangle.
/// \param[in] _pt2 Second point that defines the triangle.
/// \param[in] _pt3 Third point that defines the triangle.
public: Triangle(const math::Vector2<T> &_pt1,
const math::Vector2<T> &_pt2,
const math::Vector2<T> &_pt3)
{
this->Set(_pt1, _pt2, _pt3);
}
/// \brief Set one vertex of the triangle.
/// \param[in] _index Index of the point to set, where
/// 0 == first vertex, 1 == second vertex, and 2 == third vertex.
/// The index is clamped to the range [0, 2].
/// \param[in] _pt Value of the point to set.
public: void Set(const unsigned int _index, const math::Vector2<T> &_pt)
{
this->pts[clamp(_index, 0u, 2u)] = _pt;
}
/// \brief Set all vertices of the triangle.
/// \param[in] _pt1 First point that defines the triangle.
/// \param[in] _pt2 Second point that defines the triangle.
/// \param[in] _pt3 Third point that defines the triangle.
public: void Set(const math::Vector2<T> &_pt1,
const math::Vector2<T> &_pt2,
const math::Vector2<T> &_pt3)
{
this->pts[0] = _pt1;
this->pts[1] = _pt2;
this->pts[2] = _pt3;
}
/// \brief Get whether this triangle is valid, based on triangle
/// inequality: the sum of the lengths of any two sides must be greater
/// than the length of the remaining side.
/// \return True if the triangle inequality holds
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;
}
/// \brief Get a line segment for one side of the triangle.
/// \param[in] _index Index of the side to retreive, where
/// 0 == Line2(pt1, pt2),
/// 1 == Line2(pt2, pt3),
/// 2 == Line2(pt3, pt1)
/// The index is clamped to the range [0, 2]
/// \return Line segment of the requested side.
public: Line2<T> Side(const unsigned int _index) const
{
if (_index == 0)
return Line2<T>(this->pts[0], this->pts[1]);
else if (_index == 1)
return Line2<T>(this->pts[1], this->pts[2]);
else
return Line2<T>(this->pts[2], this->pts[0]);
}
/// \brief Check if this triangle completely contains the given line
/// segment.
/// \param[in] _line Line to check.
/// \return True if the line's start and end points are both inside
/// this triangle.
public: bool Contains(const Line2<T> &_line) const
{
return this->Contains(_line[0]) && this->Contains(_line[1]);
}
/// \brief Get whether this triangle contains the given point.
/// \param[in] _pt Point to check.
/// \return True if the point is inside or on the triangle.
public: bool Contains(const math::Vector2<T> &_pt) const
{
// Compute vectors
math::Vector2<T> v0 = this->pts[2] -this->pts[0];
math::Vector2<T> v1 = this->pts[1] -this->pts[0];
math::Vector2<T> v2 = _pt - this->pts[0];
// Compute dot products
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);
}
/// \brief Get whether the given line intersects this triangle.
/// \param[in] _line Line to check.
/// \param[out] _ipt1 Return value of the first intersection point,
/// only valid if the return value of the function is true.
/// \param[out] _ipt2 Return value of the second intersection point,
/// only valid if the return value of the function is true.
/// \return True if the given line intersects this triangle.
public: bool Intersects(const Line2<T> &_line,
math::Vector2<T> &_ipt1,
math::Vector2<T> &_ipt2) const
{
if (this->Contains(_line))
{
_ipt1 = _line[0];
_ipt2 = _line[1];
return true;
}
Line2<T> line1(this->pts[0], this->pts[1]);
Line2<T> line2(this->pts[1], this->pts[2]);
Line2<T> line3(this->pts[2], this->pts[0]);
math::Vector2<T> pt;
std::set<math::Vector2<T> > points;
if (line1.Intersect(_line, pt))
points.insert(pt);
if (line2.Intersect(_line, pt))
points.insert(pt);
if (line3.Intersect(_line, pt))
points.insert(pt);
if (points.empty())
{
return false;
}
else if (points.size() == 1)
{
auto iter = points.begin();
_ipt1 = *iter;
if (this->Contains(_line[0]))
_ipt2 = _line[0];
else
{
_ipt2 = _line[1];
}
}
else
{
auto iter = points.begin();
_ipt1 = *(iter++);
_ipt2 = *iter;
}
return true;
}
/// \brief Get the length of the triangle's perimeter.
/// \return Sum of the triangle's line segments.
public: T Perimeter() const
{
return this->Side(0).Length() + this->Side(1).Length() +
this->Side(2).Length();
}
/// \brief Get the area of this triangle.
/// \return Triangle's area.
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));
}
/// \brief Get one of points that define the triangle.
/// \param[in] _index The index, where 0 == first vertex,
/// 1 == second vertex, and 2 == third vertex.
/// The index is clamped to the range [0, 2]
/// \return The point specified by _index.
public: math::Vector2<T> operator[](const size_t _index) const
{
return this->pts[clamp(_index, IGN_ZERO_SIZE_T, IGN_TWO_SIZE_T)];
}
/// The points of the triangle
private: math::Vector2<T> pts[3];
};
/// Integer specialization of the Triangle class.
typedef Triangle<int> Trianglei;
/// Double specialization of the Triangle class.
typedef Triangle<double> Triangled;
/// Float specialization of the Triangle class.
typedef Triangle<float> Trianglef;
}
}
}
#endif
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