#include <geomObjects.h>

Inheritance diagram for geom::Triangle:

Collaboration diagram for geom::Triangle:

Public Member Functions
	Triangle ()
	Constructor.

	Triangle (double r, util::Point x=util::Point(0., 0., 0.), util::Point a=util::Point(1., 0., 0.), std::string description="uniform")
	Constructor.

	Triangle (util::Point v0, util::Point v1, util::Point v2, std::string description="vertices")
	Constructor from three vertices (arbitrary triangle, e.g. a V-notch). Params in decks: x1,y1,z1, x2,y2,z2, x3,y3,z3.

	Triangle (const Triangle &other)
	Copy constructor.

Triangle &	operator= (const Triangle &other)
	Assignment operator.

void	transform (const util::Point &translation, const double &scale, const double &angle, const util::Point &axis, const util::Point *rotationPoint) override
	Similarity about pivot \(\mathbf p\) (default: old center `d_x`), then rigid displacement \(\mathbf t\) = `translation:` \(\mathbf y = \mathbf p + s\,\mathbf R(\mathbf x-\mathbf p) + \mathbf t\). When \(\theta=0\) and \(s=1\), \(\mathbf y = \mathbf x + \mathbf t\) for every point and the center.

double	volume () const override
	Computes the volume (area in 2d, length in 1d) of object.

util::Point	center () const override
	Computes the center of object.

std::pair< util::Point, util::Point >	box () const override
	Computes the bounding box of object.

std::pair< util::Point, util::Point >	box (const double &tol) const override
	Computes the bounding box of object.

double	inscribedRadius () const override
	Computes the radius of biggest circle/sphere completely within the object.

double	boundingRadius () const override
	Computes the radius of smallest circle/sphere such that object can be fit into it.

std::string	printStr (int nt, int lvl) const override
	Returns the string containing printable information about the object.

void	print (int nt, int lvl) const override
	Prints the information about the object.

void	print () const override
	Prints the information about the object.

Interaction with point
bool	isInside (const util::Point &x) const override
	Checks if point is inside this object.

bool	isOutside (const util::Point &x) const override
	Checks if point is outside of this object.

bool	isNear (const util::Point &x, const double &tol) const override
	Checks if point is within given distance of this object.

bool	isNearBoundary (const util::Point &x, const double &tol, const bool &within) const override
	cons

bool	doesIntersect (const util::Point &x) const override
	Checks if point lies exactly on the boundary.

Interaction with box
TODO Implement methods
bool	isInside (const std::pair< util::Point, util::Point > &box) const override
	Checks if box is completely inside.

bool	isOutside (const std::pair< util::Point, util::Point > &box) const override
	Checks if box is outside of the object.

bool	isNear (const std::pair< util::Point, util::Point > &box, const double &tol) const override
	Checks if box is within given distance of this object.

bool	doesIntersect (const std::pair< util::Point, util::Point > &box) const override
	Checks if box intersects this object.

Public Member Functions inherited from geom::GeomObject
	GeomObject (std::string name="", std::string description="")
	Constructor.

virtual bool	wallContactQuery (const util::Point &x, WallContactHit &hit) const
	Closest-point / signed-gap query for analytical wall contact. Default: unsupported (returns false, clears `hit`).

Data Fields
std::vector< util::Point >	d_vertices
	Vertices.

util::Point	d_x
	Center.

double	d_r
	Distance between center and the farthest vertex of triangle.

util::Point	d_a
	Axis: defined as the vector pointing from center to the first vertex v2 +.

Data Fields inherited from geom::GeomObject
const std::string	d_name
	name of object

const std::string	d_description
	Further description of object.

std::vector< std::string >	d_tags
	Tags/attributes about the object.

Detailed Description

Defines Triangle.

Definition at line 759 of file geomObjects.h.

Constructor & Destructor Documentation

◆ Triangle() [1/4]

geom::Triangle::Triangle ( )

inline

Constructor.

Definition at line 790 of file geomObjects.h.

      : GeomObject("triangle", ""),
        d_r(0.),
        d_a(util::Point(1., 0., 0.)),
        d_x(util::Point()),
        d_vertices(std::vector<util::Point>(3, util::Point())) {
    };

◆ Triangle() [2/4]

geom::Triangle::Triangle	(	double	r,
		util::Point	x = `util::Point(0., 0., 0.)`,
		util::Point	a = `util::Point(1., 0., 0.)`,
		std::string	description = `"uniform"`
	)

inline

Constructor.

Parameters

r	Radius (distance of vertex from center)
x	Center point
a	Axis vector that will be rotated and scaled by r to find coordiantes of triangle vertices
description	Description of object (e.g., further classification or any tag)

Definition at line 806 of file geomObjects.h.

      : GeomObject("triangle", description),
        d_r(r),
        d_a(a),
        d_x(x),
        d_vertices(std::vector<util::Point>(3, util::Point())) {
      // generate vertices
      auto rotate_axis = util::Point(0., 0., 1.); // z-axis
      for (int i = 0; i < 3; i++) {
        d_vertices[i] = d_x + d_r * util::rotate(
                          d_a, i * 2. * M_PI / 3., rotate_axis);
      }
    };

References d_a, d_r, d_vertices, d_x, and util::rotate().

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◆ Triangle() [3/4]

geom::Triangle::Triangle	(	util::Point	v0,
		util::Point	v1,
		util::Point	v2,
		std::string	description = `"vertices"`
	)

inline

Constructor from three vertices (arbitrary triangle, e.g. a V-notch). Params in decks: x1,y1,z1, x2,y2,z2, x3,y3,z3.

Definition at line 826 of file geomObjects.h.

      : GeomObject("triangle", description),
        d_r(0.),
        d_a(util::Point(1., 0., 0.)),
        d_x(util::Point()),
        d_vertices({v0, v1, v2}) {
      d_x = (v0 + v1 + v2) / 3.0;
      d_r = (v0 - d_x).length();
      {
        const double r1 = (v1 - d_x).length();
        const double r2 = (v2 - d_x).length();
        if (r1 > d_r)
          d_r = r1;
        if (r2 > d_r)
          d_r = r2;
      }
      d_a = v0 - d_x;
      if (d_a.length() > 0.)
        d_a = d_a / d_a.length();
    };

◆ Triangle() [4/4]

geom::Triangle::Triangle ( const Triangle & other )

inline

Copy constructor.

Parameters

other Object to copy from

Definition at line 852 of file geomObjects.h.

      : GeomObject(other.d_name, other.d_description),
        d_r(other.d_r),
        d_a(other.d_a),
        d_x(other.d_x),
        d_vertices(other.d_vertices) {
      d_tags = other.d_tags;
    }

References geom::GeomObject::d_tags.

Member Function Documentation

◆ boundingRadius()

double geom::Triangle::boundingRadius ( ) const

overridevirtual

Computes the radius of smallest circle/sphere such that object can be fit into it.

Returns: Radius Radius of bounding circle/sphere

Reimplemented from geom::GeomObject.

Definition at line 289 of file geomObjects.cpp.

                                          {
 
      return d_r;
    }

References d_r.

◆ box() [1/2]

std::pair< util::Point, util::Point > geom::Triangle::box ( ) const

overridevirtual

Computes the bounding box of object.

Returns: Pair Left-bottom-back and right-top-front corner points of box

Reimplemented from geom::GeomObject.

Definition at line 264 of file geomObjects.cpp.

                                                      {
 
      return box(0.);
    }

References box().

Referenced by box(), doesIntersect(), isInside(), isNear(), isNear(), and isOutside().

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◆ box() [2/2]

std::pair< util::Point, util::Point > geom::Triangle::box ( const double & tol ) const

overridevirtual

Computes the bounding box of object.

Parameters

tol	Tolerance/padding used in creating bounding box

Returns: Pair Left-bottom-back and right-top-front corner points of box

Reimplemented from geom::GeomObject.

Definition at line 269 of file geomObjects.cpp.

                                                                                         {
 
      util::Point p1 = d_vertices[0], p2 = d_vertices[0];
      for (const auto &v : d_vertices) {
        p1.d_x = std::min(p1.d_x, v.d_x);
        p1.d_y = std::min(p1.d_y, v.d_y);
        p1.d_z = std::min(p1.d_z, v.d_z);
        p2.d_x = std::max(p2.d_x, v.d_x);
        p2.d_y = std::max(p2.d_y, v.d_y);
        p2.d_z = std::max(p2.d_z, v.d_z);
      }
      return {p1 - tol, p2 + tol};
    }

References d_vertices, util::Point::d_x, util::Point::d_y, and util::Point::d_z.

◆ center()

util::Point geom::Triangle::center ( ) const

overridevirtual

Computes the center of object.

Returns: Point Coordinates of center

Reimplemented from geom::GeomObject.

Definition at line 260 of file geomObjects.cpp.

                                     {
      return d_x;
    }

References d_x.

◆ doesIntersect() [1/2]

bool geom::Triangle::doesIntersect ( const std::pair< util::Point, util::Point > & box ) const

overridevirtual

Checks if box intersects this object.

Parameters

box Box

Returns: True True if intersects

Reimplemented from geom::GeomObject.

Definition at line 388 of file geomObjects.cpp.

                                                            {
 
      // need to check all four corner points
      for (auto p: geom::getCornerPoints(2, box))
        if (this->isInside(p))
          return true;
 
      return false;
    }

References box(), geom::getCornerPoints(), and isInside().

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◆ doesIntersect() [2/2]

bool geom::Triangle::doesIntersect ( const util::Point & x ) const

overridevirtual

Checks if point lies exactly on the boundary.

Parameters

x Point

Returns: True True if it lies on the boundary

Reimplemented from geom::GeomObject.

Definition at line 355 of file geomObjects.cpp.

                                                         {
 
      return isNearBoundary(x, 1.0E-8, false);
    }

References isNearBoundary().

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◆ inscribedRadius()

double geom::Triangle::inscribedRadius ( ) const

overridevirtual

Computes the radius of biggest circle/sphere completely within the object.

Returns: Radius Radius of inscribed circle/sphere

Reimplemented from geom::GeomObject.

Definition at line 284 of file geomObjects.cpp.

                                           {
 
      return d_r * std::sin(M_PI / 3);
    }

References d_r.

Referenced by isInside().

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◆ isInside() [1/2]

bool geom::Triangle::isInside ( const std::pair< util::Point, util::Point > & box ) const

overridevirtual

Checks if box is completely inside.

Parameters

box Box

Returns: True True if box lies inside

Reimplemented from geom::GeomObject.

Definition at line 360 of file geomObjects.cpp.

                                                            {
 
      for (auto p: geom::getCornerPoints(2, box))
        if (!this->isInside(p))
          return false;
 
      return true;
    }

References box(), geom::getCornerPoints(), and isInside().

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◆ isInside() [2/2]

bool geom::Triangle::isInside ( const util::Point & x ) const

overridevirtual

Checks if point is inside this object.

Parameters

x Point

Returns: True If point lies inside

Reimplemented from geom::GeomObject.

Definition at line 294 of file geomObjects.cpp.

                                                    {
 
      if ((x - d_x).length() > d_r)
        return false;
 
      if ((x - d_x).length() < this->inscribedRadius())
        return true;
 
      double a = this->volume();
      double a1 =
              std::abs(geom::triangleArea(x, d_vertices[1], d_vertices[2]));
      double a2 =
              std::abs(geom::triangleArea(d_vertices[0], x, d_vertices[2]));
      double a3 =
              std::abs(geom::triangleArea(d_vertices[0], d_vertices[1], x));
 
      return (a1 + a2 + a3 <= a * (1.0 + 1.0e-10));
    }

References d_r, d_vertices, d_x, inscribedRadius(), geom::triangleArea(), and volume().

Referenced by doesIntersect(), isInside(), isOutside(), and isOutside().

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◆ isNear() [1/2]

bool geom::Triangle::isNear	(	const std::pair< util::Point, util::Point > &	box,
		const double &	tol
	)		const

overridevirtual

Checks if box is within given distance of this object.

Parameters

box	Box
tol	Tolerance used in checking the nearness

Returns: True True if box is inside within the tol distance

Reimplemented from geom::GeomObject.

Definition at line 381 of file geomObjects.cpp.

                                     {
 
      return geom::areBoxesNear(this->box(), box, tol, 2);
    }

References geom::areBoxesNear(), and box().

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◆ isNear() [2/2]

bool geom::Triangle::isNear	(	const util::Point &	x,
		const double &	tol
	)		const

overridevirtual

Checks if point is within given distance of this object.

Parameters

x	Point
tol	Tolerance used in checking the nearness

Returns: True True if within the tol distance

Reimplemented from geom::GeomObject.

Definition at line 317 of file geomObjects.cpp.

                                                                   {
 
      // get a bigger box containing this object
      auto bbox = box(tol);
 
      return geom::isPointInsideBox(x, 2, bbox);
    }

References box(), and geom::isPointInsideBox().

Referenced by isNearBoundary().

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◆ isNearBoundary()

bool geom::Triangle::isNearBoundary	(	const util::Point &	x,
		const double &	tol,
		const bool &	within
	)		const

overridevirtual

cons

Reimplemented from geom::GeomObject.

Definition at line 326 of file geomObjects.cpp.

                                                                 {
 
      // check if particle is inside the object
      if (!isNear(x, within ? 0. : tol))
        return false;
 
      double a = this->volume();
      double l = 0.5 * std::sqrt(a);
 
      double a1 =
              std::abs(geom::triangleArea(x, d_vertices[1], d_vertices[2]));
      if (a1 < tol * l)
        return true;
 
      double a2 =
              std::abs(geom::triangleArea(d_vertices[0], x, d_vertices[2]));
      if (a2 < tol * l)
        return true;
 
      double a3 =
              std::abs(geom::triangleArea(d_vertices[0], d_vertices[1], x));
      if (a3 < tol * l)
        return true;
 
      return false;
    }

References d_vertices, isNear(), geom::triangleArea(), and volume().

Referenced by doesIntersect().

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◆ isOutside() [1/2]

bool geom::Triangle::isOutside ( const std::pair< util::Point, util::Point > & box ) const

overridevirtual

Checks if box is outside of the object.

Parameters

box Box

Returns: True True if box lies outside

Reimplemented from geom::GeomObject.

Definition at line 370 of file geomObjects.cpp.

                                                            {
 
      bool intersect = false;
      for (auto p: geom::getCornerPoints(2, box))
        if (!intersect)
          intersect = this->isInside(p);
 
      return !intersect;
    }

References box(), geom::getCornerPoints(), and isInside().

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◆ isOutside() [2/2]

bool geom::Triangle::isOutside ( const util::Point & x ) const

overridevirtual

Checks if point is outside of this object.

Parameters

x Point

Returns: True If point lies outside

Reimplemented from geom::GeomObject.

Definition at line 313 of file geomObjects.cpp.

                                                     {
      return !isInside(x);
    }

References isInside().

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◆ operator=()

Triangle & geom::Triangle::operator= ( const Triangle & other )

inline

Assignment operator.

Parameters

other Object to copy from

Returns: Reference to this object

Definition at line 866 of file geomObjects.h.

                                               {
      if (this != &other) {
        // Copy base class members
        d_tags = other.d_tags;
        
        // Copy member variables
        d_r = other.d_r;
        d_a = other.d_a;
        d_x = other.d_x;
        d_vertices = other.d_vertices;
      }
      return *this;
    }

References d_a, d_r, geom::GeomObject::d_tags, d_vertices, and d_x.

◆ print() [1/2]

void geom::Triangle::print ( ) const

inlineoverridevirtual

Prints the information about the object.

Reimplemented from geom::GeomObject.

Definition at line 1011 of file geomObjects.h.

1011{ print(0, 0); };

geom::Triangle::print

void print() const override

Prints the information about the object.

Definition geomObjects.h:1011

References print().

Referenced by print().

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◆ print() [2/2]

void geom::Triangle::print	(	int	nt,
		int	lvl
	)		const

inlineoverridevirtual

Prints the information about the object.

Parameters

nt	Number of tabs to append before printing
lvl	Information level (higher means more information)

Reimplemented from geom::GeomObject.

Definition at line 1004 of file geomObjects.h.

                                               {
      std::cout << printStr(nt, lvl);
    };

References printStr().

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◆ printStr()

std::string geom::Triangle::printStr	(	int	nt,
		int	lvl
	)		const

overridevirtual

Returns the string containing printable information about the object.

Parameters

nt	Number of tabs to append before printing
lvl	Information level (higher means more information)

Returns: string String containing printable information about the object

Reimplemented from geom::GeomObject.

Definition at line 399 of file geomObjects.cpp.

                                                      {
 
      auto tabS = util::io::getTabS(nt);
 
      std::ostringstream oss;
 
      oss << tabS << "------- Triangle --------" << std::endl << std::endl;
      oss << tabS << "Name = " << d_name << std::endl;
      oss << tabS << "Center = " << d_x.printStr(0, lvl) << std::endl;
      oss << tabS << "Radius = " << d_r << std::endl;
      oss << tabS << "Vertices = " << util::io::printStr(d_vertices)
          << std::endl;
      oss << std::endl;
 
      if (lvl == 0)
        oss << std::endl;
 
      return oss.str();
    }

References geom::GeomObject::d_name, d_r, d_vertices, d_x, util::io::getTabS(), util::io::printStr(), and util::Point::printStr().

Referenced by print().

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◆ transform()

void geom::Triangle::transform	(	const util::Point &	translation,
		const double &	scale,
		const double &	angle,
		const util::Point &	axis,
		const util::Point *	rotationPoint
	)

inlineoverridevirtual

Similarity about pivot \(\mathbf p\) (default: old center d_x), then rigid displacement \(\mathbf t\) = translation: \(\mathbf y = \mathbf p + s\,\mathbf R(\mathbf x-\mathbf p) + \mathbf t\). When \(\theta=0\) and \(s=1\), \(\mathbf y = \mathbf x + \mathbf t\) for every point and the center.

Parameters

translation	Rigid translation vector \(\mathbf t\) (added after rotate+scale about \(\mathbf p\))
scale	Uniform scale factor
angle	Rotation angle (radians)
axis	Axis of rotation
rotationPoint	If non-null, use as \(\mathbf p\); if null, use old `d_x` as pivot.

Reimplemented from geom::GeomObject.

Definition at line 880 of file geomObjects.h.

                                                                                                       {
      // Scale the radius
      d_r *= scale;
 
      const util::Point c0 = d_x;
      for (auto &v : d_vertices) {
        v = mapSimilarity(v, c0, translation, scale, angle, axis, rotationPoint);
      }
      d_x = mapSimilarity(c0, c0, translation, scale, angle, axis, rotationPoint);
      d_a = util::rotate(d_a, angle, axis);
    }

References d_a, d_r, d_vertices, d_x, geom::mapSimilarity(), and util::rotate().

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◆ volume()

double geom::Triangle::volume ( ) const

overridevirtual

Computes the volume (area in 2d, length in 1d) of object.

Returns: Volume Volume of object

Reimplemented from geom::GeomObject.

Definition at line 255 of file geomObjects.cpp.

                                  {
      // 2D area of the stored triangle (works for equilateral and vertex-defined).
      return std::abs(geom::triangleArea(d_vertices[0], d_vertices[1], d_vertices[2]));
    }

References d_vertices, and geom::triangleArea().

Referenced by isInside(), and isNearBoundary().

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Field Documentation

◆ d_a

util::Point geom::Triangle::d_a

Axis: defined as the vector pointing from center to the first vertex v2 +.

                           o           +
                           x            v1

                   +
                   v3

Axis is a vector from x to v1

Definition at line 784 of file geomObjects.h.

Referenced by operator=(), transform(), and Triangle().

◆ d_r

double geom::Triangle::d_r

Distance between center and the farthest vertex of triangle.

Definition at line 768 of file geomObjects.h.

Referenced by boundingRadius(), inscribedRadius(), isInside(), operator=(), printStr(), transform(), and Triangle().

◆ d_vertices

std::vector<util::Point> geom::Triangle::d_vertices

Vertices.

Definition at line 762 of file geomObjects.h.

Referenced by box(), isInside(), isNearBoundary(), operator=(), printStr(), transform(), Triangle(), and volume().

◆ d_x

util::Point geom::Triangle::d_x

Center.

Definition at line 765 of file geomObjects.h.

Referenced by center(), isInside(), operator=(), printStr(), transform(), and Triangle().

The documentation for this class was generated from the following files:

/home/user/project/src/geom/geomObjects.h
/home/user/project/src/geom/geomObjects.cpp

Public Member Functions

Data Fields

Detailed Description

Constructor & Destructor Documentation

◆ Triangle() [1/4]

◆ Triangle() [2/4]

◆ Triangle() [3/4]

◆ Triangle() [4/4]

Member Function Documentation

◆ boundingRadius()

◆ box() [1/2]

◆ box() [2/2]

◆ center()

◆ doesIntersect() [1/2]

◆ doesIntersect() [2/2]

◆ inscribedRadius()

◆ isInside() [1/2]

◆ isInside() [2/2]

◆ isNear() [1/2]

◆ isNear() [2/2]

◆ isNearBoundary()

◆ isOutside() [1/2]

◆ isOutside() [2/2]

◆ operator=()

◆ print() [1/2]

◆ print() [2/2]

◆ printStr()

◆ transform()

◆ volume()

Field Documentation

◆ d_a

◆ d_r

◆ d_vertices

◆ d_x