#include <geomObjects.h>

Inheritance diagram for geom::Hexagon:

Collaboration diagram for geom::Hexagon:

Public Member Functions
	Hexagon ()
	Constructor.

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

	Hexagon (const Hexagon &other)
	Copy constructor.

Hexagon &	operator= (const Hexagon &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 robustly
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 hexagon.

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

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 Hexagon.

Definition at line 1509 of file geomObjects.h.

Constructor & Destructor Documentation

◆ Hexagon() [1/3]

geom::Hexagon::Hexagon ( )

inline

Constructor.

Definition at line 1539 of file geomObjects.h.

      : GeomObject("hexagon", ""),
        d_r(0.),
        d_a(util::Point(1., 0., 0.)),
        d_x(util::Point()),
        d_vertices(std::vector<util::Point>(6, util::Point())) {
    };

◆ Hexagon() [2/3]

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

inline

Constructor.

Parameters

r	Radius (distance between center and one of the vertices)
x	Center point
a	Axis vector that will be rotated and scaled by r to obtain coordinates of vertices of hexagon
description	Description of object (e.g., further classification or any tag)

Definition at line 1555 of file geomObjects.h.

      : GeomObject("hexagon", ""),
        d_r(r),
        d_a(a),
        d_x(x),
        d_vertices(std::vector<util::Point>(6, util::Point())) {
      // generate vertices
      auto rotate_axis = util::Point(0., 0., 1.); // z-axis
      for (int i = 0; i < 6; i++) {
        d_vertices[i] = d_x + d_r * util::rotate(
                          d_a, i * M_PI / 3., rotate_axis);
      }
    };

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

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◆ Hexagon() [3/3]

geom::Hexagon::Hexagon ( const Hexagon & other )

inline

Copy constructor.

Parameters

other Object to copy from

Definition at line 1575 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::Hexagon::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 796 of file geomObjects.cpp.

                                         {
 
      return d_r;
    }

References d_r.

◆ box() [1/2]

std::pair< util::Point, util::Point > geom::Hexagon::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 778 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::Hexagon::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 783 of file geomObjects.cpp.

                                                                                        {
 
      auto p1 = d_x - util::Point(d_r + tol, d_r + tol, d_x[2] + tol);
      auto p2 = d_x + util::Point(d_r + tol, d_r + tol, d_x[2] + tol);
      return {p1, p2};
    }

References d_r, and d_x.

◆ center()

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

overridevirtual

Computes the center of object.

Returns: Point Coordinates of center

Reimplemented from geom::GeomObject.

Definition at line 774 of file geomObjects.cpp.

                                    {
      return d_x;
    }

References d_x.

◆ doesIntersect() [1/2]

bool geom::Hexagon::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 871 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::Hexagon::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 838 of file geomObjects.cpp.

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

References isNearBoundary().

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◆ inscribedRadius()

double geom::Hexagon::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 791 of file geomObjects.cpp.

                                          {
 
      return d_r * 0.5 * std::sqrt(3.);
    }

References d_r.

Referenced by isInside(), isNearBoundary(), and volume().

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◆ isInside() [1/2]

bool geom::Hexagon::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 843 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::Hexagon::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 801 of file geomObjects.cpp.

                                                   {
 
      if ((x - d_x).length() > d_r)
        return false;
 
      if ((x - d_x).length() < inscribedRadius())
        return true;
 
      return false;
    }

References d_r, d_x, and inscribedRadius().

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

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◆ isNear() [1/2]

bool geom::Hexagon::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 864 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::Hexagon::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 816 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().

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◆ isNearBoundary()

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

overridevirtual

cons

Reimplemented from geom::GeomObject.

Definition at line 825 of file geomObjects.cpp.

                                                                {
 
      if ((x - d_x).length() > d_r + tol)
        return false;
 
      if ((x - d_x).length() < inscribedRadius() - tol)
        return false;
 
      return true;
    }

References d_r, d_x, and inscribedRadius().

Referenced by doesIntersect().

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◆ isOutside() [1/2]

bool geom::Hexagon::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 853 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::Hexagon::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 812 of file geomObjects.cpp.

                                                    {
      return !isInside(x);
    }

References isInside().

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◆ operator=()

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

inline

Assignment operator.

Parameters

other Object to copy from

Returns: Reference to this object

Definition at line 1589 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::Hexagon::print ( ) const

inlineoverridevirtual

Prints the information about the object.

Reimplemented from geom::GeomObject.

Definition at line 1735 of file geomObjects.h.

1735{ print(0, 0); };

geom::Hexagon::print

void print() const override

Prints the information about the object.

Definition geomObjects.h:1735

References print().

Referenced by print().

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◆ print() [2/2]

void geom::Hexagon::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 1728 of file geomObjects.h.

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

References printStr().

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◆ printStr()

std::string geom::Hexagon::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 882 of file geomObjects.cpp.

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

References d_a, 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::Hexagon::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 1603 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::Hexagon::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 768 of file geomObjects.cpp.

                                 {
      // https://en.wikipedia.org/wiki/Hexagon
      double r_small = this->inscribedRadius();
      return 2. * std::sqrt(3.) * r_small * r_small;
    }

References inscribedRadius().

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Field Documentation

◆ d_a

util::Point geom::Hexagon::d_a

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

                   +              +


               +           o           +
                           x            v1

                   +              +

Axis is a vector from x to v1

Definition at line 1533 of file geomObjects.h.

Referenced by Hexagon(), operator=(), printStr(), and transform().

◆ d_r

double geom::Hexagon::d_r

Distance between center and the farthest vertex of hexagon.

Definition at line 1518 of file geomObjects.h.

Referenced by boundingRadius(), box(), Hexagon(), inscribedRadius(), isInside(), isNearBoundary(), operator=(), printStr(), and transform().

◆ d_vertices

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

Vertices.

Definition at line 1512 of file geomObjects.h.

Referenced by Hexagon(), operator=(), printStr(), and transform().

◆ d_x

util::Point geom::Hexagon::d_x

Center.

Definition at line 1515 of file geomObjects.h.

Referenced by box(), center(), Hexagon(), isInside(), isNearBoundary(), operator=(), printStr(), and transform().

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

◆ Hexagon() [1/3]

◆ Hexagon() [2/3]

◆ Hexagon() [3/3]

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