Ellipsoid: center \(\mathbf c\), semi-axes \(r_1,r_2,r_3\) in a body frame rotated from world by axis–angle \((\hat{\mathbf a},\theta)\) (Rodrigues). Axis-aligned case: \(\theta=0\) (axis ignored). More...

#include <geomObjects.h>

Inheritance diagram for geom::Ellipsoid:

Collaboration diagram for geom::Ellipsoid:

Public Member Functions
	Ellipsoid ()

	Ellipsoid (double a, double b, double c, util::Point x=util::Point(), std::string description="")

	Ellipsoid (double a, double b, double c, double theta, util::Point x, util::Point axis, std::string description="")
	General orientation: same semi-axes, rotation \(\theta\) about unit axis (normalized internally; zero axis with \(\theta\neq 0\) is invalid).

	Ellipsoid (const Ellipsoid &other)

Ellipsoid &	operator= (const Ellipsoid &other)

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.

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
	Checks if point is within given distance of this object.

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

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.

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.

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
util::Point	d_x

double	d_a

double	d_b

double	d_c

util::Point	d_axis
	Unit rotation axis (axis–angle); default (0,0,1) when \(\theta=0\).

double	d_theta
	Rotation angle (radians) about d_axis.

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

Ellipsoid: center \(\mathbf c\), semi-axes \(r_1,r_2,r_3\) in a body frame rotated from world by axis–angle \((\hat{\mathbf a},\theta)\) (Rodrigues). Axis-aligned case: \(\theta=0\) (axis ignored).

Definition at line 3031 of file geomObjects.h.

Constructor & Destructor Documentation

◆ Ellipsoid() [1/4]

geom::Ellipsoid::Ellipsoid ( )

inline

Definition at line 3043 of file geomObjects.h.

      : GeomObject("ellipsoid", ""),
        d_x(util::Point()),
        d_a(0.),
        d_b(0.),
        d_c(0.),
        d_axis(0., 0., 1.),
        d_theta(0.) {};

◆ Ellipsoid() [2/4]

geom::Ellipsoid::Ellipsoid	(	double	a,
		double	b,
		double	c,
		util::Point	x = `util::Point()`,
		std::string	description = `""`
	)

inline

Parameters

a	First semi-axis (body frame)
b	Second semi-axis (body frame)
c	Third semi-axis (body frame)

Definition at line 3057 of file geomObjects.h.

      : GeomObject("ellipsoid", description),
        d_x(x),
        d_a(a),
        d_b(b),
        d_c(c),
        d_axis(0., 0., 1.),
        d_theta(0.) {};

◆ Ellipsoid() [3/4]

geom::Ellipsoid::Ellipsoid	(	double	a,
		double	b,
		double	c,
		double	theta,
		util::Point	x,
		util::Point	axis,
		std::string	description = `""`
	)

inline

General orientation: same semi-axes, rotation \(\theta\) about unit axis (normalized internally; zero axis with \(\theta\neq 0\) is invalid).

Definition at line 3071 of file geomObjects.h.

      : GeomObject("ellipsoid", description),
        d_x(x),
        d_a(a),
        d_b(b),
        d_c(c),
        d_axis(axis),
        d_theta(theta) {
      
      if (std::abs(theta) > 1.0e-12 and axis.length() > 1.0e-12) {
        d_axis = axis / axis.length();
      }
    }

References d_axis, and util::Point::length().

Here is the call graph for this function:

◆ Ellipsoid() [4/4]

geom::Ellipsoid::Ellipsoid ( const Ellipsoid & other )

inline

Definition at line 3086 of file geomObjects.h.

      : GeomObject(other.d_name, other.d_description),
        d_x(other.d_x),
        d_a(other.d_a),
        d_b(other.d_b),
        d_c(other.d_c),
        d_axis(other.d_axis),
        d_theta(other.d_theta) {
      d_tags = other.d_tags;
    }

References geom::GeomObject::d_tags.

Member Function Documentation

◆ boundingRadius()

double geom::Ellipsoid::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 2151 of file geomObjects.cpp.

                                           {
      double m = d_a;
      if (d_b > m)
        m = d_b;
      if (d_c > m)
        m = d_c;
      return m;
    }

References d_a, d_b, and d_c.

◆ box() [1/2]

std::pair< util::Point, util::Point > geom::Ellipsoid::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 2118 of file geomObjects.cpp.

                                                       {
      return box(0.);
    }

References box().

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

Here is the call graph for this function:

Here is the caller graph for this function:

◆ box() [2/2]

std::pair< util::Point, util::Point > geom::Ellipsoid::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 2122 of file geomObjects.cpp.

                                                                        {
 
      const double ra = d_a + tol;
      const double rb = d_b + tol;
      const double rc = d_c + tol;
 
      double R[9];
      ellipsoidRotationMatrix(*this, R);
 
      const double hx =
              std::sqrt((ra * R[0]) * (ra * R[0]) + (rb * R[3]) * (rb * R[3]) + (rc * R[6]) * (rc * R[6]));
      const double hy =
              std::sqrt((ra * R[1]) * (ra * R[1]) + (rb * R[4]) * (rb * R[4]) + (rc * R[7]) * (rc * R[7]));
      const double hz =
              std::sqrt((ra * R[2]) * (ra * R[2]) + (rb * R[5]) * (rb * R[5]) + (rc * R[8]) * (rc * R[8]));
 
      return {util::Point(d_x.d_x - hx, d_x.d_y - hy, d_x.d_z - hz),
              util::Point(d_x.d_x + hx, d_x.d_y + hy, d_x.d_z + hz)};
    }

References d_a, d_b, d_c, d_x, util::Point::d_x, util::Point::d_y, util::Point::d_z, and geom::ellipsoidRotationMatrix().

Here is the call graph for this function:

◆ center()

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

overridevirtual

Computes the center of object.

Returns: Point Coordinates of center

Reimplemented from geom::GeomObject.

Definition at line 2114 of file geomObjects.cpp.

                                      {
      return d_x;
    }

References d_x.

◆ doesIntersect() [1/2]

bool geom::Ellipsoid::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 2222 of file geomObjects.cpp.

                                                                                {
 
      for (auto p : geom::getCornerPoints(3, box))
        if (this->isInside(p))
          return true;
 
      return false;
    }

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

Here is the call graph for this function:

◆ doesIntersect() [2/2]

bool geom::Ellipsoid::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 2194 of file geomObjects.cpp.

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

References isNearBoundary().

Here is the call graph for this function:

◆ inscribedRadius()

double geom::Ellipsoid::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 2142 of file geomObjects.cpp.

                                            {
      double m = d_a;
      if (d_b < m)
        m = d_b;
      if (d_c < m)
        m = d_c;
      return m;
    }

References d_a, d_b, and d_c.

◆ isInside() [1/2]

bool geom::Ellipsoid::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 2198 of file geomObjects.cpp.

                                                                           {
 
      for (auto p : geom::getCornerPoints(3, box))
        if (!this->isInside(p))
          return false;
 
      return true;
    }

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

Here is the call graph for this function:

◆ isInside() [2/2]

bool geom::Ellipsoid::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 2160 of file geomObjects.cpp.

                                                     {
      if (d_a <= 0. || d_b <= 0. || d_c <= 0.)
        return false;
      double R[9];
      return util::isLess(ellipsoidMetric(*this, x, R, d_a, d_b, d_c), 1. + 1.0E-12);
    }

References d_a, d_b, d_c, and util::isLess().

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

Here is the call graph for this function:

Here is the caller graph for this function:

◆ isNear() [1/2]

bool geom::Ellipsoid::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 2217 of file geomObjects.cpp.

                                                                                            {
 
      return geom::areBoxesNear(this->box(), box, tol, 3);
    }

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

Here is the call graph for this function:

◆ isNear() [2/2]

bool geom::Ellipsoid::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 2171 of file geomObjects.cpp.

                                                                      {
      if (d_a + tol <= 0. || d_b + tol <= 0. || d_c + tol <= 0.)
        return false;
      double R[9];
      return util::isLess(ellipsoidMetric(*this, x, R, d_a + tol, d_b + tol, d_c + tol),
                          1. + 1.0E-12);
    }

References d_a, d_b, d_c, and util::isLess().

Referenced by isNearBoundary().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ isNearBoundary()

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

overridevirtual

Checks if point is within given distance of this object.

Parameters

x	Point
tol	Tolerance used in checking the nearness
within	Check if the point is within (inside) the object

Returns: True True if it is near within tol distance

Reimplemented from geom::GeomObject.

Definition at line 2179 of file geomObjects.cpp.

                                                                                                  {
 
      const bool inOuter = isNear(x, tol);
      Ellipsoid shrunk = *this;
      shrunk.d_a = d_a - tol;
      shrunk.d_b = d_b - tol;
      shrunk.d_c = d_c - tol;
      if (shrunk.d_a <= 0. || shrunk.d_b <= 0. || shrunk.d_c <= 0.)
        return inOuter;
      const bool inInner = shrunk.isInside(x);
      if (within)
        return inOuter && !inInner;
      return inOuter;
    }

References d_a, d_b, d_c, isInside(), and isNear().

Referenced by doesIntersect().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ isOutside() [1/2]

bool geom::Ellipsoid::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 2207 of file geomObjects.cpp.

                                                                            {
 
      bool intersect = false;
      for (auto p : geom::getCornerPoints(3, box))
        if (!intersect)
          intersect = this->isInside(p);
 
      return !intersect;
    }

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

Here is the call graph for this function:

◆ isOutside() [2/2]

bool geom::Ellipsoid::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 2167 of file geomObjects.cpp.

                                                      {
      return !isInside(x);
    }

References isInside().

Here is the call graph for this function:

◆ operator=()

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

inline

Definition at line 3097 of file geomObjects.h.

                                                 {
      if (this != &other) {
        d_tags = other.d_tags;
        d_x = other.d_x;
        d_a = other.d_a;
        d_b = other.d_b;
        d_c = other.d_c;
        d_axis = other.d_axis;
        d_theta = other.d_theta;
      }
      return *this;
    }

References d_a, d_axis, d_b, d_c, geom::GeomObject::d_tags, d_theta, and d_x.

◆ print() [1/2]

void geom::Ellipsoid::print ( ) const

inlineoverridevirtual

Prints the information about the object.

Reimplemented from geom::GeomObject.

Definition at line 3133 of file geomObjects.h.

3133{ print(0, 0); };

geom::Ellipsoid::print

void print() const override

Prints the information about the object.

Definition geomObjects.h:3133

References print().

Referenced by print().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ print() [2/2]

void geom::Ellipsoid::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 3132 of file geomObjects.h.

3132{ std::cout << printStr(nt, lvl); };

geom::Ellipsoid::printStr

std::string printStr(int nt, int lvl) const override

Returns the string containing printable information about the object.

Definition geomObjects.cpp:2231

References printStr().

Here is the call graph for this function:

◆ printStr()

std::string geom::Ellipsoid::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 2231 of file geomObjects.cpp.

                                                       {
 
      auto tabS = util::io::getTabS(nt);
 
      std::ostringstream oss;
 
      oss << tabS << "------- Ellipsoid --------" << std::endl << std::endl;
      oss << tabS << "Name = " << d_name << std::endl;
      oss << tabS << "Center = " << d_x.printStr(0, lvl) << std::endl;
      oss << tabS << "Semi-axes a, b, c = " << d_a << ", " << d_b << ", " << d_c << std::endl;
      if (std::abs(d_theta) > 1.0e-14)
        oss << tabS << "Rotation axis (unit) = " << d_axis.printStr(0, lvl) << ", theta = " << d_theta
            << std::endl;
 
      if (lvl > 0)
        oss << tabS << "Bounding box: "
            << util::io::printBoxStr(box(0.), nt + 1);
 
      if (lvl == 0)
        oss << std::endl;
 
      return oss.str();
    }

References box(), d_a, d_axis, d_b, d_c, geom::GeomObject::d_name, d_theta, d_x, util::io::getTabS(), util::io::printBoxStr(), and util::Point::printStr().

Referenced by print().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ transform()

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

overridevirtual

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 2090 of file geomObjects.cpp.

                                                                                     {
      const util::Point c0 = d_x;
      d_a *= scale;
      d_b *= scale;
      d_c *= scale;
 
      double ow, ox, oy, oz;
      axisAngleToQuatSafe(d_axis, d_theta, ow, ox, oy, oz);
 
      double rw, rx, ry, rz;
      axisAngleToQuatSafe(axis, angle, rw, rx, ry, rz);
 
      double nw, nx, ny, nz;
      quatMul(rw, rx, ry, rz, ow, ox, oy, oz, nw, nx, ny, nz);
 
      quatToAxisAngle(nw, nx, ny, nz, d_axis, d_theta);
      d_x = mapSimilarity(c0, c0, translation, scale, angle, axis, rotationPoint);
    }

References d_a, d_axis, d_b, d_c, d_theta, d_x, and geom::mapSimilarity().

Here is the call graph for this function:

◆ volume()

double geom::Ellipsoid::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 2110 of file geomObjects.cpp.

                                   {
      return (4. / 3.) * M_PI * d_a * d_b * d_c;
    }

References d_a, d_b, and d_c.

Field Documentation

◆ d_a

double geom::Ellipsoid::d_a

Definition at line 3034 of file geomObjects.h.

Referenced by boundingRadius(), box(), mesh_gen::buildEllipsoidOcc(), inscribedRadius(), isInside(), isNear(), isNearBoundary(), operator=(), printStr(), transform(), and volume().

◆ d_axis

util::Point geom::Ellipsoid::d_axis

Unit rotation axis (axis–angle); default (0,0,1) when \(\theta=0\).

Definition at line 3038 of file geomObjects.h.

Referenced by Ellipsoid(), geom::ellipsoidRotationMatrix(), operator=(), printStr(), and transform().

◆ d_b

double geom::Ellipsoid::d_b

Definition at line 3035 of file geomObjects.h.

Referenced by boundingRadius(), box(), mesh_gen::buildEllipsoidOcc(), inscribedRadius(), isInside(), isNear(), isNearBoundary(), operator=(), printStr(), transform(), and volume().

◆ d_c

double geom::Ellipsoid::d_c

Definition at line 3036 of file geomObjects.h.

Referenced by boundingRadius(), box(), mesh_gen::buildEllipsoidOcc(), inscribedRadius(), isInside(), isNear(), isNearBoundary(), operator=(), printStr(), transform(), and volume().

◆ d_theta

double geom::Ellipsoid::d_theta

Rotation angle (radians) about d_axis.

Definition at line 3040 of file geomObjects.h.

Referenced by geom::ellipsoidRotationMatrix(), operator=(), printStr(), and transform().

◆ d_x

util::Point geom::Ellipsoid::d_x

Definition at line 3033 of file geomObjects.h.

Referenced by box(), mesh_gen::buildEllipsoidOcc(), center(), geom::anonymous_namespace{geomObjects.cpp}::ellipsoidMetric(), 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

◆ Ellipsoid() [1/4]

◆ Ellipsoid() [2/4]

◆ Ellipsoid() [3/4]

◆ Ellipsoid() [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_axis

◆ d_b

◆ d_c

◆ d_theta

◆ d_x