A SphericalCap is defined by a direction and an aperture. More...

#include <StelSphereGeometry.hpp>

Public Member Functions
	SphericalCap ()
	Construct a SphericalCap with a 90 deg aperture and an undefined direction. More...

	SphericalCap (double x, double y, double z)
	Construct a SphericalCap from its direction and assumes a 90 deg aperture. More...

	SphericalCap (const Vec3d &an, double ar)
	Construct a SphericalCap from its direction and aperture. More...

	SphericalCap (const SphericalCap &other)
	Copy constructor. More...

virtual SphericalRegionType	getType () const

virtual OctahedronPolygon	getOctahedronPolygon () const
	Return the octahedron contour representation of the polygon. More...

virtual double	getArea () const
	Get the area of the intersection of the halfspace on the sphere in steradian. More...

virtual bool	isEmpty () const
	Return true if the region is empty. More...

virtual Vec3d	getPointInside () const
	Return a point located inside the SphericalCap. More...

virtual SphericalCap	getBoundingCap () const
	Return itself. More...

virtual bool	contains (const Vec3d &v) const

virtual bool	contains (const Vec3f &v) const

virtual bool	contains (const SphericalConvexPolygon &r) const

virtual bool	contains (const SphericalCap &h) const

virtual bool	contains (const AllSkySphericalRegion &) const

virtual bool	intersects (const SphericalPolygon &r) const

virtual bool	intersects (const SphericalConvexPolygon &r) const

virtual bool	intersects (const SphericalCap &h) const
	Returns whether a SphericalCap intersects with this one. More...

virtual bool	intersects (const AllSkySphericalRegion &) const

virtual QVariantList	toQVariant () const
	Serialize the region into a QVariant map matching the JSON format. More...

virtual void	serialize (QDataStream &out) const
	Serialize the region. This method must allow as fast as possible serialization and work with deserialize(). More...

double	getRadius () const
	Return the radiusof the cap in radian. More...

bool	intersectsHalfSpace (double hn0, double hn1, double hn2) const
	Returns whether a HalfSpace (like a SphericalCap with d=0) intersects with this SphericalCap. More...

bool	clipGreatCircle (Vec3d &v1, Vec3d &v2) const
	Clip the passed great circle connecting points v1 and v2. More...

bool	operator== (const SphericalCap &other) const
	Comparison operator. More...

QVector< Vec3d >	getClosedOutlineContour () const
	Return the list of closed contours defining the polygon boundaries. More...

bool	intersectsConvexContour (const Vec3d *vertice, int nbVertice) const
	Return whether the cap intersect with a convex contour defined by nbVertice. More...

bool	containsTriangle (const Vec3d *vertice) const
	Return whether the cap contains the passed triangle. More...

bool	intersectsTriangle (const Vec3d *vertice) const
	Return whether the cap intersect with the passed triangle. More...

Public Member Functions inherited from SphericalRegion
virtual QVector< SphericalCap >	getBoundingSphericalCaps () const
	Return the list of SphericalCap bounding the ConvexPolygon. More...

virtual SphericalRegionP	getEnlarged (double margin) const
	Return an enlarged version of this SphericalRegion so that any point distant of more than the given margin now lays within the region. More...

virtual StelVertexArray	getFillVertexArray () const
	Return an openGL compatible array to be displayed using vertex arrays. More...

virtual StelVertexArray	getOutlineVertexArray () const
	Get the outline of the contours defining the SphericalPolygon. More...

virtual QVector< QVector< Vec3d > >	getSimplifiedContours () const
	Get the contours defining the SphericalPolygon when combined using a positive winding rule. More...

QByteArray	toJSON () const
	Output a JSON string representing the polygon. More...

bool	contains (const SphericalRegion *r) const
	Returns whether a SphericalRegion is contained into this region. More...

bool	contains (const SphericalRegionP r) const

virtual bool	contains (const SphericalPolygon &r) const

virtual bool	contains (const SphericalPoint &r) const

bool	contains (const EmptySphericalRegion &) const

bool	intersects (const SphericalRegion *r) const
	Returns whether a SphericalRegion intersects with this region. More...

bool	intersects (const SphericalRegionP r) const

bool	intersects (const Vec3d &p) const

virtual bool	intersects (const SphericalPoint &r) const

bool	intersects (const EmptySphericalRegion &) const

SphericalRegionP	getIntersection (const SphericalRegion *r) const
	Return a new SphericalRegion consisting of the intersection of this and the given region. More...

SphericalRegionP	getIntersection (const SphericalRegionP r) const

virtual SphericalRegionP	getIntersection (const SphericalPolygon &r) const

virtual SphericalRegionP	getIntersection (const SphericalConvexPolygon &r) const

virtual SphericalRegionP	getIntersection (const SphericalCap &r) const

virtual SphericalRegionP	getIntersection (const SphericalPoint &r) const

virtual SphericalRegionP	getIntersection (const AllSkySphericalRegion &r) const

SphericalRegionP	getIntersection (const EmptySphericalRegion &r) const

SphericalRegionP	getUnion (const SphericalRegion *r) const
	Return a new SphericalRegion consisting of the union of this and the given region. More...

SphericalRegionP	getUnion (const SphericalRegionP r) const

virtual SphericalRegionP	getUnion (const SphericalPolygon &r) const

virtual SphericalRegionP	getUnion (const SphericalConvexPolygon &r) const

virtual SphericalRegionP	getUnion (const SphericalCap &r) const

virtual SphericalRegionP	getUnion (const SphericalPoint &r) const

SphericalRegionP	getUnion (const AllSkySphericalRegion &r) const

virtual SphericalRegionP	getUnion (const EmptySphericalRegion &r) const

SphericalRegionP	getSubtraction (const SphericalRegion *r) const
	Return a new SphericalRegion consisting of the subtraction of the given region from this. More...

SphericalRegionP	getSubtraction (const SphericalRegionP r) const

virtual SphericalRegionP	getSubtraction (const SphericalPolygon &r) const

virtual SphericalRegionP	getSubtraction (const SphericalConvexPolygon &r) const

virtual SphericalRegionP	getSubtraction (const SphericalCap &r) const

virtual SphericalRegionP	getSubtraction (const SphericalPoint &r) const

SphericalRegionP	getSubtraction (const AllSkySphericalRegion &r) const

virtual SphericalRegionP	getSubtraction (const EmptySphericalRegion &r) const

Static Public Member Functions
static SphericalRegionP	deserialize (QDataStream &in)
	Deserialize the region. This method must allow as fast as possible deserialization. More...

static double	relativeAreaOverlap (const SphericalCap &c1, const SphericalCap &c2)
	Return the relative overlap between the areas of the 2 caps, i.e: min(intersectionArea/c1.area, intersectionArea/c2.area) More...

static double	relativeDiameterOverlap (const SphericalCap &c1, const SphericalCap &c2)
	Return the relative overlap between the diameter of the 2 caps, i.e: min(intersectionDistance/c1.diameter, intersectionDistance/c2.diameter) More...

static bool	intersectionPoints (const SphericalCap &h1, const SphericalCap &h2, Vec3d &p1, Vec3d &p2)
	Compute the intersection of 2 halfspaces on the sphere (usually on 2 points) and return it in p1 and p2. More...

Public Attributes
Vec3d	n
	The direction unit vector. Only if d==0, this vector doesn't need to be unit. More...

double	d
	The cos of cone radius. More...

Additional Inherited Members
Public Types inherited from SphericalRegion
enum	SphericalRegionType { Point = 0, Cap = 1, AllSky = 2, Polygon = 3, ConvexPolygon = 4, Empty = 5, Invalid = 6 }
	define types for all supported regions. More...

Detailed Description

A SphericalCap is defined by a direction and an aperture.

It forms a cone from the center of the Coordinate frame with a radius d. It is a disc on the sphere, a region above a circle on the unit sphere.

Definition at line 271 of file StelSphereGeometry.hpp.

Constructor & Destructor Documentation

SphericalCap::SphericalCap ( )

inline

Construct a SphericalCap with a 90 deg aperture and an undefined direction.

Definition at line 276 of file StelSphereGeometry.hpp.

SphericalCap::SphericalCap	(	double	x,
		double	y,
		double	z
	)

inline

Construct a SphericalCap from its direction and assumes a 90 deg aperture.

Definition at line 279 of file StelSphereGeometry.hpp.

SphericalCap::SphericalCap	(	const Vec3d &	an,
		double	ar
	)

inline

Construct a SphericalCap from its direction and aperture.

Parameters

an	a unit vector indicating the direction.
ar	cosinus of the aperture.

Definition at line 284 of file StelSphereGeometry.hpp.

SphericalCap::SphericalCap ( const SphericalCap & other )

inline

Copy constructor.

Definition at line 297 of file StelSphereGeometry.hpp.

Member Function Documentation

bool SphericalCap::clipGreatCircle	(	Vec3d &	v1,
		Vec3d &	v2
	)		const

Clip the passed great circle connecting points v1 and v2.

Returns: true if the great circle intersects with the cap, false otherwise.

bool SphericalCap::containsTriangle ( const Vec3d * vertice ) const

Return whether the cap contains the passed triangle.

static SphericalRegionP SphericalCap::deserialize ( QDataStream & in )

static

Deserialize the region. This method must allow as fast as possible deserialization.

virtual double SphericalCap::getArea ( ) const

inlinevirtual

Get the area of the intersection of the halfspace on the sphere in steradian.

Reimplemented from SphericalRegion.

Definition at line 303 of file StelSphereGeometry.hpp.

virtual SphericalCap SphericalCap::getBoundingCap ( ) const

inlinevirtual

Return itself.

Reimplemented from SphericalRegion.

Definition at line 312 of file StelSphereGeometry.hpp.

QVector<Vec3d> SphericalCap::getClosedOutlineContour ( ) const

Return the list of closed contours defining the polygon boundaries.

virtual OctahedronPolygon SphericalCap::getOctahedronPolygon ( ) const

virtual

Return the octahedron contour representation of the polygon.

It can be used for safe computation of intersection/union in the general case.

Implements SphericalRegion.

virtual Vec3d SphericalCap::getPointInside ( ) const

inlinevirtual

Return a point located inside the SphericalCap.

Reimplemented from SphericalRegion.

Definition at line 309 of file StelSphereGeometry.hpp.

double SphericalCap::getRadius ( ) const

inline

Return the radiusof the cap in radian.

Definition at line 347 of file StelSphereGeometry.hpp.

static bool SphericalCap::intersectionPoints	(	const SphericalCap &	h1,
		const SphericalCap &	h2,
		Vec3d &	p1,
		Vec3d &	p2
	)

static

Compute the intersection of 2 halfspaces on the sphere (usually on 2 points) and return it in p1 and p2.

If the 2 SphericalCap don't intersect or intersect only at 1 point, false is returned and p1 and p2 are undefined.

virtual bool SphericalCap::intersects ( const SphericalCap & h ) const

inlinevirtual

Returns whether a SphericalCap intersects with this one.

I managed to make it without sqrt or acos, so it is very fast!

See also: http://f4bien.blogspot.com/2009/05/spherical-geometry-optimisations.html for detailed explanations.

Reimplemented from SphericalRegion.

Definition at line 329 of file StelSphereGeometry.hpp.

bool SphericalCap::intersectsConvexContour	(	const Vec3d *	vertice,
		int	nbVertice
	)		const

Return whether the cap intersect with a convex contour defined by nbVertice.

bool SphericalCap::intersectsHalfSpace	(	double	hn0,
		double	hn1,
		double	hn2
	)		const

inline

Returns whether a HalfSpace (like a SphericalCap with d=0) intersects with this SphericalCap.

Parameters

hn0	the x direction of the halfspace.
hn1	the y direction of the halfspace.
hn2	the z direction of the halfspace.

Definition at line 353 of file StelSphereGeometry.hpp.

bool SphericalCap::intersectsTriangle ( const Vec3d * vertice ) const

Return whether the cap intersect with the passed triangle.

virtual bool SphericalCap::isEmpty ( ) const

inlinevirtual

Return true if the region is empty.

Reimplemented from SphericalRegion.

Definition at line 306 of file StelSphereGeometry.hpp.

bool SphericalCap::operator== ( const SphericalCap & other ) const

inline

Comparison operator.

Definition at line 364 of file StelSphereGeometry.hpp.

static double SphericalCap::relativeAreaOverlap	(	const SphericalCap &	c1,
		const SphericalCap &	c2
	)

static

Return the relative overlap between the areas of the 2 caps, i.e: min(intersectionArea/c1.area, intersectionArea/c2.area)

static double SphericalCap::relativeDiameterOverlap	(	const SphericalCap &	c1,
		const SphericalCap &	c2
	)

static

Return the relative overlap between the diameter of the 2 caps, i.e: min(intersectionDistance/c1.diameter, intersectionDistance/c2.diameter)

virtual void SphericalCap::serialize ( QDataStream & out ) const

inlinevirtual

Serialize the region. This method must allow as fast as possible serialization and work with deserialize().

Implements SphericalRegion.

Definition at line 341 of file StelSphereGeometry.hpp.

virtual QVariantList SphericalCap::toQVariant ( ) const

virtual

Serialize the region into a QVariant map matching the JSON format.

The format is ["CAP", [ra, dec], radius], with ra dec in degree in ICRS frame and radius in degree (between 0 and 180 deg)

Implements SphericalRegion.

Member Data Documentation

double SphericalCap::d

The cos of cone radius.

Definition at line 396 of file StelSphereGeometry.hpp.

Vec3d SphericalCap::n

The direction unit vector. Only if d==0, this vector doesn't need to be unit.

Definition at line 394 of file StelSphereGeometry.hpp.

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

StelSphereGeometry.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation