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.

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

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

	SphericalCap (const SphericalCap &other)
	Copy constructor.

SphericalCap &	operator= (const SphericalCap &other)

SphericalRegionType	getType () const override

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

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

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

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

SphericalCap	getBoundingCap () const override
	Return itself.

bool	contains (const Vec3d &v) const override

virtual bool	contains (const Vec3f &v) const

bool	contains (const SphericalConvexPolygon &r) const override

bool	contains (const SphericalCap &h) const override

bool	contains (const AllSkySphericalRegion &) const override

bool	intersects (const SphericalPolygon &r) const override

bool	intersects (const SphericalConvexPolygon &r) const override

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

bool	intersects (const AllSkySphericalRegion &) const override

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

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

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

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.

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

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

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

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

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

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.

virtual StelVertexArray	getFillVertexArray (const Vec3d &observerVelocityForAberration)
	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 StelVertexArray	getOutlineVertexArray (Vec3d observerVelocityForAberration)
	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	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.

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)

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)

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...

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

double	d
	The cos of cone radius.

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.

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.

Constructor & Destructor Documentation

◆ SphericalCap()

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.

Member Function Documentation

◆ clipGreatCircle()

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.

◆ getOctahedronPolygon()

OctahedronPolygon SphericalCap::getOctahedronPolygon ( ) const

overridevirtual

Return the octahedron contour representation of the polygon.

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

Implements SphericalRegion.

◆ intersectionPoints()

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.

◆ intersects()

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

inlineoverridevirtual

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.

◆ intersectsHalfSpace()

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.

◆ toQVariant()

QVariantList SphericalCap::toQVariant ( ) const

overridevirtual

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)