SphericalCap Class Reference

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

#include <StelSphereGeometry.hpp>

List of all members.

Public Member Functions
	SphericalCap ()
	SphericalCap (double x, double y, double z)
	SphericalCap (const Vec3d &an, double ar)
	SphericalCap (const SphericalCap &other)
virtual SphericalRegionType	getType () const
virtual OctahedronPolygon	getOctahedronPolygon () const
virtual double	getArea () const
virtual bool	isEmpty () const
virtual Vec3d	getPointInside () const
virtual SphericalCap	getBoundingCap () const
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
virtual bool	intersects (const AllSkySphericalRegion &) const
virtual QVariantList	toQVariant () const
virtual void	serialize (QDataStream &out) const
double	getRadius () const
bool	intersectsHalfSpace (double hn0, double hn1, double hn2) const
bool	clipGreatCircle (Vec3d &v1, Vec3d &v2) const
bool	operator== (const SphericalCap &other) const
QVector< Vec3d >	getClosedOutlineContour () const
bool	intersectsConvexContour (const Vec3d *vertice, int nbVertice) const
bool	containsTriangle (const Vec3d *vertice) const
bool	intersectsTriangle (const Vec3d *vertice) const
Static Public Member Functions
static SphericalRegionP	deserialize (QDataStream &in)
static double	relativeAreaOverlap (const SphericalCap &c1, const SphericalCap &c2)
static double	relativeDiameterOverlap (const SphericalCap &c1, const SphericalCap &c2)
static bool	intersectionPoints (const SphericalCap &h1, const SphericalCap &h2, Vec3d &p1, Vec3d &p2)
Public Attributes
Vec3d	n
double	d

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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.

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Constructor & Destructor Documentation

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.

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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.

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.

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 [inline, virtual]

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.

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.

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.