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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 ()
 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.
 SphericalCap (const SphericalCap &other)
 Copy constructor.
virtual SphericalRegionType getType () const
virtual OctahedronPolygon getOctahedronPolygon () const
 Return the octahedron contour representation of the polygon.
virtual double getArea () const
 Get the area of the intersection of the halfspace on the sphere in steradian.
virtual bool isEmpty () const
 Return true if the region is empty.
virtual Vec3d getPointInside () const
 Return a point located inside the SphericalCap.
virtual SphericalCap getBoundingCap () const
 Return itself.
bool contains (const Vec3d &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.
virtual bool intersects (const AllSkySphericalRegion &) const
virtual QVariantList toQVariant () const
 Serialize the region into a QVariant map matching the JSON format.
virtual void serialize (QDataStream &out) const
 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.
bool clipGreatCircle (Vec3d &v1, Vec3d &v2) const
 Clip the passed great circle connecting points v1 and v2.
bool operator== (const SphericalCap &other) const
 Comparison operator.
QVector< Vec3dgetClosedOutlineContour () 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 Triplet< Vec3d > triangle) const
 Does the cap contain the passed triangle?
bool intersectsTriangle (const Triplet< Vec3d > &triangle) const
 Does the cap intersect with the passed triangle?

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.

Public Attributes

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.

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 504 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 508 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 511 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 516 of file StelSphereGeometry.hpp.

SphericalCap::SphericalCap ( const SphericalCap other  )  [inline]

Copy constructor.

Definition at line 519 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 Triplet< Vec3d triangle  )  const

Does the cap contain 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 [inline, virtual]

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

Reimplemented from SphericalRegion.

Definition at line 525 of file StelSphereGeometry.hpp.

virtual SphericalCap SphericalCap::getBoundingCap (  )  const [inline, virtual]

Return itself.

Reimplemented from SphericalRegion.

Definition at line 534 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 [inline, virtual]

Return a point located inside the SphericalCap.

Reimplemented from SphericalRegion.

Definition at line 531 of file StelSphereGeometry.hpp.

double SphericalCap::getRadius (  )  const [inline]

Return the radiusof the cap in radian.

Definition at line 572 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 [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.

Definition at line 554 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 578 of file StelSphereGeometry.hpp.

bool SphericalCap::intersectsTriangle ( const Triplet< Vec3d > &  triangle  )  const

Does the cap intersect with the passed triangle?

virtual bool SphericalCap::isEmpty (  )  const [inline, virtual]

Return true if the region is empty.

Reimplemented from SphericalRegion.

Definition at line 528 of file StelSphereGeometry.hpp.

bool SphericalCap::operator== ( const SphericalCap other  )  const [inline]

Comparison operator.

Definition at line 589 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 [inline, virtual]

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

Implements SphericalRegion.

Definition at line 566 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

The cos of cone radius.

Definition at line 621 of file StelSphereGeometry.hpp.

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

Definition at line 619 of file StelSphereGeometry.hpp.


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