Package org.hipparchus.geometry.spherical.twod

Class Circle

java.lang.Object

org.hipparchus.geometry.spherical.twod.Circle

All Implemented Interfaces:

Embedding<Sphere2D,S2Point,Sphere1D,S1Point>, Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

public class Circle
extends Object
implements Hyperplane<Sphere2D,S2Point,Circle,SubCircle>, Embedding<Sphere2D,S2Point,Sphere1D,S1Point>

This class represents an oriented great circle on the 2-sphere.

An oriented circle can be defined by a center point. The circle is the set of points that are in the normal plan the center.

Since it is oriented the two spherical caps at its two sides are unambiguously identified as a left cap and a right cap. This can be used to identify the interior and the exterior in a simple way by local properties only when part of a line is used to define part of a spherical polygon boundary.

Constructor Summary

Constructors

Constructor	Description
Circle(Vector3D pole, double tolerance)	Build a great circle from its pole.
Circle(Circle circle)	Copy constructor.
Circle(S2Point first, S2Point second, double tolerance)	Build a great circle from two non-aligned points.

Method Summary

Modifier and Type	Method	Description
S2Point	arbitraryPoint()	Get an arbitrary point in the hyperplane.
Circle	copySelf()	Copy the instance.
SubCircle	emptyHyperplane()	Build a sub-hyperplane covering nothing.
Arc	getArc(S2Point a, S2Point b)	Get the arc on this circle between two defining points.
Arc	getInsideArc(Circle other)	Get the arc of the instance that lies inside the other circle.
double	getOffset(Vector3D direction)	Get the offset (oriented distance) of a direction.
double	getOffset(S2Point point)	Get the offset (oriented distance) of a point.
double	getPhase(Vector3D direction)	Get the phase angle of a direction.
Vector3D	getPointAt(double alpha)	Get a circle point from its phase around the circle.
Vector3D	getPole()	Get the pole of the circle.
Circle	getReverse()	Get the reverse of the instance.
double	getTolerance()	Get the tolerance below which points are considered to belong to the hyperplane.
static Transform<Sphere2D,S2Point,Circle,SubCircle,Sphere1D,S1Point,LimitAngle,SubLimitAngle>	getTransform(Rotation rotation)	Get a Transform embedding a 3D rotation.
Vector3D	getXAxis()	Get the X axis of the circle.
Vector3D	getYAxis()	Get the Y axis of the circle.
S2Point	moveToOffset(S2Point point, double offset)	Move point up to specified offset.
S2Point	project(S2Point point)	Project a point to the hyperplane.
void	reset(Vector3D newPole)	Reset the instance as if built from a pole.
void	revertSelf()	Revert the instance.
boolean	sameOrientationAs(Circle other)	Check if the instance has the same orientation as another hyperplane.
S2Point	toSpace(S1Point point)	Transform a sub-space point into a space point.
S1Point	toSubSpace(S2Point point)	Transform a space point into a sub-space point.
SubCircle	wholeHyperplane()	Build a sub-hyperplane covering the whole hyperplane.
SphericalPolygonsSet	wholeSpace()	Build a region covering the whole space.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Circle

public Circle(Vector3D pole,
 double tolerance)
       throws MathIllegalArgumentException

Build a great circle from its pole.

The circle is oriented in the trigonometric direction around pole.

Parameters:

pole - circle pole

tolerance - tolerance below which close sub-arcs are merged together

Throws:

MathIllegalArgumentException - if tolerance is smaller than Sphere1D.SMALLEST_TOLERANCE

Circle

public Circle(S2Point first,
 S2Point second,
 double tolerance)
       throws MathIllegalArgumentException

Build a great circle from two non-aligned points.

The circle is oriented from first to second point using the path smaller than π.

Parameters:

first - first point contained in the great circle

second - second point contained in the great circle

tolerance - tolerance below which close sub-arcs are merged together

Throws:

MathIllegalArgumentException - if tolerance is smaller than Sphere1D.SMALLEST_TOLERANCE

Circle

public Circle(Circle circle)

Copy constructor.

The created instance is completely independent from the original instance, it is a deep copy.

Parameters:

circle - circle to copy

Method Details

copySelf

public Circle copySelf()

Copy the instance.

The instance created is completely independent of the original one. A deep copy is used, none of the underlying objects are shared (except for immutable objects).

Specified by:

copySelf in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Returns:

a new hyperplane, copy of the instance

reset

public void reset(Vector3D newPole)

Reset the instance as if built from a pole.

The circle is oriented in the trigonometric direction around pole.

Parameters:

newPole - circle pole

revertSelf

public void revertSelf()

Revert the instance.

getReverse

public Circle getReverse()

Get the reverse of the instance.

Get a circle with reversed orientation with respect to the instance. A new object is built, the instance is untouched.

Returns:

a new circle, with orientation opposite to the instance orientation

project

public S2Point project(S2Point point)

Project a point to the hyperplane.

Specified by:

project in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Parameters:

point - point to project

Returns:

projected point

getTolerance

public double getTolerance()

Get the tolerance below which points are considered to belong to the hyperplane.

Specified by:

getTolerance in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Returns:

tolerance below which points are considered to belong to the hyperplane

toSubSpace

public S1Point toSubSpace(S2Point point)

Transform a space point into a sub-space point.

Specified by:

toSubSpace in interface Embedding<Sphere2D,S2Point,Sphere1D,S1Point>

Parameters:

point - n-dimension point of the space

Returns:

(n-1)-dimension point of the sub-space corresponding to the specified space point

See Also:

• getPhase(Vector3D)

getPhase

public double getPhase(Vector3D direction)

Get the phase angle of a direction.

The direction may not belong to the circle as the phase is computed for the meridian plane between the circle pole and the direction.

Parameters:

direction - direction for which phase is requested

Returns:

phase angle of the direction around the circle

See Also:

• toSubSpace(S2Point)

toSpace

public S2Point toSpace(S1Point point)

Transform a sub-space point into a space point.

Specified by:

toSpace in interface Embedding<Sphere2D,S2Point,Sphere1D,S1Point>

Parameters:

point - (n-1)-dimension point of the sub-space

Returns:

n-dimension point of the space corresponding to the specified sub-space point

See Also:

• getPointAt(double)

getPointAt

public Vector3D getPointAt(double alpha)

Get a circle point from its phase around the circle.

Parameters:

alpha - phase around the circle

Returns:

circle point on the sphere

See Also:

• toSpace(S1Point)
• getXAxis()
• getYAxis()

getXAxis

public Vector3D getXAxis()

Get the X axis of the circle.

This method returns the same value as getPointAt(0.0) but it does not do any computation and always return the same instance.

Returns:

an arbitrary x axis on the circle

See Also:

• getPointAt(double)
• getYAxis()
• getPole()

getYAxis

public Vector3D getYAxis()

Get the Y axis of the circle.

This method returns the same value as getPointAt(MathUtils.SEMI_PI) but it does not do any computation and always return the same instance.

Returns:

an arbitrary y axis point on the circle

See Also:

• getPointAt(double)
• getXAxis()
• getPole()

getPole

public Vector3D getPole()

Get the pole of the circle.

As the circle is a great circle, the pole does not belong to it.

Returns:

pole of the circle

See Also:

• getXAxis()
• getYAxis()

getInsideArc

public Arc getInsideArc(Circle other)

Get the arc of the instance that lies inside the other circle.

Parameters:

other - other circle

Returns:

arc of the instance that lies inside the other circle

wholeHyperplane

public SubCircle wholeHyperplane()

Build a sub-hyperplane covering the whole hyperplane.

Specified by:

wholeHyperplane in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Returns:

a sub-hyperplane covering the whole hyperplane

emptyHyperplane

public SubCircle emptyHyperplane()

Build a sub-hyperplane covering nothing.

Specified by:

emptyHyperplane in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Returns:

a sub-hyperplane covering nothing

wholeSpace

public SphericalPolygonsSet wholeSpace()

Build a region covering the whole space.

Specified by:

wholeSpace in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Returns:

a region containing the instance (really a SphericalPolygonsSet instance)

getOffset

public double getOffset(S2Point point)

Get the offset (oriented distance) of a point.

The offset is 0 if the point is on the underlying hyperplane, it is positive if the point is on one particular side of the hyperplane, and it is negative if the point is on the other side, according to the hyperplane natural orientation.

Specified by:

getOffset in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Parameters:

point - point to check

Returns:

offset of the point

See Also:

• getOffset(Vector3D)

getOffset

public double getOffset(Vector3D direction)

Get the offset (oriented distance) of a direction.

The offset is defined as the angular distance between the circle center and the direction minus the circle radius. It is therefore 0 on the circle, positive for directions outside of the cone delimited by the circle, and negative inside the cone.

Parameters:

direction - direction to check

Returns:

offset of the direction

See Also:

• getOffset(S2Point)

moveToOffset

public S2Point moveToOffset(S2Point point,
 double offset)

Move point up to specified offset.

Motion is orthogonal to the hyperplane

Specified by:

moveToOffset in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Parameters:

point - point to move

offset - desired offset

Returns:

moved point at desired offset

arbitraryPoint

public S2Point arbitraryPoint()

Get an arbitrary point in the hyperplane.

Specified by:

arbitraryPoint in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Returns:

arbirary point in the hyperplane

sameOrientationAs

public boolean sameOrientationAs(Circle other)

Check if the instance has the same orientation as another hyperplane.

This method is expected to be called on parallel hyperplanes. The method should not re-check for parallelism, only for orientation, typically by testing something like the sign of the dot-products of normals.

Specified by:

sameOrientationAs in interface Hyperplane<Sphere2D,S2Point,Circle,SubCircle>

Parameters:

other - other hyperplane to check against the instance

Returns:

true if the instance and the other hyperplane have the same orientation

getArc

public Arc getArc(S2Point a,
 S2Point b)

Get the arc on this circle between two defining points. Only the point's projection on the circle matters, which is computed using getPhase(Vector3D).

Parameters:

a - first point.

b - second point.

Returns:

an arc of the circle.

getTransform

public static Transform<Sphere2D,S2Point,Circle,SubCircle,Sphere1D,S1Point,LimitAngle,SubLimitAngle> getTransform(Rotation rotation)

Get a Transform embedding a 3D rotation.

Parameters:

rotation - rotation to use

Returns:

a new transform that can be applied to either Point, Line or SubHyperplane instances