Class SphericalPolygonsSet
 java.lang.Object

 org.hipparchus.geometry.partitioning.AbstractRegion<Sphere2D,Sphere1D>

 org.hipparchus.geometry.spherical.twod.SphericalPolygonsSet

public class SphericalPolygonsSet extends AbstractRegion<Sphere2D,Sphere1D>
This class represents a region on the 2sphere: a set of spherical polygons.


Nested Class Summary

Nested classes/interfaces inherited from interface org.hipparchus.geometry.partitioning.Region
Region.Location


Constructor Summary
Constructors Constructor Description SphericalPolygonsSet(double tolerance)
Build a polygons set representing the whole real 2sphere.SphericalPolygonsSet(double hyperplaneThickness, S2Point... vertices)
Build a polygon from a simple list of vertices.SphericalPolygonsSet(Collection<SubHyperplane<Sphere2D>> boundary, double tolerance)
Build a polygons set from a Boundary REPresentation (Brep).SphericalPolygonsSet(Vector3D pole, double tolerance)
Build a polygons set representing a hemisphere.SphericalPolygonsSet(Vector3D center, Vector3D meridian, double outsideRadius, int n, double tolerance)
Build a polygons set representing a regular polygon.SphericalPolygonsSet(BSPTree<Sphere2D> tree, double tolerance)
Build a polygons set from a BSP tree.

Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description SphericalPolygonsSet
buildNew(BSPTree<Sphere2D> tree)
Build a region using the instance as a prototype.protected void
computeGeometricalProperties()
Compute some geometrical properties.List<Vertex>
getBoundaryLoops()
Get the boundary loops of the polygon.EnclosingBall<Sphere2D,S2Point>
getEnclosingCap()
Get a spherical cap enclosing the polygon.
Methods inherited from class org.hipparchus.geometry.partitioning.AbstractRegion
applyTransform, checkPoint, checkPoint, checkPoint, checkPoint, contains, copySelf, getBarycenter, getBoundarySize, getSize, getTolerance, getTree, intersection, isEmpty, isEmpty, isFull, isFull, projectToBoundary, setBarycenter, setBarycenter, setSize




Constructor Detail

SphericalPolygonsSet
public SphericalPolygonsSet(double tolerance) throws MathIllegalArgumentException
Build a polygons set representing the whole real 2sphere. Parameters:
tolerance
 below which points are consider to be identical Throws:
MathIllegalArgumentException
 if tolerance is smaller thanSphere1D.SMALLEST_TOLERANCE

SphericalPolygonsSet
public SphericalPolygonsSet(Vector3D pole, double tolerance) throws MathIllegalArgumentException
Build a polygons set representing a hemisphere. Parameters:
pole
 pole of the hemisphere (the pole is in the inside half)tolerance
 below which points are consider to be identical Throws:
MathIllegalArgumentException
 if tolerance is smaller thanSphere1D.SMALLEST_TOLERANCE

SphericalPolygonsSet
public SphericalPolygonsSet(Vector3D center, Vector3D meridian, double outsideRadius, int n, double tolerance) throws MathIllegalArgumentException
Build a polygons set representing a regular polygon. Parameters:
center
 center of the polygon (the center is in the inside half)meridian
 point defining the reference meridian for first polygon vertexoutsideRadius
 distance of the vertices to the centern
 number of sides of the polygontolerance
 below which points are consider to be identical Throws:
MathIllegalArgumentException
 if tolerance is smaller thanSphere1D.SMALLEST_TOLERANCE

SphericalPolygonsSet
public SphericalPolygonsSet(BSPTree<Sphere2D> tree, double tolerance) throws MathIllegalArgumentException
Build a polygons set from a BSP tree.The leaf nodes of the BSP tree must have a
Boolean
attribute representing the inside status of the corresponding cell (true for inside cells, false for outside cells). In order to avoid building too many small objects, it is recommended to use the predefined constantsBoolean.TRUE
andBoolean.FALSE
 Parameters:
tree
 inside/outside BSP tree representing the regiontolerance
 below which points are consider to be identical Throws:
MathIllegalArgumentException
 if tolerance is smaller thanSphere1D.SMALLEST_TOLERANCE

SphericalPolygonsSet
public SphericalPolygonsSet(Collection<SubHyperplane<Sphere2D>> boundary, double tolerance) throws MathIllegalArgumentException
Build a polygons set from a Boundary REPresentation (Brep).The boundary is provided as a collection of
subhyperplanes
. Each subhyperplane has the interior part of the region on its minus side and the exterior on its plus side.The boundary elements can be in any order, and can form several nonconnected sets (like for example polygons with holes or a set of disjoint polygons considered as a whole). In fact, the elements do not even need to be connected together (their topological connections are not used here). However, if the boundary does not really separate an inside open from an outside open (open having here its topological meaning), then subsequent calls to the
checkPoint
method will not be meaningful anymore.If the boundary is empty, the region will represent the whole space.
 Parameters:
boundary
 collection of boundary elements, as a collection ofSubHyperplane
objectstolerance
 below which points are consider to be identical Throws:
MathIllegalArgumentException
 if tolerance is smaller thanSphere1D.SMALLEST_TOLERANCE

SphericalPolygonsSet
public SphericalPolygonsSet(double hyperplaneThickness, S2Point... vertices) throws MathIllegalArgumentException
Build a polygon from a simple list of vertices.The boundary is provided as a list of points considering to represent the vertices of a simple loop. The interior part of the region is on the left side of this path and the exterior is on its right side.
This constructor does not handle polygons with a boundary forming several disconnected paths (such as polygons with holes).
For cases where this simple constructor applies, it is expected to be numerically more robust than the
general constructor
usingsubhyperplanes
.If the list is empty, the region will represent the whole space.
This constructor assumes that edges between
vertices
, including the edge between the last and the first vertex, are shorter than pi. If edges longer than pi are used it may produce unintuitive results, such as reversing the direction of the edge. This implies using avertices
array of length 1 or 2 in this constructor produces an illdefined region. Use one of the other constructors orRegionFactory
instead.The list of
vertices
is reduced by selecting a subset of vertices before creating the boundary set. Every point invertices
will be on theboundary
of the constructed polygon set, but not necessarily the centerline of the boundary.Polygons with thin pikes or dents are inherently difficult to handle because they involve circles with almost opposite directions at some vertices. Polygons whose vertices come from some physical measurement with noise are also difficult because an edge that should be straight may be broken in lots of different pieces with almost equal directions. In both cases, computing the circles intersections is not numerically robust due to the almost 0 or almost π angle. Such cases need to carefully adjust the
hyperplaneThickness
parameter. A too small value would often lead to completely wrong polygons with large area wrongly identified as inside or outside. Large values are often much safer. As a rule of thumb, a value slightly below the size of the most accurate detail needed is a good value for thehyperplaneThickness
parameter. Parameters:
hyperplaneThickness
 tolerance below which points are considered to belong to the hyperplane (which is therefore more a slab). Should be greater thanFastMath.ulp(4 * FastMath.PI)
for meaningful results.vertices
 vertices of the simple loop boundary Throws:
MathIllegalArgumentException
 if tolerance is smaller thanSphere1D.SMALLEST_TOLERANCE
MathRuntimeException
 ifvertices
contains only a single vertex or repeated vertices.


Method Detail

buildNew
public SphericalPolygonsSet buildNew(BSPTree<Sphere2D> tree)
Build a region using the instance as a prototype.This method allow to create new instances without knowing exactly the type of the region. It is an application of the prototype design pattern.
The leaf nodes of the BSP tree must have a
Boolean
attribute representing the inside status of the corresponding cell (true for inside cells, false for outside cells). In order to avoid building too many small objects, it is recommended to use the predefined constantsBoolean.TRUE
andBoolean.FALSE
. The tree also must have either null internal nodes or internal nodes representing the boundary as specified in thegetTree
method).

computeGeometricalProperties
protected void computeGeometricalProperties() throws MathIllegalStateException
Compute some geometrical properties.The properties to compute are the barycenter and the size.
 Specified by:
computeGeometricalProperties
in classAbstractRegion<Sphere2D,Sphere1D>
 Throws:
MathIllegalStateException
 if the tolerance setting does not allow to build a clean nonambiguous boundary

getBoundaryLoops
public List<Vertex> getBoundaryLoops() throws MathIllegalStateException
Get the boundary loops of the polygon.The polygon boundary can be represented as a list of closed loops, each loop being given by exactly one of its vertices. From each loop start vertex, one can follow the loop by finding the outgoing edge, then the end vertex, then the next outgoing edge ... until the start vertex of the loop (exactly the same instance) is found again once the full loop has been visited.
If the polygon has no boundary at all, a zero length loop array will be returned.
If the polygon is a simple onepiece polygon, then the returned array will contain a single vertex.
All edges in the various loops have the inside of the region on their left side (i.e. toward their pole) and the outside on their right side (i.e. away from their pole) when moving in the underlying circle direction. This means that the closed loops obey the direct trigonometric orientation.
 Returns:
 boundary of the polygon, organized as an unmodifiable list of loops start vertices.
 Throws:
MathIllegalStateException
 if the tolerance setting does not allow to build a clean nonambiguous boundary See Also:
Vertex
,Edge

getEnclosingCap
public EnclosingBall<Sphere2D,S2Point> getEnclosingCap()
Get a spherical cap enclosing the polygon.This method is intended as a first test to quickly identify points that are guaranteed to be outside of the region, hence performing a full
checkPoint
only if the point status remains undecided after the quick check. It is is therefore mostly useful to speed up computation for small polygons with complex shapes (say a country boundary on Earth), as the spherical cap will be small and hence will reliably identify a large part of the sphere as outside, whereas the full check can be more computing intensive. A typical use case is therefore:// compute region, plus an enclosing spherical cap SphericalPolygonsSet complexShape = ...; EnclosingBall<Sphere2D, S2Point> cap = complexShape.getEnclosingCap(); // check lots of points for (Vector3D p : points) { final Location l; if (cap.contains(p)) { // we cannot be sure where the point is // we need to perform the full computation l = complexShape.checkPoint(v); } else { // no need to do further computation, // we already know the point is outside l = Location.OUTSIDE; } // use l ... }
In the special cases of empty or whole sphere polygons, special spherical caps are returned, with angular radius set to negative or positive infinity so the
ball.contains(point)
method return always false or true.This method is not guaranteed to return the smallest enclosing cap.
 Returns:
 a spherical cap enclosing the polygon

