org.apache.commons.geometry.euclidean.threed.shape

Class Sphere

java.lang.Object

org.apache.commons.geometry.euclidean.AbstractNSphere<Vector3D>

org.apache.commons.geometry.euclidean.threed.shape.Sphere

All Implemented Interfaces:

Region<Vector3D>, Sized, Linecastable3D

public final class Sphere
extends AbstractNSphere<Vector3D>
implements Linecastable3D

Class representing a 3 dimensional sphere in Euclidean space.

Method Summary

Modifier and Type	Method and Description
Vector3D	firstIntersection(Line3D line) Get the first intersection point between the given line and this sphere, or null if no such point exists.
static Sphere	from(Vector3D center, double radius, Precision.DoubleEquivalence precision) Construct a sphere from a center point and radius.
double	getBoundarySize()
double	getSize()
List<Vector3D>	intersections(Line3D line) Get the intersections of the given line with this sphere.
List<LinecastPoint3D>	linecast(LineConvexSubset3D subset) Intersect the given line convex subset against the boundaries in this instance, returning a list of all intersections in order of increasing distance along the line.
LinecastPoint3D	linecastFirst(LineConvexSubset3D subset) Intersect the given line convex subset against the boundaries in this instance, returning the first intersection found when traveling in the direction of the line subset from its start point.
Vector3D	project(Vector3D pt)
RegionBSPTree3D	toTree(int subdivisions) Build an approximation of this sphere using a RegionBSPTree3D.
TriangleMesh	toTriangleMesh(int subdivisions) Build an approximation of this sphere using a TriangleMesh.

Methods inherited from class org.apache.commons.geometry.euclidean.AbstractNSphere

classify, equals, firstIntersection, getCenter, getCentroid, getPrecision, getRadius, hashCode, intersections, isEmpty, isFull, project, toString

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.apache.commons.geometry.euclidean.threed.line.Linecastable3D

linecast, linecastFirst

Methods inherited from interface org.apache.commons.geometry.core.Region

contains

Methods inherited from interface org.apache.commons.geometry.core.Sized

isFinite, isInfinite

Method Detail

getSize

public double getSize()

Specified by:

getSize in interface Sized

getBoundarySize

public double getBoundarySize()

Specified by:

getBoundarySize in interface Region<Vector3D>

project

public Vector3D project(Vector3D pt)

Specified by:

project in interface Region<Vector3D>

toTree

public RegionBSPTree3D toTree(int subdivisions)

Build an approximation of this sphere using a RegionBSPTree3D. The approximation is constructed by taking an octahedron (8-sided polyhedron with triangular faces) inscribed in the sphere and subdividing each triangular face subdivisions number of times, each time projecting the newly created vertices onto the sphere surface. Each triangle subdivision produces 4 triangles, meaning that the total number of triangles inserted into tree is equal to \(8 \times 4^s\), where \(s\) is the number of subdivisions. For example, calling this method with subdivisions equal to 3 will produce a tree having \(8 \times 4^3 = 512\) triangular facets inserted. See the table below for other examples. The returned BSP tree also contains structural cuts to reduce the overall height of the tree.

Subdivisions to Triangle Counts

Subdivisions	Triangles
0	8
1	32
2	128
3	512
4	2048
5	8192

Care must be taken when using this method with large subdivision numbers so that floating point errors do not interfere with the creation of the planes and triangles in the tree. For example, if the number of subdivisions is too high, the subdivided triangle points may become equivalent according to the sphere's precision context and plane creation may fail. Or plane creation may succeed but insertion of the plane into the tree may fail for similar reasons. In general, it is best to use the lowest subdivision number practical for the intended purpose.

Parameters:

subdivisions - the number of triangle subdivisions to use when creating the tree; the total number of triangular facets inserted into the returned tree is equal to \(8 \times 4^s\), where \(s\) is the number of subdivisions

Returns:

a BSP tree containing an approximation of the sphere

Throws:

IllegalArgumentException - if subdivisions is less than zero

IllegalStateException - if tree creation fails for the given subdivision count

See Also:

toTriangleMesh(int)

toTriangleMesh

public TriangleMesh toTriangleMesh(int subdivisions)

Build an approximation of this sphere using a TriangleMesh. The approximation is constructed by taking an octahedron (8-sided polyhedron with triangular faces) inscribed in the sphere and subdividing each triangular face subdivisions number of times, each time projecting the newly created vertices onto the sphere surface. Each triangle subdivision produces 4 triangles, meaning that the total number of triangles in the returned mesh is equal to \(8 \times 4^s\), where \(s\) is the number of subdivisions. For example, calling this method with subdivisions equal to 3 will produce a mesh having \(8 \times 4^3 = 512\) triangular facets inserted. See the table below for other examples.

Subdivisions to Triangle Counts

Subdivisions	Triangles
0	8
1	32
2	128
3	512
4	2048
5	8192

BSP Tree Conversion

Inserting the boundaries of a sphere mesh approximation directly into a BSP tree will invariably result in poor performance: since the region is convex the constructed BSP tree degenerates into a simple linked list of nodes. If a BSP tree is needed, users should prefer the toTree(int) method, which creates balanced tree approximations directly, or the RegionBSPTree3D.PartitionedRegionBuilder3D class, which can be used to insert the mesh faces into a pre-partitioned tree.

Parameters:

subdivisions - the number of triangle subdivisions to use when creating the mesh; the total number of triangular faces in the returned mesh is equal to \(8 \times 4^s\), where \(s\) is the number of subdivisions

Returns:

a triangle mesh approximation of the sphere

Throws:

IllegalArgumentException - if subdivisions is less than zero

See Also:

toTree(int)

intersections

public List<Vector3D> intersections(Line3D line)

Get the intersections of the given line with this sphere. The returned list will contain either 0, 1, or 2 points.

• 2 points - The line is a secant line and intersects the sphere at two distinct points. The points are ordered such that the first point in the list is the first point encountered when traveling in the direction of the line. (In other words, the points are ordered by increasing abscissa value.)
• 1 point - The line is a tangent line and only intersects the sphere at a single point (as evaluated by the sphere's precision context).
• 0 points - The line does not intersect the sphere.

Parameters:

line - line to intersect with the sphere

Returns:

a list of intersection points between the given line and this sphere

firstIntersection

public Vector3D firstIntersection(Line3D line)

Get the first intersection point between the given line and this sphere, or null if no such point exists. The "first" intersection point is the first such point encountered when traveling in the direction of the line from infinity.

Parameters:

line - line to intersect with the sphere

Returns:

the first intersection point between the given line and this instance or null if no such point exists

linecast

public List<LinecastPoint3D> linecast(LineConvexSubset3D subset)

Intersect the given line convex subset against the boundaries in this instance, returning a list of all intersections in order of increasing distance along the line. An empty list is returned if no intersections are discovered.

Specified by:

linecast in interface Linecastable3D

Parameters:

subset - line subset to intersect

Returns:

a list of computed intersections in order of increasing distance along the line

linecastFirst

public LinecastPoint3D linecastFirst(LineConvexSubset3D subset)

Intersect the given line convex subset against the boundaries in this instance, returning the first intersection found when traveling in the direction of the line subset from its start point.

Specified by:

linecastFirst in interface Linecastable3D

Parameters:

subset - line subset to intersect

Returns:

the first intersection found or null if no intersection is found

from

public static Sphere from(Vector3D center,
                          double radius,
                          Precision.DoubleEquivalence precision)

Construct a sphere from a center point and radius.

Parameters:

center - the center of the sphere

radius - the sphere radius

precision - precision context used to compare floating point numbers

Returns:

a sphere constructed from the given center point and radius

Throws:

IllegalArgumentException - if center is not finite or radius is not finite or is less than or equal to zero as evaluated by the given precision context