stella.math
Class SphereTiles

java.lang.Object
  stella.math.SphereTiles

All Implemented Interfaces:

PI

public class SphereTiles
extends Object
implements PI

This class calculates equal-area sized almost half-sphere tiles and tries to arrange them in the following way:

• The number of tiles equals a predefined number, N.
• The first tile is a polar cap with the area of the total area of the sphere divided by the number of tiles. The total area of the sphere area is 2π(1-sin(h_min))
• Each following segment is tiled in a way that its Δaz is a plain dividor of 2π and Δaz cos(h) ~ Δh, the individula Δh closest to the principal Δh_0 given by

     Δh_0*sin(Δh_0/2)=A_sphere/N
     

• This tiling is continued until h_min
is reached.

Nested Class Summary

static class

SphereTiles.Test Test class.

Field Summary

private double	area The area per tile.
private double	dh0 The principle height, from 2hsin(h/2)=area.
private List	tiles Filled on construct, these are centers and d(az) dh of tiles.

Fields inherited from interface vec_math.PI

HOUR, PIHALF, PITWO, RADIAN

Constructor Summary

SphereTiles(int n, double h0)
Constructs a new tiling of the part of the sphere above the minimal height h_0.

Method Summary

double	getDistanceToTile(int index, double azrad, double hrad) Returns the distance of the point on the sphere indicated by azimuth and altitude to the center of the tile given by the index.
int	getNumberOfTiles() Returns the number of tiles within this sky sphere.
VectorG	getTile(int index) Retruns the tile with the given index.
int	getTileIndex(double azrad, double hrad) This method scans all tiles in this sphere and returns the index of the tile the requested position is in.
private static boolean	probeTile(VectorG v, double az, double h) Probes if a point on the sky lies within the tile specified by the 4-dimensional vector passed over.

Methods inherited from class java.lang.Object

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

Field Detail

tiles

private List tiles

Filled on construct, these are centers and d(az) dh of tiles.

area

private double area

The area per tile.

dh0

private double dh0

The principle height, from 2hsin(h/2)=area.

Constructor Detail

SphereTiles

public SphereTiles(int n,
                   double h0)

Constructs a new tiling of the part of the sphere above the minimal height h_0. The tentative number of tiles is also given. The last tile is the polar cap, it is characterized by a vector of 0, PI/2, 2PI and the length of the polar cap. Due to the requirement that all tiles should lie in belts, the true number of tiles may be different to the number of tiles requested.

Parameters:

n - Number of tiles

h0 - Starting height above the horizon, in radian.

Method Detail

getNumberOfTiles

public int getNumberOfTiles()

Returns the number of tiles within this sky sphere. Due to the requirement that all tiles should lie in belts, the true number of tiles may be different to the number of tiles requested.

getTileIndex

public int getTileIndex(double azrad,
                        double hrad)

This method scans all tiles in this sphere and returns the index of the tile the requested position is in.

Parameters:

azrad - The azimuth to probe in radians.

hrad - The altitude to probe in radians.

Returns:

-1 If the requested position is not within any tile.

getDistanceToTile

public double getDistanceToTile(int index,
                                double azrad,
                                double hrad)

Returns the distance of the point on the sphere indicated by azimuth and altitude to the center of the tile given by the index. Returns NaN if the tile does not exist.

Parameters:

azrad - The azimuth to probe in radians.

hrad - The altitude to probe in radians.

index - The tile index.

getTile

public VectorG getTile(int index)

Retruns the tile with the given index.

probeTile

private static boolean probeTile(VectorG v,
                                 double az,
                                 double h)

Probes if a point on the sky lies within the tile specified by the 4-dimensional vector passed over. The vector consists of the following components:

• 0: Central azimuth, radians.
• 1: Central height, radians.
• 2: Azimuth span, radians.
• 3: Height span, radians.