AuxiliaryAxis

```
public interface AuxiliaryAxis
```
Define an auxiliary axis, i.e. a 3rd dimension to be taken into account when computing an HEALPix index.
To compute a hash using the auxiliary axis, the values must be projected along the z-axis ranging from 0 (inclusive) to 1 (exclusive).
The maximum depth when using an auxiliary axis is 19 (4 + 19 * 3 = 61 bits). So the maximum number of intervals is 2^19 = 524288.
At a given depth, the [0.0, 1.0[ interval is divided into NSIDE (=2^depth) segments.
The resolution at a given depth is thus abs(unproject(1) - unproject(0)) / NSIDE.
If we want to represent temporal data, we can represent:
- about 1 years with intervals being time ranges of 1 min;
- 60.68 years with intervals being time ranges of 1 hour.
We recall that when a double is divided by a power of two, there is no loss in precision since the mantissa remains unchanged (only the exponent part changes).
Example: depth 12 => NSIDE = 4096 => angular resolution = 51.5 arcsec => 4096 / 365 = 11.222 years with a resolution = 1 day
Author:

F.-X. Pineau

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`java.lang.String`	`name()`	Returns the name of the auxiliary axis.
`double`	`project(double x)`	Project (or normalize) the given auxiliary axis value into the [0.0, 1.0[ range.
`double`	`unproject(double y)`	Unproject (denormalize) the value from the [0.0, 1.0[ range.

- Method Detail
  - name
```
java.lang.String name()
```
    Returns the name of the auxiliary axis.
    
    Returns:
    
    the name of the auxiliary axis.
  - project
```
double project(double x)
```
    Project (or normalize) the given auxiliary axis value into the [0.0, 1.0[ range.
    
    Parameters:
    
    x - the auxiliary axis value to be projected (normalized).
    
    Returns:
    
    the projected (normalized) value on the auxiliary axis, in [0.0, 1.0[.
  - unproject
```
double unproject(double y)
```
    Unproject (denormalize) the value from the [0.0, 1.0[ range.
    
    Parameters:
    
    y - the projected (normalized) value on the auxiliary axis, in [0.0, 1.0[
    
    Returns:
    
    the unprojected (denormalize) value on the auxiliary axis.