SARSPix

The SimilAr Radius Sphere pixelization

based on this paper (also available in the doc directory). This is not the full construction but the one described at the very beginning of section 3.3.

It relies on the projection of the faces of an inscribed cube that are further subdivided into 4 quadrants. Althought not having exact same areas pixels have quite compact inner and outer radii (see note).

The face numbering convention is the following :

0 for x=1 plane,
1 for y=1 plane
2 for x=-1
3 for y=-1
4 for z=1 (top)
5 for z=-1 (bottom).

The quadrant numbering convention (on face 0) is

| 2 | 0 |
|---|---|
| 3 | 1 |

The local index is in the form (face,quadrant,i,j) where face is in [0,5] , quadrant in [0,3] and (i,j) in [0,Nbase/2-1]
The face index is the CubedSphere one in the form (face,I,J)
(theta,phi) angles on the sphere are in radians in classical spherical conventions, ie. 0<theta<Pi and 0<phi<2Pi

There are 6 Nbase² pixels per face and 6 Nbase² pixels on the entire sphere

Author:

Stephane Plaszczynski

Note: https://arxiv.org/abs/2012.08455

Linear Supertypes

CubedSphere, Serializable, SphereTiling, AnyRef, Any

Type Hierarchy

Instance Constructors

new SARSPix(nbase: Int)

creates SARSpix tiling with resolution nbase
creates SARSpix tiling with resolution nbase
nbase
Number of points on one face in one dimension (even number)

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
val N: Int

shorthand for Nbase
shorthand for Nbase

Attributes
protected
Definition Classes
CubedSphere
val Nbase: Int

Number of points on a face in one dimension (even number).
Number of points on a face in one dimension (even number).

Definition Classes
CubedSphere → SphereTiling
val Npix: Long

number of pixels
number of pixels

Definition Classes
CubedSphere → SphereTiling
def ang2LocalIndex(face: Int, theta: Double, phi: Double): (Int, Int)

given face and angles returns the local index
given face and angles returns the local index

Definition Classes
CubedSphere
def ang2pix(theta: Double, phi: Double): Int

pixel index from angles on the sphere
pixel index from angles on the sphere
theta
colatitude (0<theta<Pi)
phi
azimuth (0<phi<2Pi)
returns
pixel index

Definition Classes
SARSPix → CubedSphere → SphereTiling
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
def coord2pix(f: Int, i: Int, j: Int): Int

transformation from local CubedSphere coordinates to pixel number
transformation from local CubedSphere coordinates to pixel number

Definition Classes
CubedSphere
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def face2localBinIndex(I: Int, J: Int): (Int, Int, Int)

convert face (I,J) coordinates to local (q,i,j) ones for bin numbers
def face2localNodeIndex(I: Int, J: Int): (Int, Int, Int)

convert face (I,J) coordinates to local (q,i,j) ones for nodes numbers
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
def getFace(p: Point3D): Int

get face number from Point on the sphere
get face number from Point on the sphere

Definition Classes
CubedSphere
def getFace(theta: Double, phi: Double): Int

get face number from angles
get face number from angles

Definition Classes
CubedSphere
def getFaceQuadrant(p: Point3D): (Int, Int)

get face and quadrant numbers for point p
def getLocalIndex(p: Point3D): (Int, Int, Int, Int)

get local coordinates (f,q,i,j) for point p
def getQuadrant(face: Int, p: Point3D): Int

get quadrant number from point p and face
def hashCode(): Int

Definition Classes
AnyRef → Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def isValidPix(ipix: Int): Boolean

check pixel number is valid
check pixel number is valid

Definition Classes
CubedSphere
def local2faceBinIndex(q: Int, i: Int, j: Int): (Int, Int)

convert local (q,i,j) coordinates to face ones (I,J) for bin numbers
def local2faceNodeIndex(q: Int, i: Int, j: Int): (Int, Int)

convert local (q,i,j) coordinates to face ones (I,J) for nodes
val maxIndex: Long

Largest possible index of the pixelization .
Largest possible index of the pixelization . Do not use to access data. use CubedSphere.pixNums instead

Definition Classes
CubedSphere
val nbase: Int

Number of points on one face in one dimension (even number)
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def neighbours(ipix: Int): Array[Int]

List of neighbour indices
List of neighbour indices
ipix
pixel index
returns
Array of pixel indices (variable size)

Definition Classes
CubedSphere → SphereTiling
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
def pix2ang(ipix: Int): Array[Double]

pixel center angles for a given index
pixel center angles for a given index
ipix
pixel index
returns
size 2 Array of angles [theta,phi] (see header for conventions)

Definition Classes
SARSPix → CubedSphere → SphereTiling
def pix2coord(ipix: Int): (Int, Int, Int)

transformation from pixel number to local coordinates
transformation from pixel number to local coordinates

Definition Classes
CubedSphere
def pixNums: IndexedSeq[Int]

list of valid pixel indices for this pixelization (do not assume it is contiguous)
list of valid pixel indices for this pixelization (do not assume it is contiguous)
returns
an indexedseq of indices

Definition Classes
CubedSphere → SphereTiling
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def toString(): String

Definition Classes
AnyRef → Any
final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
def writeCenters(fn: String): Unit

output pixel centers into file
output pixel centers into file
fn
filename

Definition Classes
CubedSphere
def writeNeighbours(ipix: Int): Unit

given a pixel number write all neigbour indices into a file named "neighbours.txt"
given a pixel number write all neigbour indices into a file named "neighbours.txt"

Definition Classes
CubedSphere

Deprecated Value Members

def neighbours8(ipix: Int): Array[Int]

automatic translation to 8 neighbouring indices putting -1 if there is less.
automatic translation to 8 neighbouring indices putting -1 if there is less.
undefined behaviour if more than 8

Definition Classes
SphereTiling
Deprecated

Related Docs: object SARSPix | package Tiling

class SARSPix extends CubedSphere

The SimilAr Radius Sphere pixelization

Author:

Instance Constructors

new SARSPix(nbase: Int)

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

val N: Int

val Nbase: Int

val Npix: Long

def ang2LocalIndex(face: Int, theta: Double, phi: Double): (Int, Int)

def ang2pix(theta: Double, phi: Double): Int

final def asInstanceOf[T0]: T0

def clone(): AnyRef

def coord2pix(f: Int, i: Int, j: Int): Int

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def face2localBinIndex(I: Int, J: Int): (Int, Int, Int)

def face2localNodeIndex(I: Int, J: Int): (Int, Int, Int)

def finalize(): Unit

final def getClass(): Class[_]

def getFace(p: Point3D): Int

def getFace(theta: Double, phi: Double): Int

def getFaceQuadrant(p: Point3D): (Int, Int)

def getLocalIndex(p: Point3D): (Int, Int, Int, Int)

def getQuadrant(face: Int, p: Point3D): Int

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

def isValidPix(ipix: Int): Boolean

def local2faceBinIndex(q: Int, i: Int, j: Int): (Int, Int)

def local2faceNodeIndex(q: Int, i: Int, j: Int): (Int, Int)

val maxIndex: Long

val nbase: Int

final def ne(arg0: AnyRef): Boolean

def neighbours(ipix: Int): Array[Int]

final def notify(): Unit

final def notifyAll(): Unit

def pix2ang(ipix: Int): Array[Double]

def pix2coord(ipix: Int): (Int, Int, Int)

def pixNums: IndexedSeq[Int]

final def synchronized[T0](arg0: ⇒ T0): T0

def toString(): String

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

def writeCenters(fn: String): Unit

def writeNeighbours(ipix: Int): Unit

Deprecated Value Members

def neighbours8(ipix: Int): Array[Int]

Inherited from CubedSphere

Inherited from Serializable

Inherited from SphereTiling

Inherited from AnyRef

Inherited from Any

Ungrouped