lsst.skymap.detail.dodecahedron Namespace Reference

Classes
class	Dodecahedron

Functions
	computeRotationMatrix (angle, axis)
	_computeCoordTransform (vec0, vec1, vec1NegativeX=False)
	_computeDodecahedronVertices (faceVecList)
	_computeFullVecList (basisSet)
	_findCloseIndexSet (vecList, ind)
	_findCloseList (vecList, vec)
	_findClosePair (vecList, ind=0)
	_sortedVectorList (vecList)

Variables
	precision
	suppress
	True
	linewidth
	vertexDodec = Dodecahedron(withFacesOnPoles=False)
	faceVec = vertexDodec.getFaceCtr(i)

Function Documentation

_computeCoordTransform()

lsst.skymap.detail.dodecahedron._computeCoordTransform ( vec0, vec1, vec1NegativeX = False )

protected

Compute a rotation matrix that puts vec0 along z and vec1 along +x in
the xz plane.

Parameters
----------
vec0 : `numpy.ndarray`
    vector 0
vec1 : `numpy.ndarray`
    vector 1
vec1NegativeX : `bool`
    If True then vec1 is rotated to face negative x.

Definition at line 138 of file dodecahedron.py.

def _computeCoordTransform(vec0, vec1, vec1NegativeX=False):
    """Compute a rotation matrix that puts vec0 along z and vec1 along +x in
    the xz plane.
 
    Parameters
    ----------
    vec0 : `numpy.ndarray`
        vector 0
    vec1 : `numpy.ndarray`
        vector 1
    vec1NegativeX : `bool`
        If True then vec1 is rotated to face negative x.
    """
    # rotate around x by angle of vec0 from z to y
    xAng = math.atan2(vec0[1], vec0[2])
    xRotMat = computeRotationMatrix(xAng, 0)
 
    # rotate around y by -angle of rotated vec0 from z to x
    vec0RotX = numpy.dot(xRotMat, vec0)
    yAng = -math.atan2(vec0RotX[0], vec0RotX[2])
    yRotMat = computeRotationMatrix(yAng, 1)
    xyRotMat = numpy.dot(yRotMat, xRotMat)
 
    # rotate around z by -angle of rotated vec1 from +/-x to y
    vec1RotXY = numpy.dot(xyRotMat, vec1)
    xVal = vec1RotXY[0]
    if vec1NegativeX:
        xVal = -xVal
    zAng = -math.atan2(vec1RotXY[1], xVal)
    zRotMat = computeRotationMatrix(zAng, 2)
    xyzRotMat = numpy.dot(zRotMat, xyRotMat)
    return xyzRotMat
 
 

_computeDodecahedronVertices()

lsst.skymap.detail.dodecahedron._computeDodecahedronVertices ( faceVecList )

protected

Given a vector of face positions of a Dodecahedron compute the vertices.

Definition at line 172 of file dodecahedron.py.

def _computeDodecahedronVertices(faceVecList):
    """Given a vector of face positions of a Dodecahedron compute the vertices.
    """
    closeIndSetList = []
    vertexDict = {}
    for i in range(len(faceVecList)):
        closeIndSet = _findCloseIndexSet(faceVecList, i)
        if len(closeIndSet) != 5:
            raise RuntimeError("Found %s vertices instead of 5 near %s: %s" %
                               (len(closeIndSet), faceVecList[i], closeIndSet))
        closeIndSetList.append(closeIndSet)
    for i, iCloseIndSet in enumerate(closeIndSetList):
        for j in iCloseIndSet:
            jCloseIndSet = closeIndSetList[j]
            sharedCloseIndSet = iCloseIndSet.intersection(jCloseIndSet)
            if len(sharedCloseIndSet) != 2:
                raise RuntimeError("Found %s vertices instead of 2 near %s and %s: %s" %
                                   (len(sharedCloseIndSet), faceVecList[i], faceVecList[j],
                                    sharedCloseIndSet))
            for k in sharedCloseIndSet:
                key = frozenset((i, j, k))
                if key in vertexDict:
                    continue
                vertexVec = faceVecList[i] + faceVecList[j] + faceVecList[k]
                vertexVec /= numpy.sqrt(numpy.sum(vertexVec**2))
                vertexDict[key] = vertexVec
    return list(vertexDict.values())
 
 

_computeFullVecList()

lsst.skymap.detail.dodecahedron._computeFullVecList ( basisSet )

protected

Given a collection of basis vectors, compute all permutations with both
signs of all nonzero values.

For example::

    [(0, 1, 2)] -> [(0, 1, 2), (0, -1, 2), (0, 1, -2), (0, -1, -2)]

Definition at line 201 of file dodecahedron.py.

def _computeFullVecList(basisSet):
    """Given a collection of basis vectors, compute all permutations with both
    signs of all nonzero values.
 
    For example::
 
        [(0, 1, 2)] -> [(0, 1, 2), (0, -1, 2), (0, 1, -2), (0, -1, -2)]
    """
    fullSet = []
    for basisVec in basisSet:
        vecLen = math.sqrt(numpy.sum(numpy.array(basisVec)**2))
        valueList = []
        for basisValue in basisVec:
            if basisValue == 0:
                valueList.append((0,))
            else:
                valueList.append((basisValue, -basisValue))
        fullSet += list(numpy.array((x, y, z))/vecLen
                        for z in valueList[2]
                        for y in valueList[1]
                        for x in valueList[0]
                        )
    return fullSet
 
 

_findCloseIndexSet()

lsst.skymap.detail.dodecahedron._findCloseIndexSet ( vecList, ind )

protected

Given a list of cartesian vectors, return a set of indices of those
closest to one of them.

This is intended for regular grids where distances are quantized.

Parameters
----------
vecList : `list`
    List of cartesian vectors.
ind : `int`
    Index of vector to be nearest.

Definition at line 226 of file dodecahedron.py.

def _findCloseIndexSet(vecList, ind):
    """Given a list of cartesian vectors, return a set of indices of those
    closest to one of them.
 
    This is intended for regular grids where distances are quantized.
 
    Parameters
    ----------
    vecList : `list`
        List of cartesian vectors.
    ind : `int`
        Index of vector to be nearest.
    """
    dotProductList = numpy.round(numpy.dot(vecList, vecList[ind]), 2)
    dotProductList[ind] = -9e99
    minDist = numpy.max(dotProductList)
    indList = numpy.arange(len(dotProductList))[dotProductList == minDist]
    return set(indList)
 
 

_findCloseList()

lsst.skymap.detail.dodecahedron._findCloseList ( vecList, vec )

protected

Given a list of cartesian vectors, return all those closest to a
specified position

This is intended for regular grids where distances are quantized

Parameters
----------
vecList : `list`
    List of cartesian vectors.
vec : `iterable` of `float`
    Vector to be near.

Returns
-------
retList : `list`
    List of closest vectors.
indList : `list`
    List if indices of those vectors.

Definition at line 246 of file dodecahedron.py.

def _findCloseList(vecList, vec):
    """Given a list of cartesian vectors, return all those closest to a
    specified position
 
    This is intended for regular grids where distances are quantized
 
    Parameters
    ----------
    vecList : `list`
        List of cartesian vectors.
    vec : `iterable` of `float`
        Vector to be near.
 
    Returns
    -------
    retList : `list`
        List of closest vectors.
    indList : `list`
        List if indices of those vectors.
    """
    dotProductList = numpy.round(numpy.dot(vecList, vec), 2)
    minDist = numpy.max(dotProductList)
    indList = numpy.arange(len(dotProductList))[dotProductList == minDist]
    retList = numpy.take(vecList, indList, 0)
    return retList, indList
 
 

_findClosePair()

lsst.skymap.detail.dodecahedron._findClosePair ( vecList, ind = 0 )

protected

Given a list of cartesian vectors and an index, return the vector and
one of its closest neighbors.

Parameters
----------
vecList : `list` of `numpy.ndarray`
    List of cartesian vectors.
ind : `int`
    Index of first vector.

Definition at line 273 of file dodecahedron.py.

def _findClosePair(vecList, ind=0):
    """Given a list of cartesian vectors and an index, return the vector and
    one of its closest neighbors.
 
    Parameters
    ----------
    vecList : `list` of `numpy.ndarray`
        List of cartesian vectors.
    ind : `int`
        Index of first vector.
    """
    vec = vecList[ind]
    otherVecList = vecList[0:ind] + vecList[ind+1:]
    ind1 = numpy.argmax(numpy.dot(otherVecList, vec))
    return vec, otherVecList[ind1]
 
 

_sortedVectorList()

lsst.skymap.detail.dodecahedron._sortedVectorList ( vecList )

protected

Return a list of cartesian vectors sorted by decreasing latitude and
increasing longitude.

Definition at line 290 of file dodecahedron.py.

def _sortedVectorList(vecList):
    """Return a list of cartesian vectors sorted by decreasing latitude and
    increasing longitude.
    """
    def vecToSort(vec):
        ang = round(math.atan2(vec[1], vec[0]), 2)
        if ang < 0:
            ang += 2.0 * math.pi
        return (-round(vec[2], 1), ang, vec)
 
    decoratedList = [vecToSort(v) for v in vecList]
    decoratedList.sort()
    return [d[2] for d in decoratedList]
 
 

computeRotationMatrix()

lsst.skymap.detail.dodecahedron.computeRotationMatrix	(		angle,
			axis )

Return a 3D rotation matrix for rotation by a specified amount around a
specified axis.

Parameters
----------
angle : `float`
    Amount of rotation (rad).
axis : `int`
    Axis of rotation; one of 0, 1 or 2 for x, y or z.

Definition at line 116 of file dodecahedron.py.

def computeRotationMatrix(angle, axis):
    """Return a 3D rotation matrix for rotation by a specified amount around a
    specified axis.
 
    Parameters
    ----------
    angle : `float`
        Amount of rotation (rad).
    axis : `int`
        Axis of rotation; one of 0, 1 or 2 for x, y or z.
    """
    cosAng = math.cos(angle)
    sinAng = math.sin(angle)
    rotMat = numpy.zeros((3, 3), dtype=float)
    rotMat[axis, axis] = 1
    rotMat[(axis + 1) % 3, (axis + 1) % 3] = cosAng
    rotMat[(axis + 2) % 3, (axis + 1) % 3] = sinAng
    rotMat[(axis + 1) % 3, (axis + 2) % 3] = -sinAng
    rotMat[(axis + 2) % 3, (axis + 2) % 3] = cosAng
    return rotMat
 
 

Variable Documentation

faceVec

lsst.skymap.detail.dodecahedron.faceVec = vertexDodec.getFaceCtr(i)

Definition at line 311 of file dodecahedron.py.

linewidth

lsst.skymap.detail.dodecahedron.linewidth

Definition at line 306 of file dodecahedron.py.

precision

lsst.skymap.detail.dodecahedron.precision

Definition at line 306 of file dodecahedron.py.

suppress

lsst.skymap.detail.dodecahedron.suppress

Definition at line 306 of file dodecahedron.py.

True

lsst.skymap.detail.dodecahedron.True

Definition at line 306 of file dodecahedron.py.

vertexDodec

lsst.skymap.detail.dodecahedron.vertexDodec = Dodecahedron(withFacesOnPoles=False)

Definition at line 309 of file dodecahedron.py.