def testWrap(self):
for wrap in (-1000, -10, -1, 0, 1, 10, 1000):
for offset in (-360, -180, -90, 0, 90, 180, 270, 360):
for epsMult in (-3, -2, -1, 0, 1, 2, 3):
ang = offset + (wrap * 360)
ang += ang * DoubleEpsilon * epsMult
sinAng = sind(ang)
cosAng = cosd(ang)
pvt = PVT(ang, ang, 35.0) # pick anything for vel and time
posAng = wrapPos(ang)
self.assertGreaterEqual(posAng, 0.0)
self.assertLess(posAng, 360.0)
# prove that posAng and ang are the same angle
# sin and cos are a sanity check on wrapCtr
self.assertAlmostEqual(wrapCtr(posAng - ang), 0)
self.assertAlmostEqual(sind(posAng), sinAng)
self.assertAlmostEqual(cosd(posAng), cosAng)
posPvt = wrapPos(pvt)
self.assertEqual(posPvt.pos, posAng)
self.assertEqual(posPvt.vel, pvt.vel)
self.assertEqual(posPvt.t, pvt.t)
ctrAng = wrapCtr(ang)
self.assertGreaterEqual(ctrAng, -180.0)
self.assertLess(ctrAng, 180.0)
# prove that ctrAng and ang are the same angle
self.assertAlmostEqual(wrapCtr(ctrAng - ang), 0)
self.assertAlmostEqual(sind(ctrAng), sinAng)
self.assertAlmostEqual(cosd(ctrAng), cosAng)
ctrPvt = wrapCtr(pvt)
self.assertEqual(ctrPvt.pos, ctrAng)
self.assertEqual(ctrPvt.vel, pvt.vel)
self.assertEqual(ctrPvt.t, pvt.t)
for refAngBase in (-180, 0, 180, 360):
for refEpsMult in (-3, -2, -1, 0, 1, 2, 3):
refAng = refAngBase
refAng += refAng * refEpsMult * DoubleEpsilon
nearAng = wrapNear(ang, refAng)
self.assertGreaterEqual(nearAng - refAng, -180)
self.assertLess(nearAng - refAng, 180)
# prove that nearAng and ang are the same angle
self.assertAlmostEqual(wrapCtr(nearAng - ang), 0)
self.assertAlmostEqual(sind(nearAng), sinAng)
self.assertAlmostEqual(cosd(nearAng), cosAng)
def testWrap(self):
for wrap in (-1000, -10, -1, 0, 1, 10, 1000):
for offset in (-360, -180, -90, 0, 90, 180, 270, 360):
for epsMult in (-3, -2, -1, 0, 1, 2, 3):
ang = offset + (wrap * 360)
ang += ang * DoubleEpsilon * epsMult
sinAng = sind(ang)
cosAng = cosd(ang)
pvt = PVT(ang, ang, 35.0) # pick anything for vel and time
posAng = wrapPos(ang)
self.assertGreaterEqual(posAng, 0.0)
self.assertLess(posAng, 360.0)
# prove that posAng and ang are the same angle
# sin and cos are a sanity check on wrapCtr
self.assertAlmostEqual(wrapCtr(posAng - ang), 0)
self.assertAlmostEqual(sind(posAng), sinAng)
self.assertAlmostEqual(cosd(posAng), cosAng)
posPvt = wrapPos(pvt)
self.assertEqual(posPvt.pos, posAng)
self.assertEqual(posPvt.vel, pvt.vel)
self.assertEqual(posPvt.t, pvt.t)
ctrAng = wrapCtr(ang)
self.assertGreaterEqual(ctrAng, -180.0)
self.assertLess(ctrAng, 180.0)
# prove that ctrAng and ang are the same angle
self.assertAlmostEqual(wrapCtr(ctrAng - ang), 0)
self.assertAlmostEqual(sind(ctrAng), sinAng)
self.assertAlmostEqual(cosd(ctrAng), cosAng)
ctrPvt = wrapCtr(pvt)
self.assertEqual(ctrPvt.pos, ctrAng)
self.assertEqual(ctrPvt.vel, pvt.vel)
self.assertEqual(ctrPvt.t, pvt.t)
for refAngBase in (-180, 0, 180, 360):
for refEpsMult in (-3, -2, -1, 0, 1, 2, 3):
refAng = refAngBase
refAng += refAng * refEpsMult * DoubleEpsilon
nearAng = wrapNear(ang, refAng)
self.assertGreaterEqual(nearAng - refAng, -180)
self.assertLess(nearAng - refAng, 180)
# prove that nearAng and ang are the same angle
self.assertAlmostEqual(wrapCtr(nearAng - ang), 0)
self.assertAlmostEqual(sind(nearAng), sinAng)
self.assertAlmostEqual(cosd(nearAng), cosAng)
def makePVTFromPair(posPair, tai, deltaT, isAngle):
pos = posPair[0]
if (isAngle):
vel = coordConv.wrapCtr(posPair[1] - posPair[0]) / deltaT
else:
vel = (posPair[1] - posPair[0]) / deltaT
return coordConv.PVT(pos, vel, tai)
def measureOrientationToErr():
"""Measure error in Coord.orientationTo for tiny offsets
For best results modify Coord::orientationTo to not short-circuit tiny values of sinVal, cosVal
"""
errDict = {} # dict of distArcSec: (max orient error, max(sinVal, cosVal))
for fromPolarAng in (-89, -72, -45.0, -30, 0.01, 12.5, 31, 47, 56, 68, 89):
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = coordConv.Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-90, -72, -45.0, -30, 0.01, 0, 12.5, 31, 45, 56, 68, 89):
# offset by such small distances that toOrient=fromOrient
# by 1e-6 the error is starting to go up, indicating that the approximation is failing
for distArcSec in (5e-5, 1e-4, 2e-4, 3e-4, 4e-4, 5e-4, 1e-3, 1e-2):
toCoord, dumToOrient = fromCoord.offset(fromOrient, distArcSec / 3600)
toOrient = coordConv.wrapCtr(180 + toCoord.orientationTo(fromCoord))
# expect fromOrient = toOrient
newErrArcSec = abs(toOrient - fromOrient) * 3600
oldErrArcSec = errDict.get(distArcSec, (0, 0))[0]
if newErrArcSec > oldErrArcSec:
toU = toCoord.getVecPos()
toU /= numpy.linalg.norm(toU)
fromU = fromCoord.getVecPos()
fromU /= numpy.linalg.norm(fromU)
sinVal = (toU[1] * fromU[0]) - (toU[0] * fromU[1])
cosVal = (toU[2] * ((fromU[0] * fromU[0]) + (fromU[1] * fromU[1]))) \
- (fromU[2] * ((toU[0] * fromU[0]) + (toU[1] * fromU[1])))
errDict[distArcSec] = (newErrArcSec, max(sinVal, cosVal))
distKeys = sorted(errDict.keys())
print "Note that by 0.01 arcsec the error creeps up, indicating that the approximation toOrient=fromOrient is failing"
for distArcSec in distKeys:
errArcSec, maxSinCos = errDict[distArcSec]
print "distArcSec=%0.3g arcsec, maxErr=%0.3g arcsec, maxSin/Cos=%0.3g" % (distArcSec, errArcSec, maxSinCos)
def makePVTFromPair(posPair, tai, deltaT, isAngle):
pos = posPair[0]
if (isAngle):
vel = coordConv.wrapCtr(posPair[1] - posPair[0]) / deltaT
else:
vel = (posPair[1] - posPair[0]) / deltaT
return coordConv.PVT(pos, vel, tai)
def refPolarFromXY(x, y, tai):
"""Reference implementation of PVT.polarFromXY
"""
atPole = False
rArr = []
thetaArr = []
for testTAI in (tai, tai + DeltaT):
ap, r, theta = coordConv.polarFromXY(x.getPos(testTAI), y.getPos(testTAI))
rArr.append(r)
thetaArr.append(theta)
atPole = atPole or ap
rPVT = coordConv.PVT()
rPVT.pos = rArr[0]
rPVT.vel = (rArr[1] - rArr[0]) / DeltaT
rPVT.t = tai
thetaPVT = coordConv.PVT()
thetaPVT.pos = thetaArr[0]
thetaPVT.vel = coordConv.wrapCtr(thetaArr[1] - thetaArr[0]) / DeltaT
thetaPVT.t = tai
return atPole, rPVT, thetaPVT
def measureOrientationToErr():
"""Measure error in Coord.orientationTo for tiny offsets
For best results modify Coord::orientationTo to not short-circuit tiny values of sinVal, cosVal
"""
errDict = {} # dict of distArcSec: (max orient error, max(sinVal, cosVal))
for fromPolarAng in (-89, -72, -45.0, -30, 0.01, 12.5, 31, 47, 56, 68, 89):
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = coordConv.Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-90, -72, -45.0, -30, 0.01, 0, 12.5, 31, 45, 56,
68, 89):
# offset by such small distances that toOrient=fromOrient
# by 1e-6 the error is starting to go up, indicating that the approximation is failing
for distArcSec in (5e-5, 1e-4, 2e-4, 3e-4, 4e-4, 5e-4, 1e-3,
1e-2):
toCoord, dumToOrient = fromCoord.offset(
fromOrient, distArcSec / 3600)
toOrient = coordConv.wrapCtr(
180 + toCoord.orientationTo(fromCoord))
# expect fromOrient = toOrient
newErrArcSec = abs(toOrient - fromOrient) * 3600
oldErrArcSec = errDict.get(distArcSec, (0, 0))[0]
if newErrArcSec > oldErrArcSec:
toU = toCoord.getVecPos()
toU /= numpy.linalg.norm(toU)
fromU = fromCoord.getVecPos()
fromU /= numpy.linalg.norm(fromU)
sinVal = (toU[1] * fromU[0]) - (toU[0] * fromU[1])
cosVal = (toU[2] * ((fromU[0] * fromU[0]) + (fromU[1] * fromU[1]))) \
- (fromU[2] * ((toU[0] * fromU[0]) + (toU[1] * fromU[1])))
errDict[distArcSec] = (newErrArcSec,
max(sinVal, cosVal))
distKeys = sorted(errDict.keys())
print "Note that by 0.01 arcsec the error creeps up, indicating that the approximation toOrient=fromOrient is failing"
for distArcSec in distKeys:
errArcSec, maxSinCos = errDict[distArcSec]
print "distArcSec=%0.3g arcsec, maxErr=%0.3g arcsec, maxSin/Cos=%0.3g" % (
distArcSec, errArcSec, maxSinCos)