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SFCIndex.py
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SFCIndex.py
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'''
Author: Neeraj Sirdeshmukh
Delft University Of Technology, Netherlands, 2018
'''
import math
from math import *
from pyproj import *
from laspy.file import File
import numpy as np
import time
import pandas
import os
import psycopg2
from psycopg2.extras import *
from io import StringIO
class isea_pt(object):
def __init__(self, x, y):
self.x = x
self.y = y
class isea_geo(object):
# in radians
def __init__(self, lon, lat):
self.lon = lon
self.lat = lat
# Set constants
M_PI = 3.14159265358979323846
E = 52.62263186
F = 10.81231696
DEG60 =1.04719755119659774614
DEG120= 2.09439510239319549229
DEG72 =1.25663706143591729537
DEG90 =1.57079632679489661922
DEG144= 2.51327412287183459075
DEG36 =0.62831853071795864768
DEG108 =1.88495559215387594306
DEG180= M_PI
ISEA_SCALE=0.8301572857837594396028083
# Degrees: 26.565051177065900134
V_LAT = 0.46364760899944494524
RAD2DEG = 180.0/M_PI
DEG2RAD = M_PI/180.0
# Icosahedron constants, radians
g =37.37736814 * DEG2RAD
G =36.0 * DEG2RAD
theta =30.0 * DEG2RAD
# vertices of triangles
vertex = [isea_geo(0.0,DEG90),
isea_geo(DEG180,V_LAT),
isea_geo(-DEG108,V_LAT),
isea_geo(-DEG36,V_LAT),
isea_geo(DEG36,V_LAT),
isea_geo(DEG108,V_LAT),
isea_geo(-DEG144,-V_LAT),
isea_geo(-DEG72,-V_LAT),
isea_geo(0.0,-V_LAT),
isea_geo(DEG72,-V_LAT),
isea_geo(DEG144,-V_LAT),
isea_geo(0.0,-DEG90)
]
E_RAD =0.91843818702186776133
F_RAD =0.18871053072122403508
# icosahedron triangle centers
icostriangles = [
isea_geo(0.0, 0.0),
isea_geo(-DEG144, E_RAD),
isea_geo(-DEG72, E_RAD),
isea_geo(0.0, E_RAD),
isea_geo(DEG72, E_RAD),
isea_geo(DEG144, E_RAD),
isea_geo(-DEG144, F_RAD),
isea_geo(-DEG72, F_RAD),
isea_geo(0.0, F_RAD),
isea_geo(DEG72, F_RAD),
isea_geo(DEG144, F_RAD),
isea_geo(-DEG108, -F_RAD),
isea_geo(-DEG36, -F_RAD),
isea_geo(DEG36, -F_RAD),
isea_geo(DEG108, -F_RAD),
isea_geo(DEG180, -F_RAD),
isea_geo(-DEG108, -E_RAD),
isea_geo(-DEG36, -E_RAD),
isea_geo(DEG36, -E_RAD),
isea_geo(DEG108, -E_RAD),
isea_geo(DEG180, -E_RAD)
]
# Parameters taken from Snyder (1992)
TABLE_G = 0.6615845383
TABLE_H = 0.1909830056
RPRIME = 0.91038328153090290025
tri_v1 = [0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 2, 3, 4, 5, 1, 11, 11, 11, 11, 11]
NEWORIGX = -0.6022955012659694 # TABLE_G * (-1) #old:
NEWORIGY = -0.3477354703761901 # TABLE_H * (-2) #old:
TANTHETA = tan(theta)
COTTHETA = 1.0 / TANTHETA
SINUPPERG = sin(G)
COSUPPERG = cos(G)
COSLOWERG = cos(g)
TANLOWERG = tan(g)
# parameters for WGS84 ellipsoid
R = 6378137 # semi-major axis, meters
b = 6356752.314245 # semi-minor axis, meters
flattening = 1/298.257223563
def az_adjustment(triangle):
v = vertex[tri_v1[triangle]] # vertex ID of triangle
c = icostriangles[triangle] # center of triangle
# Azimuth from vertex to center of triangle
adj = atan2(cos(v.lat) * sin(v.lon - c.lon),cos(c.lat) * sin(v.lat)- sin(c.lat) * cos(v.lat) * cos(v.lon - c.lon))
return adj
def isea_snyder_forward(ll):
for i in range(1,21):
center = icostriangles[i];
# step 1 , returns z(scaled meters) and Az (in radians)
z, Az = vincentyInverse(center.lat, center.lon, ll.lat, ll.lon)
if (Az > M_PI):
Az = Az - (2*M_PI)
# not on this triangle
if (z > g):
continue
# step 2
# This calculates a vertex coordinate whose azimuth is going to be assigned 0
az_offset = az_adjustment(i)
# This gives that vertex an azimuth of 0. For south pointing triangles the range of azimuths changes
# from [-3.14 - 3.14] to [-6.28 0].
# For north pointing triangles, makes no difference.
Az -= az_offset
# Adjust Az to fall between 0 and 120 degrees, record adjustment amount
Az_adjust_multiples = 0;
while Az < 0.0:
Az += DEG120
Az_adjust_multiples-=1
while (Az > DEG120):
Az -= DEG120
Az_adjust_multiples+=1
# Calculate q from eq 9.
q = atan(TANLOWERG/(cos(Az) + (sin(Az)*COTTHETA)))
# not in this triangle
if (z > q):
continue
# Apply equations 5-8 and 10-12 in order
# eq 6
H = acos((sin(Az) * SINUPPERG * COSLOWERG) - (cos(Az) * COSUPPERG))
#eq 7
AG = (Az + G + H - DEG180)
# eq 8
Azprime = atan2((2.0 * AG), ((RPRIME * RPRIME* TANLOWERG * TANLOWERG) - (2.0 * AG * COTTHETA)))
# eq 10
dprime = (RPRIME * TANLOWERG) / (cos(Azprime) + (sin(Azprime) * COTTHETA))
# eq 11
f = dprime / (2.0 * RPRIME * sin(q / 2.0))
# eq 12
rho = 2.0 * RPRIME * f * sin(z / 2.0)
#add back the same 120 degree multiple adjustment from step 2 to Azprime
Azprime += DEG120 * Az_adjust_multiples
# calculate rectangular coordinates
x = rho * sin(Azprime)
y = rho * cos(Azprime)
out = isea_pt(x,y)
return out, i
def computeMorton2D(longitude, latitude, res):
point = isea_geo(longitude * DEG2RAD, latitude * DEG2RAD)
# out contains coordinates from center of triangle
out, face = isea_snyder_forward(point)
# Find new coordinates of point from lower left/upper left origin
newPointX = 0
newPointY= 0
if ((face >= 1 and face <=5) or (face>=11 and face <=15)):
newPointX = out.x - NEWORIGX
newPointY = out.y - NEWORIGY
else:
newPointX = (out.x + NEWORIGX) * (-1)
newPointY = (out.y - NEWORIGY) * (-1)
# Rotate the axes, round down to nearest integer since addressing begins at 0
# Scale coordinates of all dimensions to match resolution of DGGS
origX = ((newPointX - ((1/(sqrt(3))) * newPointY)) /(NEWORIGX *(-2))) * totRange
origY = ((newPointX + ((1/(sqrt(3))) * newPointY))/(NEWORIGX *(-2))) * totRange
rotatedX = int(origX)
rotatedY = int(origY)
# Convert to binary
xBin = ('{0:0' + str(res) + 'b}').format(rotatedX)
yBin = ('{0:0' + str(res) + 'b}').format(rotatedY)
# Convert binary to int and use Morton formula
morton = ('{0:0' + str(res) + '}').format(2 * int(yBin) + int(xBin))
# Convert triangle face number to rhombus face number
if face == 1 or face == 6:
face = 0
elif face == 11 or face == 16:
face = 1
elif face == 2 or face == 7:
face = 2
elif face == 12 or face == 17:
face = 3
elif face == 3 or face == 8:
face = 4
elif face == 13 or face == 18:
face = 5
elif face == 4 or face == 9:
face = 6
elif face == 14 or face == 19:
face = 7
elif face == 5 or face == 10:
face = 8
else:
face = 9
fullCode = str(face) + morton
return fullCode
def computeMorton3D(longitude, latitude, height, hrange, res):
point = isea_geo(longitude * DEG2RAD, latitude * DEG2RAD)
#out contains coordinates from center of triangle
out, face = isea_snyder_forward(point)
# Find new coordinates of point from lower left/upper left origin
newPointX = 0
newPointY= 0
if ((face >= 1 and face <=5) or (face>=11 and face <=15)):
newPointX = out.x - NEWORIGX
newPointY = out.y - NEWORIGY
else:
newPointX = (out.x + NEWORIGX) * (-1)
newPointY = (out.y - NEWORIGY) * (-1)
# Rotate the axes, round down to nearest integer since addressing begins at 0
# Scale coordinates of all dimensions to match resolution of DGGS
origX = ((newPointX - ((1/(sqrt(3))) * newPointY)) /(NEWORIGX *(-2))) * totRange
origY = ((newPointX + ((1/(sqrt(3))) * newPointY))/(NEWORIGX *(-2))) * totRange
Z = 0
if height <=0:
Z = ((hrange - ((-1) * height)) / (hrange * 2)) * totRange
else:
Z = ((hrange + height) / (hrange * 2)) * totRange
rotatedX = int(origX)
rotatedY = int(origY)
intZ = int(Z)
# Convert to binary
xBin = ('{0:0' + str(res) + 'b}').format(rotatedX)
yBin = ('{0:0' + str(res) + 'b}').format(rotatedY)
zBin = ('{0:0' + str(res) + 'b}').format(intZ)
# Convert binary to int and use Morton formula
morton = ('{0:0' + str(res) + '}').format(4 * int(zBin) + 2 * int(yBin) + int(xBin))
# Convert triangle face number to rhombus face number
if face == 1 or face == 6:
face = 0
elif face == 11 or face == 16:
face = 1
elif face == 2 or face == 7:
face = 2
elif face == 12 or face == 17:
face = 3
elif face == 3 or face == 8:
face = 4
elif face == 13 or face == 18:
face = 5
elif face == 4 or face == 9:
face = 6
elif face == 14 or face == 19:
face = 7
elif face == 5 or face == 10:
face = 8
else:
face = 9
fullCode = str(face) + morton
return fullCode
def computeMorton4D(longitude, latitude, height, timeSec, hrange, trange, res):
point = isea_geo(longitude * DEG2RAD, latitude * DEG2RAD)
#out contains coordinates from center of triangle
out, face = isea_snyder_forward(point)
# Find new coordinates of point from lower left/upper left origin
newPointX = 0
newPointY= 0
if ((face >= 1 and face <=5) or (face>=11 and face <=15)):
newPointX = out.x - NEWORIGX
newPointY = out.y - NEWORIGY
else:
newPointX = (out.x + NEWORIGX) * (-1)
newPointY = (out.y - NEWORIGY) * (-1)
# Rotate the axes, round down to nearest integer since addressing begins at 0
# Scale coordinates of all dimensions to match resolution of DGGS
origX = ((newPointX - ((1/(sqrt(3))) * newPointY)) /(NEWORIGX *(-2))) * totRange
origY = ((newPointX + ((1/(sqrt(3))) * newPointY))/(NEWORIGX *(-2))) * totRange
Z = 0
if height <=0:
Z = ((hrange - ((-1) * height)) / (hrange * 2)) * totRange
else:
Z = ((hrange + height) / (hrange * 2)) * totRange
# Subtract 18 seconds to get UTC time
T = ((timeSec - 18)/trange) * totRange
rotatedX = int(origX)
rotatedY = int(origY)
intZ = int(Z)
intT = int(T)
# Convert to binary
xBin = ('{0:0' + str(res) + 'b}').format(rotatedX)
yBin = ('{0:0' + str(res) + 'b}').format(rotatedY)
zBin = ('{0:0' + str(res) + 'b}').format(intZ)
tBin = ('{0:0' + str(res) + 'b}').format(intT)
tVal = int('0'.join(str(8 * int(tBin))))
zVal = int('0'.join(str(4 * int(zBin))))
yVal = int('0'.join(str(2 * int(yBin))))
xVal = int('0'.join(str(int(xBin))))
total = tVal + zVal + yVal + xVal
# Convert binary to int and use Morton formula
# Drop 0 (if any) after face number to save 1 bit!
morton3D = ('{0:0' + str(res) + '}').format(4 * int(zBin) + 2 * int(yBin) + int(xBin))
morton4D = ('{0:0' + str((2* res)) + '}').format(total)
# Convert triangle face number to rhombus face number
if face == 1 or face == 6:
face = 0
elif face == 11 or face == 16:
face = 1
elif face == 2 or face == 7:
face = 2
elif face == 12 or face == 17:
face = 3
elif face == 3 or face == 8:
face = 4
elif face == 13 or face == 18:
face = 5
elif face == 4 or face == 9:
face = 6
elif face == 14 or face == 19:
face = 7
elif face == 5 or face == 10:
face = 8
else:
face = 9
fullCode4D = str(face) + morton4D
fullCode3D = str(face) + morton3D
return fullCode4D, fullCode3D
def decodeMortonToXY(mortonCode):
# Get face number and morton code
face = mortonCode[0] # First number indicates rhombus face!
morton = mortonCode[1:len(mortonCode)] # String
res = len(morton) #discrete!
lastDig = int(morton[-1:])
numXValues = totRange # Amount of possible X values
numYValues = totRange # Amount of possible Y values
# Compute the X, Y, and Z values on rhombus... markers = middle value
xMarker = numXValues/2
yMarker = numYValues/2
for i in range(res-1):
if (int(morton[i]) %2 ==0):
numXValues = numXValues/2
xMarker = xMarker - numXValues/2
else:
numXValues = numXValues/2
xMarker = xMarker + numXValues/2
if (int(morton[i]) <= 1):
numYValues = numYValues/2
yMarker = yMarker - numYValues/2
else:
numYValues = numYValues/2
yMarker = yMarker + numYValues/2
# Look at last digit
if lastDig %2 ==0:
xMarker = (xMarker - 1)
else:
xMarker = (xMarker)
if lastDig <=1:
yMarker = (yMarker -1)
else:
yMarker = (yMarker)
return (xMarker,yMarker,int(face), res)
def decodeMortonToXYH(mortonCode):
# Get face number and Morton code
face = mortonCode[0] # First number indicates rhombus face!
morton = mortonCode[1:len(mortonCode)] # String
res = len(morton) # discrete!
lastDig = int(morton[-1:])
numXValues = totRange # Amount of possible X values
numYValues = totRange # Amount of possible Y values
numZValues = totRange # Amount of possible Z values
# Compute the X, Y, and Z values on rhombus... markers = middle value
xMarker = numXValues/2
yMarker = numYValues/2
zMarker = numZValues/2
yVals = [0,1,4,5]
for i in range(res-1):
if (int(morton[i]) %2 ==0):
numXValues = numXValues/2
xMarker = xMarker - numXValues/2
else:
numXValues = numXValues/2
xMarker = xMarker + numXValues/2
if (int(morton[i]) in yVals):
numYValues = numYValues/2
yMarker = yMarker - numYValues/2
else:
numYValues = numYValues/2
yMarker = yMarker + numYValues/2
if (int(morton[i]) <= 3):
numZValues = numZValues/2
zMarker = zMarker - numZValues/2
else:
numZValues = numZValues/2
zMarker = zMarker + numZValues/2
# Look at last digit
if lastDig %2 ==0: # 0,2
xMarker = (xMarker - 1)
else:
xMarker = (xMarker)
if lastDig in yVals:
yMarker = (yMarker -1)
else:
yMarker = (yMarker)
if lastDig <= 3:
zMarker = (zMarker -1)
else:
zMarker = (zMarker)
return (xMarker,yMarker, zMarker, int(face), res)
def decodeMortonToXYHT(mortonCode):
# Get face number and morton code
face = mortonCode[0] # First number indicates rhombus face!
morton = mortonCode[1:len(mortonCode)] # String
res = len(morton) /2
lastDig = int(morton[-2:])
numXValues = totRange # Amount of possible X values
numYValues = totRange# Amount of possible Y values
numZValues = totRange # Amount of possible Z values
numTValues = totRange # Amount of possible T values
# Compute the X, Y, Z, and T values on rhombus... markers = middle value
xMarker = numXValues/2
yMarker = numYValues/2
zMarker = numZValues/2
tMarker = numTValues/2
yVals = [0,1,4,5,8,9,12,13]
zVals = [0,1,2,3,8,9,10,11]
for i in range(res-1):
i = i * 2
if (int(morton[i:i+2]) %2 ==0):
numXValues = numXValues/2
xMarker = xMarker - numXValues/2
else:
numXValues = numXValues/2
xMarker = xMarker + numXValues/2
if (int(morton[i:i+2]) in yVals):
numYValues = numYValues/2
yMarker = yMarker - numYValues/2
else:
numYValues = numYValues/2
yMarker = yMarker + numYValues/2
if (int(morton[i:i+2]) in zVals):
numZValues = numZValues/2
zMarker = zMarker - numZValues/2
else:
numZValues = numZValues/2
zMarker = zMarker + numZValues/2
if (int(morton[i:i+2]) <= 7):
numTValues = numTValues/2
tMarker = tMarker - numTValues/2
else:
numTValues = numTValues/2
tMarker = tMarker + numTValues/2
# Look at last digit
if lastDig %2 ==0:
xMarker = (xMarker - 1)
else:
xMarker = (xMarker)
if lastDig in yVals:
yMarker = (yMarker -1)
else:
yMarker = (yMarker)
if lastDig in zVals:
zMarker = (zMarker -1)
else:
zMarker = (zMarker)
if lastDig <=7:
tMarker = (tMarker -1)
else:
tMarker = (tMarker)
return (xMarker,yMarker, zMarker, tMarker, int(face), res)
def MortonToLatLong2D(x,y, face, res):
# Scale coordinates to scale of Cartesian system
scaledX = (x/totRange) * (-NEWORIGX *2)
scaledY = (y/totRange)*(-NEWORIGX*2)
# Convert coordinates from skewed system to Cartesian system (origin at left)
a = np.array([[1,(-1/sqrt(3))], [1,(1/sqrt(3))]])
b = np.array([scaledX,scaledY])
x = np.linalg.solve(a, b)
xCoord = x[0]
yCoord = x[1]
# Get triangle face from rhombus face based on values of y.
# If y is negative, triangles will be downward oriented
if yCoord >=0:
if (face == 0):
face = 1
elif (face == 1):
face = 11
elif (face == 2):
face = 2
elif (face == 3):
face = 12
elif (face == 4):
face = 3
elif (face == 5):
face = 13
elif (face == 6):
face = 4
elif (face == 7):
face = 14
elif (face == 8):
face = 5
elif (face == 9):
face = 15
else:
if (face == 0):
face = 6
elif (face == 1):
face = 16
elif (face == 2):
face = 7
elif (face == 3):
face = 17
elif (face == 4):
face = 8
elif (face == 5):
face = 18
elif (face == 6):
face = 9
elif (face == 7):
face = 19
elif (face == 8):
face = 10
elif (face == 9):
face = 20
# Translate coordinates to center (origin) of icosahedron triangle,
# taking into account triangle orientation
xOrigin = 0
yOrigin = 0
if ((face >= 1 and face <=5) or (face>=11 and face <=15)):
xOrigin = ((-NEWORIGX) - xCoord) * (-1)
yOrigin = ((-NEWORIGY) - yCoord) * (-1)
else:
xOrigin = (-NEWORIGX) - xCoord
yOrigin = ((-NEWORIGY) + yCoord) * (-1)
# Equation 17
Azprime = atan2(xOrigin, yOrigin)
# Equation 18
rho = sqrt((pow(xOrigin,2) + pow(yOrigin,2)))
# Adjust Azprime to fall within 0 to 120 degrees
Azprime_adjust_multiples = 0;
while Azprime < 0.0:
Azprime += DEG120
Azprime_adjust_multiples-=1
while (Azprime > DEG120):
Azprime -= DEG120
Azprime_adjust_multiples+=1
AzprimeCopy = Azprime
# Equation 19
AG = (pow(RPRIME,2) * pow(TANLOWERG,2)) / (2 * ((1/(tan(Azprime))) + COTTHETA))
# Iteration, Azprime (plane) converges to Az (sphere)
for i in range(4):
H = acos((sin(Azprime) * SINUPPERG * COSLOWERG) - (cos(Azprime) * COSUPPERG))
FAZ = (AG - G - H - Azprime + DEG180)
FPRIMEAZ = (((cos(Azprime) * SINUPPERG * COSLOWERG) + (sin(Azprime) * COSUPPERG)) / (sin(H))) - 1
DeltaAzprime = -FAZ/(FPRIMEAZ)
Azprime = Azprime + DeltaAzprime
Az = Azprime
# Equations 9-11, 23 to obtain z
q = atan((TANLOWERG)/(cos(Az) + (sin(Az)*COTTHETA)))
# eq 10
dprime = ((RPRIME * TANLOWERG) / (cos(AzprimeCopy) + (sin(AzprimeCopy) * COTTHETA)))
# eq 11
f = dprime / (2.0 * RPRIME * sin(q / 2.0))
# eq 23, obtain z
z = 2 * asin((rho)/(2*RPRIME*f))
# Add back 120 degree adjustments to Az
Az += DEG120 * Azprime_adjust_multiples
# Adjust Az to be clockwise from north (needed for final calculation)
if (face >=1 and face<=5) or (face>=11 and face<=15):
if (Az <0):
Az = (M_PI - (Az * (-1))) + M_PI
else:
if (Az <0):
Az = M_PI - (Az * (-1))
else:
Az = Az + M_PI
z = z * R
# triangle center
center = icostriangles[face]
lat2, lon2 = vincentyDirect(flattening, R, center.lat * RAD2DEG, center.lon * RAD2DEG, Az * RAD2DEG, z)
return lat2, lon2
def MortonToLatLong3D(x,y,h,face, res):
# Convert h/Z to height above/below ellipsoid
height = ((-1) * hrange) + ((h / totRange) * (2 * hrange))
# Scale coordinates to scale of Cartesian system
scaledX = (x/totRange) * (-NEWORIGX *2)
scaledY = (y/totRange)*(-NEWORIGX*2)
# Convert coordinates from skewed system to Cartesian system (origin at left)
a = np.array([[1,(-1/sqrt(3))], [1,(1/sqrt(3))]])
b = np.array([scaledX,scaledY])
x = np.linalg.solve(a, b)
xCoord = x[0]
yCoord = x[1]
# Get triangle face from rhombus face based on values of y.
# If y is negative, triangles will be downward oriented
if yCoord >=0:
if (face == 0):
face = 1
elif (face == 1):
face = 11
elif (face == 2):
face = 2
elif (face == 3):
face = 12
elif (face == 4):
face = 3
elif (face == 5):
face = 13
elif (face == 6):
face = 4
elif (face == 7):
face = 14
elif (face == 8):
face = 5
elif (face == 9):
face = 15
else:
if (face == 0):
face = 6
elif (face == 1):
face = 16
elif (face == 2):
face = 7
elif (face == 3):
face = 17
elif (face == 4):
face = 8
elif (face == 5):
face = 18
elif (face == 6):
face = 9
elif (face == 7):
face = 19
elif (face == 8):
face = 10
elif (face == 9):
face = 20
# Translate coordinates to center (origin) of icosahedron triangle,
# taking into account triangle orientation
xOrigin = 0
yOrigin = 0
if ((face >= 1 and face <=5) or (face>=11 and face <=15)):
xOrigin = ((-NEWORIGX) - xCoord) * (-1)
yOrigin = ((-NEWORIGY) - yCoord) * (-1)
else:
xOrigin = (-NEWORIGX) - xCoord
yOrigin = ((-NEWORIGY) + yCoord) * (-1)
# Equation 17
Azprime = atan2(xOrigin, yOrigin)
# Equation 18
rho = sqrt((pow(xOrigin,2) + pow(yOrigin,2)))
# Adjust Azprime to fall within 0 to 120 degrees
Azprime_adjust_multiples = 0;
while Azprime < 0.0:
Azprime += DEG120
Azprime_adjust_multiples-=1
while (Azprime > DEG120):
Azprime -= DEG120
Azprime_adjust_multiples+=1
AzprimeCopy = Azprime
#Equation 19
AG = (pow(RPRIME,2) * pow(TANLOWERG,2)) / (2 * ((1/(tan(Azprime))) + COTTHETA))
# Iteration, Azprime (plane) converges to Az (ellipsoid)
for i in range(4):
H = acos((sin(Azprime) * SINUPPERG * COSLOWERG) - (cos(Azprime) * COSUPPERG))
FAZ = (AG - G - H - Azprime + DEG180)
FPRIMEAZ = (((cos(Azprime) * SINUPPERG * COSLOWERG) + (sin(Azprime) * COSUPPERG)) / (sin(H))) - 1
DeltaAzprime = -FAZ/(FPRIMEAZ)
Azprime = Azprime + DeltaAzprime
Az = Azprime
# Equations 9-11, 23 to obtain z
q = atan((TANLOWERG)/(cos(Az) + (sin(Az)*COTTHETA)))
# eq 10
dprime = ((RPRIME * TANLOWERG) / (cos(AzprimeCopy) + (sin(AzprimeCopy) * COTTHETA)))
# eq 11
f = dprime / (2.0 * RPRIME * sin(q / 2.0))
#eq 23, obtain z
z = 2 * asin((rho)/(2*RPRIME*f))
# Add back 120 degree adjustments to Az
Az += DEG120 * Azprime_adjust_multiples
# Adjust Az to be clockwise from north (needed for final calculation)
if (face >=1 and face<=5) or (face>=11 and face<=15):
if (Az <0):
Az = (M_PI - (Az * (-1))) + M_PI
else:
if (Az <0):
Az = M_PI - (Az * (-1))
else:
Az = Az + M_PI
z = z * R
# triangle center
center = icostriangles[face]
lat2, lon2 = vincentyDirect(flattening, R, center.lat * RAD2DEG, center.lon * RAD2DEG, Az * RAD2DEG, z)
return lat2, lon2, height
def MortonToLatLong4D(x,y,h,t, face, res):
# Convert h to height above sphere/ellipsoid
height = ((-1) * hrange) + ((h / totRange) * (2 * hrange))