127 lines
5.1 KiB
Python
127 lines
5.1 KiB
Python
import csv
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import math
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import numpy as np
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class bilinearInterpolator():
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"""
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This class takes a collection of 3-dimensional points from a .csv file.
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It contains a bilinear interpolator to find unknown points within the grid.
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"""
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@property
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def probedGrid(self):
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return self._probedGrid
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"""
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Constructor takes a file with a .csv extension and creates an evenly-spaced 'ideal' grid from the data points.
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This is done to get around any floating point errors that may exist in the data
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"""
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def __init__(
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self,
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pointsFile
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):
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self.pointsFile = pointsFile
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self.points = np.loadtxt(self.pointsFile, delimiter=',')
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self.xMin, self.xMax, self.xSpacing, self.xCount = self._axisParams(0)
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self.yMin, self.yMax, self.ySpacing, self.yCount = self._axisParams(1)
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# generate ideal grid to match actually probed points -- this is due to floating-point error issues
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idealGrid = ([
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[(x,y) for x in np.linspace(self.xMin,self.xMax,self.xCount, True)]
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for y in np.linspace(self.yMin,self.yMax,self.yCount, True)
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])
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self._probedGrid = [[0] * self.yCount for i in range(0, self.xCount)]
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# align ideal grid indices with probed data points
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for rowIndex, row in enumerate(idealGrid):
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for colIndex, idealPoint in enumerate(row):
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minSqDist = math.inf
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for probed in self.points:
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# find closest point in ideal grid that corresponds to actual tested point
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# put z value in correct index
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sqDist = pow(probed[0] - idealPoint[0], 2) + pow(probed[1] - idealPoint[1],2)
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if sqDist <= minSqDist:
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minSqDist = sqDist
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indexX = rowIndex
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indexY = colIndex
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closestProbed = probed
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self.probedGrid[indexY][indexX] = closestProbed
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"""
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Bilinear interpolation method to determine unknown z-values within grid of known z-values.
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NOTE: If one axis is outside the grid, linear interpolation is used instead.
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If both axes are outside of the grid, the z-value of the closest corner of the grid is returned.
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"""
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def Interpolate(self, point):
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lin = False
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if point[0] < self.xMin:
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ix1 = 0
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lin = True
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elif point[0] > self.xMax:
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ix1 = self.xCount-1
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lin = True
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else:
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ix1 = math.floor((point[0] - self.xMin)/self.xSpacing)
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ix2 = math.ceil((point[0] - self.xMin)/self.xSpacing)
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def interpolatePoint(p1, p2, p, axis):
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return (p2[2]*(p[axis] - p1[axis]) + p1[2]*(p2[axis] - p[axis]))/(p2[axis] - p1[axis])
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if point[1] < self.yMin:
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if lin:
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return self.probedGrid[ix1][0][2]
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return interpolatePoint(self.probedGrid[ix1][0], self.probedGrid[ix2][0], point, 0)
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elif point[1] > self.yMax:
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if lin:
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return self.probedGrid[ix1][self.yCount - 1][2]
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return interpolatePoint(self.probedGrid[ix1][self.yCount - 1], self.probedGrid[ix2][self.yCount - 1], point, 0)
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else:
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iy1 = math.floor((point[1] - self.yMin)/self.ySpacing)
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iy2 = math.ceil((point[1] - self.yMin)/self.ySpacing)
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#if x was at an extrema, but y was not, perform linear interpolation on x axis
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if lin:
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return interpolatePoint(self.probedGrid[ix1][iy1], self.probedGrid[ix1][iy2], point, 1)
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def specialDiv(a, b):
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if b == 0:
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return 0.5
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else:
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return a/b
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x1 = self.probedGrid[ix1][iy1][0]
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x2 = self.probedGrid[ix2][iy1][0]
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y1 = self.probedGrid[ix2][iy1][1]
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y2 = self.probedGrid[ix2][iy2][1]
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Q11 = self.probedGrid[ix1][iy1][2]
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Q12 = self.probedGrid[ix1][iy2][2]
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Q21 = self.probedGrid[ix2][iy1][2]
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Q22 = self.probedGrid[ix2][iy2][2]
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r1 = specialDiv(point[0]-x1, x2-x1)*Q21 + specialDiv(x2-point[0], x2-x1)*Q11
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r2 = specialDiv(point[0]-x1, x2-x1)*Q22 + specialDiv(x2-point[0], x2-x1)*Q12
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p = specialDiv(point[1]-y1, y2-y1)*r2 + specialDiv(y2-point[1], y2-y1)*r1
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return p
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# Returns the min, max, spacing and size of one axis of the 2D grid
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def _axisParams(self, sortAxis):
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# sort the set and eliminate the previous, unsorted set
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srtSet = sorted(self.points, key=lambda x: x[sortAxis])
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dists = []
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for item0, item1 in zip(srtSet[:(len(srtSet)-2)], srtSet[1:]):
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dists.append(float(item1[sortAxis]) - float(item0[sortAxis]))
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axisSpacing = max(dists)
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# add an extra one for axisCount to account for the starting point
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axisMin = float(min(srtSet, key=lambda x: x[sortAxis])[sortAxis])
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axisMax = float(max(srtSet, key=lambda x: x[sortAxis])[sortAxis])
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axisRange = axisMax - axisMin
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axisCount = round((axisRange/axisSpacing) + 1)
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return axisMin, axisMax, axisSpacing, axisCount |