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87 lines
2.5 KiB
Python
87 lines
2.5 KiB
Python
# Titan Robotics Team 2022: CPU fitting models
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# Written by Dev Singh
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# Notes:
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# this module is cuda-optimized (as appropriate) and vectorized (except for one small part)
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# setup:
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__version__ = "0.0.2"
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# changelog should be viewed using print(analysis.fits.__changelog__)
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__changelog__ = """changelog:
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0.0.2:
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- renamed module to Fit
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0.0.1:
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- initial release, add circle fitting with LSC
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"""
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__author__ = (
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"Dev Singh <dev@devksingh.com>"
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)
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__all__ = [
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'CircleFit'
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]
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import numpy as np
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class CircleFit:
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"""Class to fit data to a circle using the Least Square Circle (LSC) method"""
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# For more information on the LSC method, see:
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# http://www.dtcenter.org/sites/default/files/community-code/met/docs/write-ups/circle_fit.pdf
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def __init__(self, x, y, xy=None):
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self.ournp = np #todo: implement cupy correctly
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if type(x) == list:
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x = np.array(x)
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if type(y) == list:
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y = np.array(y)
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if type(xy) == list:
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xy = np.array(xy)
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if xy != None:
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self.coords = xy
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else:
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# following block combines x and y into one array if not already done
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self.coords = self.ournp.vstack(([x.T], [y.T])).T
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def calc_R(x, y, xc, yc):
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"""Returns distance between center and point"""
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return self.ournp.sqrt((x-xc)**2 + (y-yc)**2)
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def f(c, x, y):
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"""Returns distance between point and circle at c"""
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Ri = calc_R(x, y, *c)
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return Ri - Ri.mean()
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def LSC(self):
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"""Fits given data to a circle and returns the center, radius, and variance"""
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x = self.coords[:, 0]
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y = self.coords[:, 1]
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# guessing at a center
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x_m = self.ournp.mean(x)
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y_m = self.ournp.mean(y)
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# calculation of the reduced coordinates
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u = x - x_m
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v = y - y_m
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# linear system defining the center (uc, vc) in reduced coordinates:
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# Suu * uc + Suv * vc = (Suuu + Suvv)/2
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# Suv * uc + Svv * vc = (Suuv + Svvv)/2
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Suv = self.ournp.sum(u*v)
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Suu = self.ournp.sum(u**2)
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Svv = self.ournp.sum(v**2)
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Suuv = self.ournp.sum(u**2 * v)
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Suvv = self.ournp.sum(u * v**2)
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Suuu = self.ournp.sum(u**3)
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Svvv = self.ournp.sum(v**3)
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# Solving the linear system
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A = self.ournp.array([ [ Suu, Suv ], [Suv, Svv]])
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B = self.ournp.array([ Suuu + Suvv, Svvv + Suuv ])/2.0
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uc, vc = self.ournp.linalg.solve(A, B)
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xc_1 = x_m + uc
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yc_1 = y_m + vc
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# Calculate the distances from center (xc_1, yc_1)
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Ri_1 = self.ournp.sqrt((x-xc_1)**2 + (y-yc_1)**2)
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R_1 = self.ournp.mean(Ri_1)
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# calculate residual error
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residu_1 = self.ournp.sum((Ri_1-R_1)**2)
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return (xc_1, yc_1, R_1, residu_1) |