Remove notebooks for the time being; they are still in history
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from __future__ import print_function
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from numpy import *
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# evaluates cubic bezier at t, return point
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def q(ctrlPoly, t):
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return (1.0-t)**3 * ctrlPoly[0] + 3*(1.0-t)**2 * t * ctrlPoly[1] + 3*(1.0-t)* t**2 * ctrlPoly[2] + t**3 * ctrlPoly[3]
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# evaluates cubic bezier first derivative at t, return point
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def qprime(ctrlPoly, t):
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return 3*(1.0-t)**2 * (ctrlPoly[1]-ctrlPoly[0]) + 6*(1.0-t) * t * (ctrlPoly[2]-ctrlPoly[1]) + 3*t**2 * (ctrlPoly[3]-ctrlPoly[2])
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# evaluates cubic bezier second derivative at t, return point
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def qprimeprime(ctrlPoly, t):
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return 6*(1.0-t) * (ctrlPoly[2]-2*ctrlPoly[1]+ctrlPoly[0]) + 6*(t) * (ctrlPoly[3]-2*ctrlPoly[2]+ctrlPoly[1])
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import numpy as np
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import csv
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import matplotlib.pyplot as plt
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def import_csv_data(filename):
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stylus_x = []
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stylus_y = []
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stylus_pressure = []
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time = []
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with open(filename) as csv_fp:
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reader = csv.reader(csv_fp)
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next(reader) # skip header
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for row in reader:
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for i, v in enumerate([stylus_x, stylus_y]): #, stylus_pressure, time]):
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v.append(float(row[i]))
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stylus_pos = np.array([stylus_x, stylus_y])
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time = np.array(time)
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return time, stylus_pos
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@ -1,189 +0,0 @@
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x,y,pressure,time_usec
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|
||||
543.5109098954965,1185.694402420575,0.4759462759462759,1821336836
|
||||
553.7679136739627,1166.639636913767,0.42466422466422465,1821346788
|
||||
565.0910576301188,1142.472617246596,0.33601953601953605,1821351772
|
||||
574.9804268645539,1115.981845688351,0.3045177045177045,1821361778
|
||||
|
||||
(1821361778-1820009777)*10**-6 = 1.352001 (seconds)
|
||||
|
||||
entries = 183-2+1 = 182
|
||||
|
||||
entries/sec = 182/1.352001 = 134.61528504786608
|
||||
|
|
@ -1,217 +0,0 @@
|
|||
x,y,pressure,time_usec
|
||||
327.70943254927323,457.5467473524962,0.36800976800976803,13341423266
|
||||
327.04769037001734,459.1733736762481,0.3916971916971917,13341433267
|
||||
326.09184055553663,461.7295007564297,0.4129426129426129,13341438262
|
||||
324.9521734690404,465.6798789712557,0.4358974358974359,13341448260
|
||||
323.8860332913504,470.2111951588502,0.463003663003663,13341453253
|
||||
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||||
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|
||||
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||||
320.43026857745855,497.28290468986387,0.5641025641025641,13341483253
|
||||
319.8420533070089,504.95128593040846,0.5711843711843712,13341493262
|
||||
319.43765530857473,511.80635400907715,0.5758241758241758,13341498256
|
||||
319.547945671784,515.7567322239032,0.5782661782661783,13341507264
|
||||
320.31997821424926,516.4538577912255,0.5804639804639805,13341512275
|
||||
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|
||||
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|
||||
328.3711747285291,494.4944024205749,0.6034188034188034,13341537276
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
343.51771794260816,552.8205748865355,0.8522588522588522,13341716309
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||||
342.1574701296933,569.3192133131619,0.8305250305250306,13341721310
|
||||
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||||
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|
||||
324.69482928821867,676.7927382753404,0.7587301587301587,13341746310
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||||
316.717159682745,720.1307110438729,0.7467643467643468,13341751319
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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398.6628995472649,702.1216338880484,0.7992673992673993,13342139461
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|
||||
622.4788099533649,1241.115885022693,0.7914529914529914,13342865317
|
||||
618.9495183306668,1287.1261724659607,0.8266178266178266,13342870306
|
||||
619.5744970555196,1310.9446293494705,0.842979242979243,13342879268
|
||||
624.5007999455356,1311.525567322239,0.8578754578754578,13342884305
|
||||
633.6549000919086,1288.0556732223904,0.873992673992674,13342894318
|
||||
647.0735609490417,1241.5806354009078,0.8886446886446886,13342899308
|
||||
664.3523845185009,1178.2583963691377,0.8986568986568987,13342909263
|
||||
684.8296286210301,1101.8069591527988,0.9037851037851038,13342914264
|
||||
707.6229703509548,1021.753706505295,0.8964590964590965,13342924326
|
||||
731.7030329849882,943.3270801815431,0.873992673992674,13342929322
|
||||
754.8640092589441,875.705900151286,0.8068376068376069,13342939295
|
||||
776.3706300847601,822.4919818456883,0.7152625152625153,13342944339
|
||||
793.4656363822038,788.6813918305597,0.6205128205128205,13342954311
|
||||
805.2667052456003,775.900756429652,0.5377289377289377,13342959312
|
||||
810.8179868604691,784.6148260211801,0.5111111111111111,13342969315
|
||||
809.9724274091976,814.3588502269289,0.5238095238095238,13342974319
|
||||
803.9064574326854,862.3443267776097,0.575091575091575,13342984318
|
||||
793.7597440174286,926.2475037821482,0.6371184371184371,13342989318
|
||||
781.7013309732104,1000.7237518910741,0.7040293040293041,13342999313
|
||||
768.6503046601083,1082.4036308623297,0.7645909645909645,13343004304
|
||||
756.9227627055179,1163.6187594553708,0.8075702075702076,13343014303
|
||||
747.1436838342921,1240.1863842662633,0.841025641025641,13343019254
|
||||
740.5630254961364,1304.4381240544628,0.8517704517704517,13343029277
|
||||
737.8057664159036,1353.469288956127,0.8527472527472527,13343034308
|
||||
739.1292507744154,1383.5618759455372,0.8312576312576313,13343044329
|
||||
744.6805323892842,1394.0187594553706,0.7819291819291819,13343049309
|
||||
754.496374714913,1384.9561270801814,0.765079365079365,13343058360
|
||||
|
|
|
@ -1,162 +0,0 @@
|
|||
""" Python implementation of
|
||||
Algorithm for Automatically Fitting Digitized Curves
|
||||
by Philip J. Schneider
|
||||
"Graphics Gems", Academic Press, 1990
|
||||
"""
|
||||
from __future__ import print_function
|
||||
from numpy import *
|
||||
import bezier
|
||||
|
||||
|
||||
# Fit one (ore more) Bezier curves to a set of points
|
||||
def fitCurve(points, maxError):
|
||||
leftTangent = normalize(points[1] - points[0])
|
||||
rightTangent = normalize(points[-2] - points[-1])
|
||||
return fitCubic(points, leftTangent, rightTangent, maxError)
|
||||
|
||||
|
||||
def fitCubic(points, leftTangent, rightTangent, error):
|
||||
# Use heuristic if region only has two points in it
|
||||
if (len(points) == 2):
|
||||
dist = linalg.norm(points[0] - points[1]) / 3.0
|
||||
bezCurve = [points[0], points[0] + leftTangent * dist, points[1] + rightTangent * dist, points[1]]
|
||||
return [bezCurve]
|
||||
|
||||
# Parameterize points, and attempt to fit curve
|
||||
u = chordLengthParameterize(points)
|
||||
bezCurve = generateBezier(points, u, leftTangent, rightTangent)
|
||||
# Find max deviation of points to fitted curve
|
||||
maxError, splitPoint = computeMaxError(points, bezCurve, u)
|
||||
if maxError < error:
|
||||
return [bezCurve]
|
||||
|
||||
# If error not too large, try some reparameterization and iteration
|
||||
if maxError < error**2:
|
||||
for i in range(20):
|
||||
uPrime = reparameterize(bezCurve, points, u)
|
||||
bezCurve = generateBezier(points, uPrime, leftTangent, rightTangent)
|
||||
maxError, splitPoint = computeMaxError(points, bezCurve, uPrime)
|
||||
if maxError < error:
|
||||
return [bezCurve]
|
||||
u = uPrime
|
||||
|
||||
# Fitting failed -- split at max error point and fit recursively
|
||||
beziers = []
|
||||
centerTangent = normalize(points[splitPoint-1] - points[splitPoint+1])
|
||||
beziers += fitCubic(points[:splitPoint+1], leftTangent, centerTangent, error)
|
||||
beziers += fitCubic(points[splitPoint:], -centerTangent, rightTangent, error)
|
||||
|
||||
return beziers
|
||||
|
||||
|
||||
def generateBezier(points, parameters, leftTangent, rightTangent):
|
||||
bezCurve = [points[0], None, None, points[-1]]
|
||||
|
||||
# compute the A's
|
||||
A = zeros((len(parameters), 2, 2))
|
||||
for i, u in enumerate(parameters):
|
||||
A[i][0] = leftTangent * 3*(1-u)**2 * u
|
||||
A[i][1] = rightTangent * 3*(1-u) * u**2
|
||||
|
||||
# Create the C and X matrices
|
||||
C = zeros((2, 2))
|
||||
X = zeros(2)
|
||||
|
||||
for i, (point, u) in enumerate(zip(points, parameters)):
|
||||
C[0][0] += dot(A[i][0], A[i][0])
|
||||
C[0][1] += dot(A[i][0], A[i][1])
|
||||
C[1][0] += dot(A[i][0], A[i][1])
|
||||
C[1][1] += dot(A[i][1], A[i][1])
|
||||
|
||||
tmp = point - bezier.q([points[0], points[0], points[-1], points[-1]], u)
|
||||
|
||||
X[0] += dot(A[i][0], tmp)
|
||||
X[1] += dot(A[i][1], tmp)
|
||||
|
||||
# Compute the determinants of C and X
|
||||
det_C0_C1 = C[0][0] * C[1][1] - C[1][0] * C[0][1]
|
||||
det_C0_X = C[0][0] * X[1] - C[1][0] * X[0]
|
||||
det_X_C1 = X[0] * C[1][1] - X[1] * C[0][1]
|
||||
|
||||
# Finally, derive alpha values
|
||||
alpha_l = 0.0 if det_C0_C1 == 0 else det_X_C1 / det_C0_C1
|
||||
alpha_r = 0.0 if det_C0_C1 == 0 else det_C0_X / det_C0_C1
|
||||
|
||||
# If alpha negative, use the Wu/Barsky heuristic (see text) */
|
||||
# (if alpha is 0, you get coincident control points that lead to
|
||||
# divide by zero in any subsequent NewtonRaphsonRootFind() call. */
|
||||
segLength = linalg.norm(points[0] - points[-1])
|
||||
epsilon = 1.0e-6 * segLength
|
||||
if alpha_l < epsilon or alpha_r < epsilon:
|
||||
# fall back on standard (probably inaccurate) formula, and subdivide further if needed.
|
||||
bezCurve[1] = bezCurve[0] + leftTangent * (segLength / 3.0)
|
||||
bezCurve[2] = bezCurve[3] + rightTangent * (segLength / 3.0)
|
||||
|
||||
else:
|
||||
# First and last control points of the Bezier curve are
|
||||
# positioned exactly at the first and last data points
|
||||
# Control points 1 and 2 are positioned an alpha distance out
|
||||
# on the tangent vectors, left and right, respectively
|
||||
bezCurve[1] = bezCurve[0] + leftTangent * alpha_l
|
||||
bezCurve[2] = bezCurve[3] + rightTangent * alpha_r
|
||||
|
||||
return bezCurve
|
||||
|
||||
|
||||
def reparameterize(bezier, points, parameters):
|
||||
return [newtonRaphsonRootFind(bezier, point, u) for point, u in zip(points, parameters)]
|
||||
|
||||
|
||||
def newtonRaphsonRootFind(bez, point, u):
|
||||
"""
|
||||
Newton's root finding algorithm calculates f(x)=0 by reiterating
|
||||
x_n+1 = x_n - f(x_n)/f'(x_n)
|
||||
|
||||
We are trying to find curve parameter u for some point p that minimizes
|
||||
the distance from that point to the curve. Distance point to curve is d=q(u)-p.
|
||||
At minimum distance the point is perpendicular to the curve.
|
||||
We are solving
|
||||
f = q(u)-p * q'(u) = 0
|
||||
with
|
||||
f' = q'(u) * q'(u) + q(u)-p * q''(u)
|
||||
|
||||
gives
|
||||
u_n+1 = u_n - |q(u_n)-p * q'(u_n)| / |q'(u_n)**2 + q(u_n)-p * q''(u_n)|
|
||||
"""
|
||||
d = bezier.q(bez, u)-point
|
||||
numerator = (d * bezier.qprime(bez, u)).sum()
|
||||
denominator = (bezier.qprime(bez, u)**2 + d * bezier.qprimeprime(bez, u)).sum()
|
||||
|
||||
if denominator == 0.0:
|
||||
return u
|
||||
else:
|
||||
return u - numerator/denominator
|
||||
|
||||
|
||||
def chordLengthParameterize(points):
|
||||
u = [0.0]
|
||||
for i in range(1, len(points)):
|
||||
u.append(u[i-1] + linalg.norm(points[i] - points[i-1]))
|
||||
|
||||
for i, _ in enumerate(u):
|
||||
u[i] = u[i] / u[-1]
|
||||
|
||||
return u
|
||||
|
||||
|
||||
def computeMaxError(points, bez, parameters):
|
||||
maxDist = 0.0
|
||||
splitPoint = len(points)/2
|
||||
for i, (point, u) in enumerate(zip(points, parameters)):
|
||||
dist = linalg.norm(bezier.q(bez, u)-point)**2
|
||||
if dist > maxDist:
|
||||
maxDist = dist
|
||||
splitPoint = i
|
||||
|
||||
return maxDist, splitPoint
|
||||
|
||||
|
||||
def normalize(v):
|
||||
return v / linalg.norm(v)
|
||||
|
||||
|
||||
File diff suppressed because one or more lines are too long
|
|
@ -1,11 +0,0 @@
|
|||
coord_x,coord_y
|
||||
54.7409,336.133
|
||||
54.6683,336.496
|
||||
54.6441,336.81
|
||||
54.6441,337.052
|
||||
54.6925,337.197
|
||||
54.8135,337.294
|
||||
54.9345,337.343
|
||||
55.0071,337.367
|
||||
55.0797,337.367
|
||||
55.0797,337.367
|
||||
|
|
|
@ -1,17 +0,0 @@
|
|||
coord_x,coord_y
|
||||
129.974,375.019
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||||
129.418,374.97
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||||
129.515,375.067
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||||
129.756,375.164
|
||||
130.168,375.285
|
||||
130.579,375.454
|
||||
131.063,375.599
|
||||
131.523,375.769
|
||||
132.007,375.914
|
||||
132.467,376.035
|
||||
132.927,376.083
|
||||
133.338,376.156
|
||||
133.628,376.204
|
||||
133.87,376.204
|
||||
134.064,376.156
|
||||
134.088,376.108
|
||||
|
|
|
@ -1,12 +0,0 @@
|
|||
coord_x,coord_y
|
||||
49.2962,365.485
|
||||
49.0059,365.823
|
||||
48.9333,366.114
|
||||
48.8849,366.307
|
||||
48.8849,366.404
|
||||
48.9333,366.477
|
||||
48.9575,366.477
|
||||
48.9575,366.477
|
||||
48.9575,366.477
|
||||
48.9575,366.477
|
||||
49.2236,366.453
|
||||
|
|
|
@ -1,32 +0,0 @@
|
|||
coord_x,coord_y
|
||||
22.8714,262.763
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||||
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||||
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||||
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||||
23.4522,263.44
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||||
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|
||||
23.6457,263.489
|
||||
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|
||||
23.6457,263.392
|
||||
23.6216,263.392
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
21.0081,259.472
|
||||
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|
||||
20.4273,257.996
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||||
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|
||||
20.4273,256.859
|
||||
20.7419,256.375
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||||
21.1775,256.06
|
||||
21.9034,255.915
|
||||
22.7988,255.818
|
||||
23.8877,255.842
|
||||
24.9525,255.987
|
||||
25.9204,256.036
|
||||
26.8158,256.084
|
||||
27.5417,256.181
|
||||
28.2677,256.205
|
||||
29.0178,256.326
|
||||
|
|
|
@ -1,34 +0,0 @@
|
|||
coord_x,coord_y
|
||||
78.8427,264.311
|
||||
78.7943,264.481
|
||||
78.7943,264.505
|
||||
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|
||||
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|
||||
78.3345,264.021
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
79.2783,258.891
|
||||
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|
||||
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|
||||
78.8185,258.673
|
||||
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|
||||
78.6975,258.964
|
||||
78.7701,259.181
|
||||
78.9637,259.472
|
||||
|
|
|
@ -1,75 +0,0 @@
|
|||
coord_x,coord_y
|
||||
80.101,260.996
|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
86.1507,259.907
|
||||
86.2959,260.149
|
||||
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|
||||
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|
||||
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|
||||
86.7556,260.125
|
||||
86.7556,259.907
|
||||
86.8524,259.544
|
||||
86.8766,259.157
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
88.2318,257.851
|
||||
88.6431,257.899
|
||||
89.1513,258.117
|
||||
89.6595,258.431
|
||||
90.1676,258.867
|
||||
90.6274,259.351
|
||||
90.9178,259.859
|
||||
91.1356,260.391
|
||||
91.1356,260.803
|
||||
91.063,261.093
|
||||
90.7726,261.311
|
||||
90.3854,261.48
|
||||
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|
||||
89.2723,261.553
|
||||
88.7399,261.432
|
||||
88.2318,261.238
|
||||
87.772,261.069
|
||||
87.4816,260.779
|
||||
87.3606,260.512
|
||||
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|
||||
87.3122,260.028
|
||||
87.409,259.907
|
||||
87.5784,259.956
|
||||
87.9656,260.101
|
||||
88.3769,260.319
|
||||
|
|
|
@ -1,18 +0,0 @@
|
|||
coord_x,coord_y
|
||||
92.2003,269.078
|
||||
92.1277,269.151
|
||||
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|
||||
91.7889,268.643
|
||||
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|
||||
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|
||||
91.5712,266.078
|
||||
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|
||||
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|
||||
91.9825,262.956
|
||||
92.1277,262.23
|
||||
92.2971,261.529
|
||||
92.5149,260.9
|
||||
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|
||||
92.9263,260.028
|
||||
93.0957,259.762
|
||||
93.0473,259.617
|
||||
|
|
|
@ -1,34 +0,0 @@
|
|||
coord_x,coord_y
|
||||
49.635,248.413
|
||||
50.1432,246.381
|
||||
50.0706,245.994
|
||||
50.0464,245.606
|
||||
50.0948,245.122
|
||||
50.24,244.638
|
||||
50.4578,244.276
|
||||
50.7482,244.034
|
||||
51.0385,244.009
|
||||
51.3289,244.009
|
||||
51.6193,244.251
|
||||
51.9097,244.469
|
||||
52.2001,244.808
|
||||
52.4905,245.316
|
||||
52.7324,245.703
|
||||
52.926,246.163
|
||||
52.9986,246.55
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119.641,287.033
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
|
|
@ -1,70 +0,0 @@
|
|||
coord_x,coord_y
|
||||
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|
||||
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||||
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|
||||
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||||
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||||
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|
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|
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|
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|
||||
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|
||||
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|
||||
|
|
|
@ -1,41 +0,0 @@
|
|||
coord_x,coord_y
|
||||
27.8079,281.952
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|
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|
|
|
@ -1,53 +0,0 @@
|
|||
coord_x,coord_y
|
||||
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|
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|
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|
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|
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|
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|
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|
||||
|
|
|
@ -1,37 +0,0 @@
|
|||
coord_x,coord_y
|
||||
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|
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|
||||
|
|
|
@ -1,35 +0,0 @@
|
|||
coord_x,coord_y
|
||||
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59.8468,278.927
|
||||
60.3792,279.459
|
||||
|
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Reference in New Issue