Remove notebooks for the time being; they are still in history

notebooks/bezier.py

@@ -1,18 +0,0 @@
-from __future__ import print_function
-from numpy import *
-
-
-# evaluates cubic bezier at t, return point
-def q(ctrlPoly, t):
-    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]
-
-
-# evaluates cubic bezier first derivative at t, return point
-def qprime(ctrlPoly, t):
-    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])
-
-
-# evaluates cubic bezier second derivative at t, return point
-def qprimeprime(ctrlPoly, t):
-    return 6*(1.0-t) * (ctrlPoly[2]-2*ctrlPoly[1]+ctrlPoly[0]) + 6*(t) * (ctrlPoly[3]-2*ctrlPoly[2]+ctrlPoly[1])
-

notebooks/common.py

@@ -1,18 +0,0 @@
-import numpy as np
-import csv
-import matplotlib.pyplot as plt
-
-def import_csv_data(filename):
-    stylus_x = []
-    stylus_y = []
-    stylus_pressure = []
-    time = []
-    with open(filename) as csv_fp:
-        reader = csv.reader(csv_fp)
-        next(reader) # skip header
-        for row in reader:
-            for i, v in enumerate([stylus_x, stylus_y]): #, stylus_pressure, time]):
-                v.append(float(row[i]))
-    stylus_pos = np.array([stylus_x, stylus_y])
-    time = np.array(time)
-    return time, stylus_pos

notebooks/fast_data.csv

@@ -1,217 +0,0 @@
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notebooks/fitCurves.py

@@ -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)
-
-

notebooks/w_data.csv

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