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Last active June 17, 2017 22:08
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How to use a root-finding algorithm to find points over a parametric curve where it becomes orthogonal to some given point in space
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finding orthogonal points in a parametric curve\n",
"============================\n",
"\n",
"Take a parametric curve defined by (fx(t), fy(t)) and a point p. We want to find points on the curve where the relative direction of p is orthogonal to the curve direction.\n",
"\n",
"## The curve\n",
"We start by creating an example curve, defined by applying cubic spline to two arrays. The curve must be wiggly to create a lot of solution points."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Bp/bc/fe6pM6r+euDwxkOgGzCsgkAkm3+fGn99aXOq6tgQsTefwAAIGPV1EgFBXb/v/Zg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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f48868790b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import matplotlib as mpl\n",
"mpl.rcParams['figure.figsize'] = (10,10)\n",
"\n",
"from pylab import *\n",
"\n",
"from scipy.interpolate import CubicSpline\n",
"import scipy.optimize\n",
"\n",
"tt = mgrid[1:41.0] ## Control points that define the function\n",
"ttt = mgrid[0:40.01:0.01] # For plotting the function\n",
"\n",
"phi = 0.3\n",
"omega = 2 * pi * 11 / 87\n",
"# Curve is a weird wiggly function, rotated\n",
"ff = 3.0*cos(omega * tt) + ((tt - 20)/7.0)**2\n",
"xx = cos(phi) * tt - sin(phi) * ff # Control points x\n",
"yy = sin(phi) * tt + cos(phi) * ff # Control points y\n",
"\n",
"fx = CubicSpline(tt, xx)\n",
"fy = CubicSpline(tt, yy)\n",
"\n",
"p = array([14.0, 20.0])\n",
"\n",
"mm = array([-1, 1]) ## For plotting the tangential directions\n",
"\n",
"figure(1, figsize=(10, 10))\n",
"def plot_curve():\n",
" plot(p[0], p[1], 'rs')\n",
" plot(xx, yy, 'bo')\n",
" plot(fx(ttt), fy(ttt), 'b-')\n",
" grid()\n",
" axis('equal');\n",
"plot_curve()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Measuring the direction\n",
"In order to measure the direction of the point p relative to the tangential direction of the curve at point q, we first pick (p-q), then the tangential direction. From these vectors you can find the relative direction, but what we are actually going to use is the dot product between the normalized vectors. This gives us the cosine of the angle between them, that is going to be zero at 90 degrees."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [],
"source": [
"def point_direction_cosine(t, p):\n",
" '''On the curve point 'q=(fx(t), fy(t))', calculates the cosine of angle between\n",
" vector 'p-q' and curve tangential direction. A value of zero means 'p' is ortogonal\n",
" to the curve at the given point 'q' corresponding to 't'.'''\n",
" q = array([fx(t), fy(t)])\n",
" v = p - q\n",
" d = array([fx(t, 1), fy(t, 1)])\n",
" return dot(v, d)/norm(v)/norm(d)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Figure 2 shows this cosine of the angle from our example curve as a function of the x coordinate, on top, and as a function of t on the bottom. The top graph helps to compare with Figure 1.\n",
"\n",
"You can see the function goes to zero when the curve is orthogonal, then goes to 1 and to -1 when the curve direction becomes tangential to the point."
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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eE5HrgDeMMY8BF4rIWKAWWA2c7a3BdQwebIOL9ettMXVSZdOzIUlKTVunTvYP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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4884bd7eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fff = array([point_direction_cosine(t, p) for t in ttt])\n",
"\n",
"figure(2)\n",
"suptitle('Cosine of angle between \"p-q\" and tangential direction')\n",
"subplot(2,1,1)\n",
"plot(fx(ttt), fff)\n",
"plot([-5, 35], [0, 0], 'k--', lw=2)\n",
"xlabel('x coordinate')\n",
"ylabel(\"ang(p-q, q')\")\n",
"xlim(-5,35)\n",
"grid()\n",
"\n",
"subplot(2,1,2)\n",
"def plot_direction():\n",
" plot(ttt, fff)\n",
" plot([0, 40], [0, 0], 'k--', lw=2)\n",
" xlabel('t parameter')\n",
" ylabel(\"ang(p-q, q')\")\n",
" xlim(0,40)\n",
" grid()\n",
"plot_direction()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Roots, orthogonal roots\n",
"There are basically two ways we can go about finding our orthogonal points. One way is to walk around the curve testing point after point until we get pretty close to 0, than try to refine. This would mean basically some kind of brute-force linear search. It does have an important merit that is tackling the fact there are multiple possible solutions, and many more sophisticated but naive approaches might not be able to handle that. But as a linear search, it is inherently costly compared to existing alternatives.\n",
"\n",
"It should be more fast and accurate to use something like a binary search. Or even better: because the points we seek are the roots of this smooth function from Figure 2, we can actually employ a root-finding algorithm such as Newton's method, or the secant method, or even something more fancy and reliable such as the Brent-Dekker method from the glorious 1970s.\n",
"\n",
"The problem with these methods, like we said, is that they start with a certain range and assume there is one and only one root inside it. What we'll do to handle this problem is to actually employ a linear search on top, to sweep the whole curve, but then we'll assume there is a maximum distance between the roots, and then this gives us the size of our starting range, and the size of our step in the linear search. This way we can make steps that are larger than what you might take if you relied just on the linear search, combining its robustness with the performance and accuracy of the binary-search-like algorithms."
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [],
"source": [
"## The step in the underlying linear search, (assumed) minimum possible distance between roots.\n",
"min_root_dist = 2.0\n",
"\n",
"## Limits from the search intervals.\n",
"search_points = mgrid[0:40+min_root_dist:min_root_dist]\n",
"\n",
"## Traverse linearly list of intervals, skipping invalids, and accumulate results from root search.\n",
"roots = []\n",
"for a,b in zip(search_points, search_points[1:]):\n",
" fa = point_direction_cosine(a, p)\n",
" fb = point_direction_cosine(b, p)\n",
" ## Test if interval contains a sign change.\n",
" if sign(fa) != sign(fb):\n",
" roots.append(scipy.optimize.brentq(point_direction_cosine, a, b, args=(p,)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Results"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.3176569879575573 -3.76305156321e-14\n",
"3.642217773395081 -1.91649383014e-13\n",
"8.28198934063367 -4.77553729518e-16\n",
"11.807689040279525 1.08994893794e-15\n",
"15.888363243609673 5.69546222206e-16\n",
"19.79772573148449 3.95159913989e-16\n",
"23.61312917650969 4.24847225829e-14\n",
"27.78830197841825 -3.08949456148e-14\n",
"31.206825778391398 2.18267996784e-16\n",
"35.95104198083556 1.38604164372e-15\n",
"38.20567856241386 -4.90536172491e-16\n"
]
}
],
"source": [
"for tn in roots:\n",
" print(tn, point_direction_cosine(tn, p))"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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/Izc3ohjUunUrzJ59H1yuarjggvfRv/94zJnzqN9X/wWDLRWISM4YWXHpv9Mp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\nTKqIiIiIdPD/Pv2okKwbByQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4884c46be0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figure(3)\n",
"plot_curve()\n",
"for tn in roots:\n",
" qn = array([fx(tn), fy(tn)])\n",
" plot(qn[0], qn[1], 'ys')\n",
" plot(qn[0] + mm * fx(tn, 1), qn[1] + mm * fy(tn, 1), 'y-')\n",
" plot([p[0], qn[0]], [p[1], qn[1]], 'r:')"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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AVVcVf00oebGN5MUOwYq2EKdIkyxEoEyWKm0jI6b6y3ml7MSJ/lq0+GZoyLx3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\nIyUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4886aac748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figure(4)\n",
"plot_direction()\n",
"for sp in search_points:\n",
" plot([sp,sp], 0.1*mm, 'g-', lw=2)\n",
" plot(sp, 0, 'gd')\n",
"for tn in roots:\n",
" plot(tn, point_direction_cosine(tn, p), 'ys')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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