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Created November 1, 2021 13:39
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Demo.ipynb
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"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_formats = {'svg',}\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"from bspline import *\n",
"import bspline.plotting as splt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A few utility plotting functions for this demo."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def get_info(spline):\n",
" return repr(spline)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def plot_spline(s):\n",
" splt.plot(s, with_knots=True)\n",
" plt.title(get_info(s))\n",
" ax = plt.gca()\n",
" ax.grid(lw=.5, ls='-', alpha=.2)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def plot_ex(ex):\n",
" s = BSpline(**ex)\n",
" plot_spline(s)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Spline examples"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
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{
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"source": [
"ex1 = {\n",
"'control_points': np.array([[0.,2], [3,3], [3,5], [0,6]]),\n",
"'knots': np.array([3.,3.,3.,4.,4.,4.])\n",
"}\n",
"\n",
"plt.subplot(1,2,1)\n",
"b = BSpline(ex1['control_points'])\n",
"splt.plot(b)\n",
"plt.title(\"Bézier\")\n",
"plt.axis('equal')\n",
"plt.subplot(1,2,2)\n",
"b_ = BSpline(**ex1)\n",
"splt.plot(b_)\n",
"plt.title(\"BSpline\")\n",
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},
{
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"execution_count": 7,
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"e=.1\n",
"axis=(1-e,2+e,2-e,9+e)\n",
"ex2 = {\n",
"'control_points': np.array([[1.,2], [2,3], [2,5], [1,6], [1,9]]),\n",
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"b2 = BSpline(**ex2)\n",
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{
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"metadata": {},
"source": [
"### Continuous but not differentiable"
]
},
{
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"execution_count": 8,
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"text": [
"[(3.0, 4.0), (4.0, 4.0), (4.0, 4.0), (4.0, 5.0)]\n"
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"source": [
"ex3 = {\n",
"'control_points': np.array([[-4.,7], [-2,2], [5,6], [1,6], [1,9], [4,11], [7,9]]),\n",
"'knots': np.array([1.,2.,3.,4.,4.,4.,5.,6.,6.])\n",
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"plot_ex(ex3)\n",
"plt.axis('equal')\n",
"s3 = BSpline(**ex3)\n",
"print([s.interval for s in s3])"
]
},
{
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"metadata": {},
"source": [
"### Discontinuous cubic"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
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"outputs_hidden": false
}
},
"outputs": [
{
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"output_type": "stream",
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"ex4 = {\n",
"'control_points': np.array([[5.,2], [10,3], [10,5], [5,6], [5,9], [10,11], [10,9], [8,8]]),\n",
"'knots': np.array([1.,2.,3.,4.,4.,4.,4.,5.,6.,6.])\n",
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"plot_ex(ex4)\n",
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{
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"metadata": {},
"source": [
"### Discontinous quadratic"
]
},
{
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"execution_count": 10,
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{
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"source": [
"ex_d2 = {\n",
"'control_points': np.array([[5.,2], [10,3], [5,6], [5,9], [10,11], [8,8]]),\n",
"'knots': np.array([1.,1.,2.,2.,2.,3.,3.,])\n",
"}\n",
"plot_ex(ex_d2)\n",
"s_d2 = BSpline(**ex_d2)\n",
"plt.axis('equal')\n",
"plt.figure()\n",
"from bspline.knots import Knots\n",
"k = Knots(s_d2.knots, s_d2.degree)\n",
"for i in range(6):\n",
" splt.plot(k.get_basis(i))\n",
"print([s.interval for s in s_d2])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
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"outputs_hidden": false
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"output_type": "display_data"
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"source": [
"pretzel = {'control_points': np.array([[-0.8 , 1.5 ],\n",
" [-0.5 , 1.5 ],\n",
" [ 1. , -0.5 ],\n",
" [ 1.7 , 1.25],\n",
" [-1.7 , 1.25],\n",
" [-1. , -0.5 ],\n",
" [ 0.5 , 1.5 ],\n",
" [ 0.8 , 1.5 ]]),\n",
"'knots': np.array([1.,1.,1.,1.2,1.4,1.6,1.8,2.,2.,2.])}\n",
"plot_ex(pretzel)\n",
"plt.axis('equal')\n",
"spretzel = BSpline(**pretzel)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Basis plots"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"from bspline.knots import *"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
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"text/plain": [
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},
"metadata": {
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],
"source": [
"for i in range(3,8):\n",
" k = get_basis_knots(np.arange(i)/(i-1))\n",
" s = k.get_basis()\n",
" splt.plot(s, with_knots=True)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
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"name": "python3"
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