ewjoachim/bezier.ipynb

## bezier.ipynb
{"nbformat_minor": 0, "cells": [{"execution_count": 1, "cell_type": "code", "source": "from collections import namedtuple\n\n\nclass Point(namedtuple(\"BasePoint\", (\"x\", \"y\"))):\n    \"\"\"\n    This is a 2D point that can be accessed as a tuple or as an object with x and y properties\n    \"\"\"\n    # We can make this a 3D point just by adding a \"z\" in the definition\n    \n    # Note : common operations are defined in this class to ease manipulation\n    @property\n    def point(self):\n        # This is for compatibility with BezierPoint\n        return self\n    \n    # Operations\n    def __add__(self, other_point):\n        \"\"\"\n        Handles Point() + Point()\n        \"\"\"\n        return Point(*(sum(dim) for dim in zip(self, other_point)))\n    \n    def __mul__(self, scalar):\n        \"\"\"\n        Handles Point() * scalar\n        \"\"\"\n        # Point() \n        return Point(*(scalar * dim for dim in self))\n    \n    def __rmul__(self, scalar):\n        \"\"\"\n        Handles scalar * Point()\n        \"\"\"\n        return self * scalar\n    \n    def __sub__(self, other_point):\n        \"\"\"\n        Handles Point() - Point()\n        \"\"\"\n        return self + (other_point * -1)\n    \n    # More complicated operations\n    \n    def lerp(self, other_point, alpha):\n        \"\"\"\n        Linear interpolation between 2 points.\n        \n        >>> p1 = Point(1, 2)\n        >>> p2 = Point(3, 4)\n        >>> p1.lerp(p2, 0)\n        Point(1, 2)\n        \n        >>> p1.lerp(p2, 1)\n        Point(3, 4)\n        \n        >>> p1.lerp(p2, 0.5)\n        Point(2, 3)\n        \n        \"\"\"\n        return self + alpha * (other_point - self)\n\n    # display\n    \n    def __repr__(self):\n        return \"{}{}\".format(self.__class__.__name__, tuple(self))", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 41, "cell_type": "code", "source": "class BezierPoint(object):\n    \"\"\"\n    Class for a simple Bezier point, which is a point\n    and a control point (there's only 1 control point, that's not a cubic bezier)\n    \"\"\"\n    def __init__(self, point, control_point):\n        self.point = point\n        self.control_point = control_point\n        \n    def bezierPoint(self, other_point, alpha):\n        \"\"\"\n        Returns a point in the bezier curve between 2 points, for a given\n        alpha value (0 < alpha < 1)\n        \"\"\"\n        p1 = self.point.lerp(self.control_point, alpha)\n        p2 = self.control_point.lerp(other_point.point, alpha)\n        curve_point = p1.lerp(p2, alpha)\n        return curve_point\n    \n    def bezierPoints(self, end_point, steps):\n        \"\"\"\n        Returns <steps> points on the bezier curve between this point and the end_point\n        \"\"\"\n        return [self.bezierPoint(end_point, alpha) for alpha in float_range(step=1. / steps, include_end=True)]", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 42, "cell_type": "code", "source": "start_point = BezierPoint(Point(1,2), control_point=Point(1, 7))\nend_point = Point(3, 2)\nsteps = 100", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 43, "cell_type": "code", "source": "def float_range(start=0, end=1, step=0.1, include_end=False):\n    while start < end:\n        yield start\n        start += step\n    if include_end:\n        yield end", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 44, "cell_type": "code", "source": "curve = start_point.bezierPoints(end_point, steps)", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 45, "cell_type": "code", "source": "import matplotlib.pyplot as plt\n%matplotlib inline  ", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 46, "cell_type": "code", "source": "def plot_curve(curve):\n    plt.plot([e.x for e in curve], [e.y for e in curve])\n    \nplot_curve(curve)", "outputs": [{"output_type": "display_data", "data": {"image/png": 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"text/plain": "<matplotlib.figure.Figure at 0x108600e10>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 47, "cell_type": "code", "source": "def double_iterator(iterable):\n    it = iter(iterable)\n    old_val = next(it)\n    val = next(it)\n    while True:\n        yield (old_val, val)\n        old_val, val = val, next(it)", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 48, "cell_type": "code", "source": "def bezier_curve(points, steps):\n    return [\n        curve_point\n        for point1, point2 in double_iterator(points)\n        for curve_point in point1.bezierPoints(point2, steps)\n    ]\n        ", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 64, "cell_type": "code", "source": "points = [\n    BezierPoint(Point(1, 2), control_point=Point(3, 7)),\n    BezierPoint(Point(2, 6), control_point=Point(1, 8)),\n    Point(4, 7),\n]\ncurve = bezier_curve(points, steps)", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 65, "cell_type": "code", "source": "plot_curve(curve)", "outputs": [{"output_type": "display_data", "data": {"image/png": 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XZGYt5NDuIBIrAVcCjwMHRLAwcUlm1mIO7Q4hsSpwLfAwcLC3CDPrTA7tDiCxJnADMBP4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\n28ysQhzaZmYV4tA2M6sQh7aZWYX8P4ejIjrEn8H3AAAAAElFTkSuQmCC\n", "text/plain": "<matplotlib.figure.Figure at 0x107f93c50>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": null, "cell_type": "code", "source": "", "outputs": [], "metadata": {"collapsed": true, "trusted": true}}, {"execution_count": 61, "cell_type": "code", "source": "from IPython.html import widgets\nfrom IPython.display import display\n\ndef bezier_with_steps(steps=1):\n    plot_curve(bezier_curve(points, steps))\n\nw=widgets.interactive(bezier_with_steps,steps=widgets.IntSliderWidget(min=1, max=100, step=1, value=1))\ndisplay(w)", "outputs": [{"output_type": "display_data", "data": {"image/png": 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0Jzbc0Toj2zmsc365zqHtw2wfWn3+NEmvk7Rrw2E5z93C88t17iQpIi6LiKMj4rmS3ijp\nexFx7obDGs1frQdG2b5R0umSDrN9r6T3S9qvGtR1EXGz7TNt/07SPyW9teG59WrR+Ul6g6QLbf9H\n0hOa/sPPySskvVnSnbbX/0BcJukYqYg5XHh+yncOj5R0ve1tmi6yPhcRt9q+QCpi7haen/Kdu3lC\nklaZP26uAYCMpPgf+wIAEiG0ASAjhDYAZITQBoCMENoAkBFCGwAyQmgDQEYIbQDIyP8AKVH1FieS\nv7oAAAAASUVORK5CYII=\n", "text/plain": "<matplotlib.figure.Figure at 0x1097095d0>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": null, "cell_type": "code", "source": "", "outputs": [], "metadata": {"collapsed": true, "trusted": true}}], "nbformat": 4, "metadata": {"kernelspec": {"display_name": "Python 2", "name": "python2", "language": "python"}, "language_info": {"mimetype": "text/x-python", "nbconvert_exporter": "python", "version": "2.7.9", "name": "python", "file_extension": ".py", "pygments_lexer": "ipython2", "codemirror_mode": {"version": 2, "name": "ipython"}}}}