171 lines
5.1 KiB
Plaintext
171 lines
5.1 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "97dbdadd-7a94-4939-8ed5-c8551b662917",
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"metadata": {},
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"source": [
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"# Circle Segment Intersection (for interpolation)\n",
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"Here is an interactive plot that demonstrates the functionality of the formula to calculate the intersection of a line segment, and a circle centered at the origin."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "d31dc723-a6dc-400d-8b31-fe84ea6d5e45",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "cbfad4e8309a4ee2bef53994add83330",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"VBox(children=(Label(value='A and B can be moved with the mouse. One must be inside the circle, and one must b…"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"from bqplot import *\n",
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"import numpy as np\n",
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"import ipywidgets as widgets\n",
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"\n",
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"\n",
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"def circle_segment_intersection(p1, p2, r):\n",
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" x1, y1 = p1\n",
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" x2, y2 = p2\n",
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" dx = x2 - x1\n",
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" dy = y2 - y1\n",
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" dr2 = dx ** 2 + dy ** 2\n",
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" D = x1 * y2 - x2 * y1\n",
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" d1 = x1 ** 2 + y1 ** 2\n",
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" d2 = x2 ** 2 + y2 ** 2\n",
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" dd = d2 - d1\n",
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" sqrt_term = np.sqrt(r ** 2 * dr2 - D ** 2)\n",
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" x = (D * dy + np.copysign(1.0, dd) * dx * sqrt_term) / dr2\n",
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" y = (-D * dx + np.copysign(1.0, dd) * dy * sqrt_term) / dr2\n",
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" return x, y\n",
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"\n",
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"\n",
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"MAX = 5.0\n",
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"x_sc = LinearScale(min=-MAX, max=MAX)\n",
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"y_sc = LinearScale(min=-MAX, max=MAX)\n",
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"\n",
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"ax_x = Axis(label=\"x\", scale=x_sc, tick_format=\"0.0f\")\n",
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"ax_y = Axis(label=\"y\", scale=y_sc, orientation=\"vertical\", tick_format=\"0.0f\")\n",
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"\n",
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"points = Scatter(\n",
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" names=[\"A\", \"B\"], x=[0.0, 3.0], y=[2.0, 4.0], scales={\"x\": x_sc, \"y\": y_sc}, enable_move=True\n",
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")\n",
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"\n",
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"\n",
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"def get_circle(r):\n",
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" t = np.linspace(0, 2 * np.pi)\n",
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" x = r * np.cos(t)\n",
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" y = r * np.sin(t)\n",
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" return x, y\n",
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"\n",
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"radius_slider = widgets.FloatSlider(min=0.0, max=MAX, value=3.0, description=\"Circle radius\")\n",
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"circle_x, circle_y = get_circle(radius_slider.value)\n",
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"\n",
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"circle = Lines(x=circle_x, y=circle_y, scales={\"x\": x_sc, \"y\": y_sc}, colors=[\"green\"])\n",
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"\n",
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"x1, x2 = points.x\n",
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"y1, y2 = points.y\n",
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"xi, yi = circle_segment_intersection((x1, y1), (x2, y2), radius_slider.value)\n",
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"\n",
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"intersection = Scatter(\n",
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" names=[\"C\"],\n",
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" x=[xi],\n",
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" y=[yi],\n",
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" scales={\"x\": x_sc, \"y\": y_sc},\n",
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" enable_move=False,\n",
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" colors=[\"purple\"],\n",
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")\n",
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"\n",
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"fig = Figure(axes=[ax_x, ax_y], marks=[circle, points, intersection])\n",
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"\n",
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"fig.max_aspect_ratio = 1\n",
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"fig.min_aspect_ratio = 1\n",
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"\n",
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"\n",
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"def both_inside_or_both_outside_circle(points, r):\n",
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" x1, x2 = points.x\n",
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" y1, y2 = points.y\n",
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" d1 = x1 ** 2 + y1 ** 2\n",
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" d2 = x2 ** 2 + y2 ** 2\n",
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" if d1 < r ** 2 and d2 < r ** 2:\n",
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" return True\n",
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" elif d1 > r ** 2 and d2 > r ** 2:\n",
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" return True\n",
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" else:\n",
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" return False\n",
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"\n",
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"\n",
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"def update_circle(message):\n",
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" circle_x, circle_y = get_circle(radius_slider.value)\n",
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" circle.x = circle_x\n",
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" circle.y = circle_y\n",
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" update_intersection(message)\n",
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"\n",
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"\n",
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"def update_intersection(message):\n",
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" x1, x2 = points.x\n",
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" y1, y2 = points.y\n",
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" r = radius_slider.value\n",
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" if both_inside_or_both_outside_circle(points, r):\n",
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" circle.colors = [\"red\"]\n",
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" intersection.x = []\n",
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" intersection.y = []\n",
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" else:\n",
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" circle.colors = [\"green\"]\n",
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" xi, yi = circle_segment_intersection((x1, y1), (x2, y2), r)\n",
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" intersection.x = [xi]\n",
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" intersection.y = [yi]\n",
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"\n",
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"\n",
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"points.observe(update_intersection, [\"x\", \"y\"])\n",
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"\n",
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"radius_slider.observe(update_circle, \"value\")\n",
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"\n",
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"widgets.VBox(\n",
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" [\n",
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" widgets.Label(\n",
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" \"A and B can be moved with the mouse. One must be inside the circle, and one must be outside.\",\n",
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" fixed=True,\n",
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" ),\n",
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" radius_slider,\n",
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" fig,\n",
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" ]\n",
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")"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.10"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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