{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simple Way to Draw a Curve"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.507346Z",
"iopub.status.busy": "2026-01-27T17:09:29.507276Z",
"iopub.status.idle": "2026-01-27T17:09:29.510334Z",
"shell.execute_reply": "2026-01-27T17:09:29.510041Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"from lets_plot import *\n",
"LetsPlot.setup_html()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.527426Z",
"iopub.status.busy": "2026-01-27T17:09:29.527328Z",
"iopub.status.idle": "2026-01-27T17:09:29.528916Z",
"shell.execute_reply": "2026-01-27T17:09:29.528532Z"
}
},
"outputs": [],
"source": [
"BG_CLR = '#253494'\n",
"EC_CLR = '#ffffcc'"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.529690Z",
"iopub.status.busy": "2026-01-27T17:09:29.529613Z",
"iopub.status.idle": "2026-01-27T17:09:29.531108Z",
"shell.execute_reply": "2026-01-27T17:09:29.530895Z"
}
},
"outputs": [],
"source": [
"# Curve parametrized equation\n",
"def ec_eq(*, a=0, b=0):\n",
" return lambda x, y: y ** 2 - x ** 3 - a * x - b"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.531803Z",
"iopub.status.busy": "2026-01-27T17:09:29.531732Z",
"iopub.status.idle": "2026-01-27T17:09:29.533206Z",
"shell.execute_reply": "2026-01-27T17:09:29.532984Z"
}
},
"outputs": [],
"source": [
"def level(X, Y, *, eq, c=1):\n",
" level_map = lambda z: np.exp(-c * np.abs(z))\n",
" return level_map(eq(X, Y))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.533797Z",
"iopub.status.busy": "2026-01-27T17:09:29.533728Z",
"iopub.status.idle": "2026-01-27T17:09:29.536012Z",
"shell.execute_reply": "2026-01-27T17:09:29.535798Z"
}
},
"outputs": [],
"source": [
"dx, dy = 1.0 / 30.0, 1.0 / 10.0\n",
"\n",
"x = np.arange(-3, 3, dx)\n",
"y = np.arange(-3, 3, dy)\n",
"X, Y = np.meshgrid(x, y)\n",
"curve_eq = ec_eq(a=-1, b=0)\n",
"Z = level(X, Y, eq=curve_eq, c=10)\n",
"\n",
"df = pd.DataFrame(dict(x=X.reshape(-1), y=Y.reshape(-1), z=Z.reshape(-1)))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.536686Z",
"iopub.status.busy": "2026-01-27T17:09:29.536614Z",
"iopub.status.idle": "2026-01-27T17:09:29.538599Z",
"shell.execute_reply": "2026-01-27T17:09:29.538371Z"
}
},
"outputs": [],
"source": [
"theme_layer = scale_color_gradient(low=BG_CLR, high=EC_CLR) + scale_fill_gradient(low=BG_CLR, high=EC_CLR) + \\\n",
" xlim(df.x.min(), df.x.max()) + ylim(df.y.min(), df.y.max()) + ggsize(600, 450) + \\\n",
" theme_void() + theme(panel_background=element_rect(color=BG_CLR, fill=BG_CLR))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.539353Z",
"iopub.status.busy": "2026-01-27T17:09:29.539281Z",
"iopub.status.idle": "2026-01-27T17:09:29.574646Z",
"shell.execute_reply": "2026-01-27T17:09:29.574415Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_point(aes(x='x', y='y', color='z'), data=df[df.z > 0.5].sort_values(by='z')) + \\\n",
" coord_fixed() + theme_layer + \\\n",
" ggtitle('Elliptic Curve by Points')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.575651Z",
"iopub.status.busy": "2026-01-27T17:09:29.575562Z",
"iopub.status.idle": "2026-01-27T17:09:29.656660Z",
"shell.execute_reply": "2026-01-27T17:09:29.656366Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_bin2d(aes(x='x', y='y', fill='z'), data=df, stat='identity', color=BG_CLR) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by 2D-Bins')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.660192Z",
"iopub.status.busy": "2026-01-27T17:09:29.660094Z",
"iopub.status.idle": "2026-01-27T17:09:29.739319Z",
"shell.execute_reply": "2026-01-27T17:09:29.738960Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_tile(aes(x='x', y='y', fill='z'), data=df, color=BG_CLR) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by Tiles')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.741643Z",
"iopub.status.busy": "2026-01-27T17:09:29.741564Z",
"iopub.status.idle": "2026-01-27T17:09:29.821079Z",
"shell.execute_reply": "2026-01-27T17:09:29.820800Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_raster(aes(x='x', y='y', fill='z'), data=df) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by Raster')"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.823614Z",
"iopub.status.busy": "2026-01-27T17:09:29.823536Z",
"iopub.status.idle": "2026-01-27T17:09:29.873537Z",
"shell.execute_reply": "2026-01-27T17:09:29.872974Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_contour(aes(x='x', y='y', z='z', color='..level..'), data=df, bins=4) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by Contours')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"execution": {
"iopub.execute_input": "2026-01-27T17:09:29.874541Z",
"iopub.status.busy": "2026-01-27T17:09:29.874458Z",
"iopub.status.idle": "2026-01-27T17:09:29.931387Z",
"shell.execute_reply": "2026-01-27T17:09:29.931081Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_contourf(aes(x='x', y='y', z='z', fill='..level..'), data=df, binwidth=.3) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by Filled Contours')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.10.13"
}
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