{ "cells": [ { "cell_type": "markdown", "id": "e2d737c4", "metadata": {}, "source": [ "# 13 · Outline Areas: the shoelace formula, its gradient, and its Hessian\n", "\n", "A **closed outline** (or *chamber*) is a loop of edges through a shared set of 2D\n", "vertices. simkit measures the **signed area** each loop encloses with\n", "`outline_areas`, and provides its first and second derivatives with\n", "`outline_areas_gradient` and `outline_areas_hessian`. This notebook walks through\n", "all three, top to bottom:\n", "\n", "1. **Known areas.** Measure a triangle, a square, and a regular polygon, and watch\n", " the polygon's area converge to $\\pi r^2$ as it gains sides.\n", "2. **Orientation = sign.** Walk the same loop clockwise vs counter-clockwise and\n", " watch the sign flip. This is why simkit keeps the *signed* area: it is a smooth\n", " polynomial of the vertices, differentiable everywhere.\n", "3. **The gradient inflates the shape.** $\\nabla A$ is the direction each vertex\n", " should move to grow the area; it points along the outward normal. We draw that\n", " field, then follow it to inflate a star while the area climbs monotonically.\n", "4. **Checking the derivatives.** The analytic gradient and (constant) Hessian are\n", " compared against finite differences, the same checks the unit tests make." ] }, { "cell_type": "code", "execution_count": 1, "id": "e8ad3963", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:35:37.981281Z", "iopub.status.busy": "2026-06-09T05:35:37.981099Z", "iopub.status.idle": "2026-06-09T05:35:39.177597Z", "shell.execute_reply": "2026-06-09T05:35:39.177343Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib.animation import FuncAnimation\n", "\n", "import simkit\n", "import utils\n", "\n", "# A small consistent palette.\n", "POS_C = \"#2a9d8f\" # positive / CCW area\n", "NEG_C = \"#e76f51\" # negative / CW area\n", "EDGE_C = \"#264653\"\n", "GRAD_C = \"#e9c46a\"\n", "\n", "\n", "def regular_polygon(n, r=1.0, center=(0.0, 0.0)):\n", " # n vertices spaced counter-clockwise on a circle of radius r.\n", " theta = np.linspace(0.0, 2.0 * np.pi, n, endpoint=False)\n", " return np.column_stack([center[0] + r * np.cos(theta),\n", " center[1] + r * np.sin(theta)])\n", "\n", "\n", "def draw_outline(ax, X, color, fill=True, lw=2.5):\n", " # Draw a closed outline (and optionally fill it) on ax.\n", " loop = np.vstack([X, X[0]])\n", " if fill:\n", " ax.fill(X[:, 0], X[:, 1], color=color, alpha=0.18, zorder=1)\n", " ax.plot(loop[:, 0], loop[:, 1], \"-o\", color=color, lw=lw, ms=5, zorder=3)" ] }, { "cell_type": "markdown", "id": "bb5a54d0", "metadata": {}, "source": [ "## 1 · Known areas: the shoelace formula on shapes we can check by hand\n", "\n", "For a closed loop of vertices the **signed** area is the shoelace (Gauss) formula\n", "\n", "$$\n", "A = \\tfrac{1}{2} \\sum_{(i,j)\\in E} \\big(x_i\\, y_j - x_j\\, y_i\\big).\n", "$$\n", "\n", "Each term is twice the signed area of the triangle (origin, $p_i$, $p_j$); summing\n", "around the loop, the parts outside the polygon cancel and only the enclosed area\n", "survives. We test it on three shapes whose area we already know:\n", "\n", "* right triangle with legs 1  →  $A = \\tfrac12$\n", "* unit square  →  $A = 1$\n", "* regular $n$-gon of radius $r$  →  $A = \\tfrac12 n r^2 \\sin(2\\pi/n)$\n", "\n", "That last one is the nicest: a regular polygon is just a circle we have not\n", "finished drawing, so its shoelace area marches up to $\\pi r^2$ as $n$ grows." ] }, { "cell_type": "code", "execution_count": 2, "id": "0baa838b", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:35:39.178896Z", "iopub.status.busy": "2026-06-09T05:35:39.178802Z", "iopub.status.idle": "2026-06-09T05:35:39.311803Z", "shell.execute_reply": "2026-06-09T05:35:39.311601Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "shapes = [\n", " (\"right triangle\", np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]]), 0.5),\n", " (\"unit square\", np.array([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]), 1.0),\n", " (\"regular octagon\\n(r = 1)\", regular_polygon(8, r=1.0),\n", " 0.5 * 8 * 1.0 ** 2 * np.sin(2 * np.pi / 8)),\n", "]\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(13, 4.2))\n", "for ax, (name, X, exact) in zip(axes, shapes):\n", " E = simkit.closed_polyline(X)\n", " A = simkit.outline_areas(X, [E])[0]\n", " draw_outline(ax, X, POS_C)\n", " utils.setup_axes(ax, title=f\"{name}\\nshoelace A = {A:.4f} (exact {exact:.4f})\")\n", "fig.suptitle(\"Signed area of closed outlines via simkit.outline_areas\", y=1.03)\n", "fig.tight_layout()\n", "fig.savefig(\"media/13_known_areas.png\", dpi=130, bbox_inches=\"tight\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "id": "dd8dd0b5", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:35:39.312765Z", "iopub.status.busy": "2026-06-09T05:35:39.312696Z", "iopub.status.idle": "2026-06-09T05:35:39.515953Z", "shell.execute_reply": "2026-06-09T05:35:39.515739Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Convergence of the regular n-gon area to the circle pi r^2.\n", "r = 1.0\n", "ns = np.unique(np.round(np.logspace(np.log10(3), np.log10(2000), 40)).astype(int))\n", "err = []\n", "for n in ns:\n", " Xn = regular_polygon(int(n), r=r)\n", " En = simkit.closed_polyline(Xn)\n", " A = simkit.outline_areas(Xn, [En])[0]\n", " err.append(abs(A - np.pi * r ** 2))\n", "\n", "fig, ax = plt.subplots(figsize=(6.5, 4.4))\n", "ax.loglog(ns, err, \"-o\", color=EDGE_C, ms=4, lw=2)\n", "ax.loglog(ns, 0.5 * np.pi ** 3 / ns ** 2, \"--\", color=NEG_C, lw=1.5,\n", " label=r\"$\\mathcal{O}(1/n^2)$ reference\")\n", "ax.set_xlabel(\"number of polygon sides $n$\")\n", "ax.set_ylabel(r\"$|A_{\\mathrm{shoelace}} - \\pi r^2|$\")\n", "ax.set_title(\"Regular polygon area converges to the circle\")\n", "ax.grid(True, which=\"both\", color=\"0.92\")\n", "ax.legend()\n", "fig.tight_layout()\n", "fig.savefig(\"media/13_circle_convergence.png\", dpi=130, bbox_inches=\"tight\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2ed8c2db", "metadata": {}, "source": [ "## 2 · Orientation is the sign of the area\n", "\n", "The shoelace area is **signed**: traverse a loop counter-clockwise and you get a\n", "positive number, traverse the *exact same loop* clockwise and you get its negative.\n", "simkit deliberately keeps this sign instead of taking $|A|$, because the signed area\n", "is a smooth polynomial in the vertex coordinates — so its gradient and Hessian\n", "(sections 3-4) are exact everywhere, including the degenerate $A = 0$ case where\n", "$|A|$ has a non-differentiable kink." ] }, { "cell_type": "code", "execution_count": 4, "id": "8f261dd3", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:35:39.517026Z", "iopub.status.busy": "2026-06-09T05:35:39.516975Z", "iopub.status.idle": "2026-06-09T05:35:39.611265Z", "shell.execute_reply": "2026-06-09T05:35:39.611047Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "counter-clockwise A = +1.600, clockwise A = -1.600\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.array([[0.0, 0.0], [1.6, 0.0], [1.6, 1.0], [0.0, 1.0]])\n", "E_ccw = simkit.closed_polyline(X)\n", "E_cw = E_ccw[::-1, ::-1] # same loop, walked the other way\n", "\n", "A_ccw = simkit.outline_areas(X, [E_ccw])[0]\n", "A_cw = simkit.outline_areas(X, [E_cw])[0]\n", "print(f\"counter-clockwise A = {A_ccw:+.3f}, clockwise A = {A_cw:+.3f}\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(10, 4.4))\n", "for ax, (E, A, c, label) in zip(\n", " axes,\n", " [(E_ccw, A_ccw, POS_C, \"counter-clockwise\"),\n", " (E_cw, A_cw, NEG_C, \"clockwise\")],\n", "):\n", " draw_outline(ax, X, c)\n", " for a, b in E: # arrowheads showing the winding direction\n", " mid = 0.5 * (X[a] + X[b])\n", " d = X[b] - X[a]\n", " ax.annotate(\"\", xy=mid + 0.18 * d, xytext=mid - 0.18 * d,\n", " arrowprops=dict(arrowstyle=\"-|>\", color=c, lw=2))\n", " utils.setup_axes(ax, title=f\"{label}\\nA = {A:+.3f}\")\n", "fig.suptitle(\"Same four vertices, opposite winding: the sign flips\", y=1.03)\n", "fig.tight_layout()\n", "fig.savefig(\"media/13_orientation_sign.png\", dpi=130, bbox_inches=\"tight\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "db2f6a8e", "metadata": {}, "source": [ "## 3 · The gradient inflates the shape\n", "\n", "`outline_areas_gradient` returns $\\partial A/\\partial x$ for every vertex of the\n", "loop, stacked as `[dx0, dy0, dx1, dy1, ...]`. Geometrically\n", "\n", "$$\n", "\\frac{\\partial A}{\\partial x_i} = \\tfrac12 (y_{i+1} - y_{i-1}), \\qquad\n", "\\frac{\\partial A}{\\partial y_i} = -\\tfrac12 (x_{i+1} - x_{i-1}),\n", "$$\n", "\n", "so the area grows fastest when vertex $i$ moves along its **outward normal**, by an\n", "amount proportional to the length of its two incident edges. The gradient field is\n", "therefore a ring of outward arrows.\n", "\n", "Follow that field — $x \\leftarrow x + \\mathrm{d}t\\,\\nabla A$ — and the\n", "loop inflates: every step is guaranteed to increase the area because we move\n", "straight uphill on $A$. We start from a spiky star so the inflation is dramatic." ] }, { "cell_type": "code", "execution_count": 5, "id": "939b9ca7", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:35:39.612258Z", "iopub.status.busy": "2026-06-09T05:35:39.612204Z", "iopub.status.idle": "2026-06-09T05:35:39.663942Z", "shell.execute_reply": "2026-06-09T05:35:39.663756Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A 10-point star: alternate far / near radii.\n", "n_arms = 10\n", "ang = np.linspace(0.0, 2.0 * np.pi, 2 * n_arms, endpoint=False)\n", "rad = np.where(np.arange(2 * n_arms) % 2 == 0, 1.0, 0.42)\n", "X0 = np.column_stack([rad * np.cos(ang), rad * np.sin(ang)])\n", "E = simkit.closed_polyline(X0)\n", "\n", "# Per-vertex area gradient reshaped to (n, 2) in this loop's vertex order.\n", "g = simkit.outline_areas_gradient(X0, [E])[0].reshape(-1, 2)\n", "\n", "fig, ax = plt.subplots(figsize=(5.6, 5.6))\n", "draw_outline(ax, X0, EDGE_C, fill=True, lw=2)\n", "ax.quiver(X0[:, 0], X0[:, 1], g[:, 0], g[:, 1],\n", " color=GRAD_C, angles=\"xy\", scale_units=\"xy\", scale=1.0,\n", " width=0.012, zorder=5)\n", "utils.setup_axes(ax, (-1.5, 1.5), (-1.5, 1.5),\n", " title=\"area gradient $\\\\nabla A$ (points outward)\")\n", "fig.tight_layout()\n", "fig.savefig(\"media/13_gradient_field.png\", dpi=130, bbox_inches=\"tight\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "c7a6f70a", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:35:39.664883Z", "iopub.status.busy": "2026-06-09T05:35:39.664824Z", "iopub.status.idle": "2026-06-09T05:35:39.668720Z", "shell.execute_reply": "2026-06-09T05:35:39.668531Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "area grew from 1.298 to 126.337 (monotone: True)\n" ] } ], "source": [ "# Gradient ascent: inflate the star, recording the area at every step.\n", "dt, n_steps = 0.08, 90\n", "states = [X0.copy()]\n", "areas = [simkit.outline_areas(X0, [E])[0]]\n", "X = X0.copy()\n", "for _ in range(n_steps):\n", " g = simkit.outline_areas_gradient(X, [E])[0].reshape(-1, 2)\n", " X = X + dt * g # one step straight uphill on A\n", " states.append(X.copy())\n", " areas.append(simkit.outline_areas(X, [E])[0])\n", "print(f\"area grew from {areas[0]:.3f} to {areas[-1]:.3f} \"\n", " f\"(monotone: {np.all(np.diff(areas) > 0)})\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "bbebcc22", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:35:39.669627Z", "iopub.status.busy": "2026-06-09T05:35:39.669579Z", "iopub.status.idle": "2026-06-09T05:35:42.126442Z", "shell.execute_reply": "2026-06-09T05:35:42.126185Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Animate the inflation with the area curve filling in beside it.\n", "fig, (ax_s, ax_a) = plt.subplots(1, 2, figsize=(11, 5))\n", "lim = 1.05 * np.max(np.abs(states[-1]))\n", "utils.setup_axes(ax_s, (-lim, lim), (-lim, lim), title=\"inflating the star\")\n", "(loop_line,) = ax_s.plot([], [], \"-o\", color=POS_C, lw=2.5, ms=4)\n", "fill_holder = {\"p\": None}\n", "\n", "ax_a.set_xlim(0, n_steps)\n", "ax_a.set_ylim(areas[0] * 0.9, areas[-1] * 1.05)\n", "ax_a.set_xlabel(\"gradient-ascent step\")\n", "ax_a.set_ylabel(\"enclosed area $A$\")\n", "ax_a.set_title(\"area climbs every step\")\n", "ax_a.grid(True, color=\"0.92\")\n", "(area_line,) = ax_a.plot([], [], color=POS_C, lw=2.5)\n", "\n", "def update(k):\n", " Xk = states[k]\n", " loop = np.vstack([Xk, Xk[0]])\n", " loop_line.set_data(loop[:, 0], loop[:, 1])\n", " if fill_holder[\"p\"] is not None:\n", " fill_holder[\"p\"].remove()\n", " fill_holder[\"p\"] = ax_s.fill(Xk[:, 0], Xk[:, 1], color=POS_C, alpha=0.18, zorder=1)[0]\n", " area_line.set_data(np.arange(k + 1), areas[:k + 1])\n", " return loop_line, area_line\n", "\n", "anim = FuncAnimation(fig, update, frames=len(states), interval=50, blit=False)\n", "fig.suptitle(\"Following $\\\\nabla A$ inflates the loop and grows its area\", y=1.0)\n", "fig.tight_layout()\n", "utils.show_video(fig, anim, \"media/13_inflate.mp4\", fps=20)" ] }, { "cell_type": "markdown", "id": "83a5d5e0", "metadata": {}, "source": [ "## 4 · Checking the gradient and Hessian against finite differences\n", "\n", "The analytic derivatives should match a brute-force central finite difference of\n", "`outline_areas`. We show that as heatmaps: analytic vs FD, plus the tiny residual.\n", "The Hessian is especially clean — the signed area is **bilinear** in the\n", "coordinates, so $\\partial^2 A/\\partial x^2$ is a *constant* matrix that only couples\n", "the $x$ of one endpoint to the $y$ of the other (the checkerboard pattern below),\n", "and it does not depend on where the vertices are at all." ] }, { "cell_type": "code", "execution_count": 8, "id": "fe97be68", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:35:42.127578Z", "iopub.status.busy": "2026-06-09T05:35:42.127499Z", "iopub.status.idle": "2026-06-09T05:35:42.368195Z", "shell.execute_reply": "2026-06-09T05:35:42.367957Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |grad - fd| = 6.78e-10\n", "max |Hess - fd| = 5.14e-10\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.array([[0.0, 0.0], [2.0, -0.3], [2.4, 1.1],\n", " [1.0, 2.0], [-0.5, 1.2]]) # irregular pentagon\n", "E = simkit.closed_polyline(X)\n", "z = X.flatten()\n", "\n", "def area_flat(zz): # all verts in one loop ->\n", " return simkit.outline_areas(zz.reshape(-1, 2), [E]) # local dofs == X.flatten()\n", "\n", "g = simkit.outline_areas_gradient(X, [E])[0].flatten()\n", "g_fd = simkit.gradient_cfd(area_flat, z, 1e-6).flatten()\n", "H = simkit.outline_areas_hessian(X, [E])[0]\n", "H_fd = simkit.hessian_cfd(area_flat, z, 1e-3).reshape(H.shape)\n", "print(f\"max |grad - fd| = {np.max(np.abs(g - g_fd)):.2e}\")\n", "print(f\"max |Hess - fd| = {np.max(np.abs(H - H_fd)):.2e}\")\n", "\n", "fig = plt.figure(figsize=(12, 6.5))\n", "ax_g = fig.add_subplot(2, 3, 1)\n", "idx = np.arange(len(g))\n", "ax_g.bar(idx - 0.2, g, width=0.4, color=POS_C, label=\"analytic\")\n", "ax_g.bar(idx + 0.2, g_fd, width=0.4, color=NEG_C, alpha=0.7, label=\"finite diff\")\n", "ax_g.set_title(\"gradient $\\\\nabla A$\"); ax_g.set_xlabel(\"local dof [x0,y0,x1,y1,...]\")\n", "ax_g.legend(fontsize=8)\n", "\n", "ax_gr = fig.add_subplot(2, 3, 4)\n", "ax_gr.bar(idx, g - g_fd, color=EDGE_C)\n", "ax_gr.set_title(f\"gradient residual (max {np.max(np.abs(g-g_fd)):.1e})\")\n", "ax_gr.set_xlabel(\"local dof\")\n", "\n", "vmax = max(np.max(np.abs(H)), 1e-9)\n", "for col, (M, title) in enumerate([(H, \"analytic Hessian\"), (H_fd, \"finite-diff Hessian\")]):\n", " ax = fig.add_subplot(2, 3, 2 + col)\n", " im = ax.imshow(M, cmap=\"coolwarm\", vmin=-vmax, vmax=vmax)\n", " ax.set_title(title); fig.colorbar(im, ax=ax, fraction=0.046)\n", "ax_hr = fig.add_subplot(2, 3, 6)\n", "im = ax_hr.imshow(H - H_fd, cmap=\"coolwarm\")\n", "ax_hr.set_title(f\"Hessian residual (max {np.max(np.abs(H-H_fd)):.1e})\")\n", "fig.colorbar(im, ax=ax_hr, fraction=0.046)\n", "\n", "fig.suptitle(\"simkit.outline_areas derivatives match finite differences\", y=1.02)\n", "fig.tight_layout()\n", "fig.savefig(\"media/13_derivative_checks.png\", dpi=130, bbox_inches=\"tight\")\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "simkit", "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": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }