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‎Computational-Geometry-Tutorial.pdf

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‎PA1.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# PA1: Poly2mask\n",
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"\n",
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"实现扫描线将给定的多边形转变为梯形mask, 辅助函数和整体框架已实现, 请填补`poly2mask`函数中缺失的部分, 最终效果如下图:\n",
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"![pa1_show](./data/pa1_show.png)"
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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": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from PIL import Image\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"`line_inter`求直线AB和CD的交点.\n",
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"\n",
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"`get_trapezoids`接收相邻两条扫描线和多边形的交点`bottom_inter`(下底交点)/`top_inter`(上底交点), 返回两条扫描线之间能构成的梯形列表."
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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": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def line_inter(A, B, C, D):\n",
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" return A + (B - A) * np.cross(C - A, D - C) / np.cross(B - A, D - C)\n",
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"\n",
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"\n",
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"def get_trapezoids(top_inter, bottom_inter):\n",
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" assert len(top_inter) % 2 == 0 and len(top_inter) == len(bottom_inter)\n",
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"\n",
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" if len(top_inter) == 0:\n",
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" return []\n",
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"\n",
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" top_inter = top_inter[np.argsort(top_inter[:, 0])]\n",
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" bottom_inter = bottom_inter[np.argsort(bottom_inter[:, 0])]\n",
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"\n",
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" trape_list = list()\n",
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" for i in range(0, len(bottom_inter), 2):\n",
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" trape_list.append(\n",
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" np.concatenate([top_inter[[i, i + 1]], bottom_inter[[i + 1, i]]])\n",
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" )\n",
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" return trape_list\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"`poly2mask`流程:\n",
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"1. 接收多边形`poly`, 将顶点按照Y从小到大排序, 遍历顶点.\n",
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"2. 利用`line_inter`函数求当前扫描线作为梯形上底时和多边形的交点`top_inter`.\n",
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"3. (当前扫描线为首条时跳过此步) 由上一条扫描线作为梯形下底, 当前扫描线作为梯形上底, 调用`get_trapezoids`函数得到当前扫描线和上一条扫描线之间的梯形.\n",
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"4. 更新当前顶点`idx`相邻的边: 若已遍历过从`edge_set`中删除, 未遍历过则加入`edge_set`.\n",
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"5. 利用`line_inter`函数求当前扫描线作为梯形下底时和多边形的交点`bottom_inter` (遍历到下条扫描线时才会用到)."
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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": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def poly2mask(poly):\n",
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" N = len(poly)\n",
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"\n",
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" # Q1: sort indices of vertices by Y (use np.argsort)\n",
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" sorted_indices = None\n",
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"\n",
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" edge_set = set()\n",
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" trape_list = list()\n",
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" bottom_inter = None\n",
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"\n",
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" for idx in sorted_indices:\n",
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" cur_y = poly[idx][1]\n",
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"\n",
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" top_inter = list()\n",
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" for e in edge_set:\n",
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" # Q2: get intersection of edge e and line Y = cur_y\n",
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" inter = None\n",
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" top_inter.append(inter)\n",
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"\n",
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" if bottom_inter:\n",
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" trape_list.extend(\n",
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" get_trapezoids(np.stack(bottom_inter), np.stack(top_inter))\n",
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" )\n",
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"\n",
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" le_idx = (idx + N - 1) % N # left neighbor vertex\n",
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" if poly[le_idx, 1] <= cur_y: # if the left edge is lower than cur_y\n",
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" # Q3: remove edge le_idx from edge_set\n",
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" pass\n",
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" else:\n",
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" # Q4: add edge le_idx into edge_set\n",
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" pass\n",
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"\n",
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" ri_idx = (idx + 1) % N # right neighbor vertex\n",
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" if poly[ri_idx, 1] <= cur_y: # if the right edge is lower than cur_y\n",
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" # Q5: remove edge idx from edge_set\n",
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" pass\n",
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" else:\n",
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" # Q6: add edge le_idx into edge_set\n",
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" pass\n",
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"\n",
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" bottom_inter = list()\n",
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" for e in edge_set:\n",
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" # Q7: get intersection of edge e and line y = cur_y\n",
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" inter = None\n",
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" bottom_inter.append(inter)\n",
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"\n",
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" return trape_list\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"运行下面代码块得到可视化结果, 验证代码实现的正确性."
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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": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"img = Image.open(\"./data/pa1.png\")\n",
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"with open(\"./data/pa1.txt\", \"r\") as f:\n",
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" poly = []\n",
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" for line in f.readlines():\n",
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" x, y = map(int, line.split(\",\"))\n",
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" poly.append([x, y])\n",
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" poly = np.array(poly)\n",
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"\n",
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"ax = plt.subplots(1, 2, figsize=(15, 15))[1]\n",
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"ax[0].imshow(img)\n",
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"ax[0].plot(poly[:, 0], poly[:, 1], linewidth=5)\n",
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"\n",
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"ax[1].imshow(img)\n",
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"trape_list = poly2mask(poly)\n",
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"for tr in trape_list:\n",
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" ax[1].fill(tr[:, 0], tr[:, 1], alpha=0.8)\n",
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"\n",
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"plt.tight_layout()\n",
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"plt.show()\n"
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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 3.7.13 ('tvm': venv)",
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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": "3.7.13"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "341a80c59a3ec9d769ab0e0928ba401a5b9b98de67015334e0ba45c81c270ad5"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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