[\u56fe\u7247\uff1aDP\u7b97\u6cd5\u539f\u7406\u52a8\u6001\u793a\u610f\u56fe\uff0c\u5c55\u793a\u9012\u5f52\u5206\u5272\u548c\u9608\u503c\u5224\u65ad\u8fc7\u7a0b]<\/code><\/p>\nJava\u4ee3\u7801\u5b9e\u73b0\u4e0e\u8be6\u89e3<\/h4>\n
\u4e0b\u9762\u662f\u4e00\u4e2aDP\u7b97\u6cd5\u7684\u6838\u5fc3Java\u5b9e\u73b0\u3002\u4ee3\u7801\u4e2d\u5305\u542b\u4e86\u70b9\u5bf9\u8c61\u7684\u5b9a\u4e49\u3001\u6838\u5fc3\u7684\u9012\u5f52\u538b\u7f29\u903b\u8f91\u4ee5\u53ca\u8ba1\u7b97\u70b9\u5230\u7ebf\u6bb5\u8ddd\u79bb\u7684\u8f85\u52a9\u65b9\u6cd5\u3002<\/p>\n
import java.util.ArrayList;import java.util.List;\/\/ \u5b9a\u4e49GPS\u70b9\u5bf9\u8c61class Point { double x; \/\/ \u7ecf\u5ea6 double y; \/\/ \u7eac\u5ea6 public Point(double x, double y) { this.x = x; this.y = y; }}public class DouglasPeucker { \/** * \u8ba1\u7b97\u70b9\u5230\u7ebf\u6bb5\u7684\u5782\u76f4\u8ddd\u79bb * @param p \u5f85\u8ba1\u7b97\u7684\u70b9 * @param start \u7ebf\u6bb5\u8d77\u70b9 * @param end \u7ebf\u6bb5\u7ec8\u70b9 * @return \u70b9\u5230\u7ebf\u6bb5\u7684\u8ddd\u79bb *\/ private double perpendicularDistance(Point p, Point start, Point end) { double dx = end.x - start.x; double dy = end.y - start.y; \/\/ \u5904\u7406\u7ebf\u6bb5\u8d77\u70b9\u548c\u7ec8\u70b9\u91cd\u5408\u7684\u7279\u6b8a\u60c5\u51b5 if (dx == 0 && dy == 0) { return Math.sqrt(Math.pow(p.x - start.x, 2) + Math.pow(p.y - start.y, 2)); } \/\/ \u8ba1\u7b97\u70b9p\u5728\u7ebf\u6bb5\u6295\u5f71\u7684\u6bd4\u4f8b double t = ((p.x - start.x) * dx + (p.y - start.y) * dy) \/ (dx * dx + dy * dy); Point projection; if (t < 0) { \/\/ \u6295\u5f71\u70b9\u5728\u7ebf\u6bb5\u8d77\u70b9\u5916 projection = start; } else if (t > 1) { \/\/ \u6295\u5f71\u70b9\u5728\u7ebf\u6bb5\u7ec8\u70b9\u5916 projection = end; } else { \/\/ \u6295\u5f71\u70b9\u5728\u7ebf\u6bb5\u4e0a projection = new Point(start.x + t * dx, start.y + t * dy); } \/\/ \u8fd4\u56de\u70b9p\u5230\u6295\u5f71\u70b9\u7684\u8ddd\u79bb return Math.sqrt(Math.pow(p.x - projection.x, 2) + Math.pow(p.y - projection.y, 2)); } \/** * Douglas-Peucker\u7b97\u6cd5\u6838\u5fc3\u5b9e\u73b0 * @param points \u539f\u59cb\u8f68\u8ff9\u70b9\u5217\u8868 * @param epsilon \u8ddd\u79bb\u9608\u503c * @return \u538b\u7f29\u540e\u7684\u8f68\u8ff9\u70b9\u5217\u8868 *\/ public List compress(List points, double epsilon) { if (points == null || points.size() < 3) { return points; } List result = new ArrayList<>(); \/\/ \u9012\u5f52\u51fd\u6570\u7684\u5165\u53e3 compressRecursive(points, 0, points.size() - 1, epsilon, result); \/\/ \u786e\u4fdd\u6700\u540e\u4e00\u4e2a\u70b9\u88ab\u6dfb\u52a0 result.add(points.get(points.size() - 1)); return result; } private void compressRecursive(List points, int startIndex, int endIndex, double epsilon, List result) { \/\/ \u9012\u5f52\u57fa\uff1a\u7ebf\u6bb5\u4e0a\u53ea\u6709\u4e24\u4e2a\u70b9\uff0c\u76f4\u63a5\u4fdd\u7559\u8d77\u70b9 if (startIndex >= endIndex) { if (result.isEmpty() || result.get(result.size() - 1) != points.get(startIndex)) { result.add(points.get(startIndex)); } return; } double maxDist = 0; int index = 0; \/\/ \u627e\u5230\u8ddd\u79bb\u7ebf\u6bb5[startIndex, endIndex]\u6700\u8fdc\u7684\u70b9 for (int i = startIndex + 1; i < endIndex; i++) { double dist = perpendicularDistance(points.get(i), points.get(startIndex), points.get(endIndex)); if (dist > maxDist) { maxDist = dist; index = i; } } \/\/ \u5982\u679c\u6700\u5927\u8ddd\u79bb\u5927\u4e8e\u9608\u503c\uff0c\u5219\u4fdd\u7559\u8be5\u70b9\uff0c\u5e76\u4ee5\u8be5\u70b9\u4e3a\u754c\uff0c\u5bf9\u4e24\u8fb9\u8fdb\u884c\u9012\u5f52 if (maxDist > epsilon) { compressRecursive(points, startIndex, index, epsilon, result); compressRecursive(points, index, endIndex, epsilon, result); } else { \/\/ \u5982\u679c\u6700\u5927\u8ddd\u79bb\u5c0f\u4e8e\u9608\u503c\uff0c\u5219\u820d\u5f03\u4e2d\u95f4\u6240\u6709\u70b9\uff0c\u53ea\u4fdd\u7559\u8d77\u70b9 \/\/ \u7ec8\u70b9\u5c06\u5728\u4e0a\u4e00\u5c42\u9012\u5f52\u6216\u6700\u7ec8\u8c03\u7528\u4e2d\u88ab\u6dfb\u52a0 if (result.isEmpty() || result.get(result.size() - 1) != points.get(startIndex)) { result.add(points.get(startIndex)); } } }}<\/code><\/pre>\n\u4f18\u7f3a\u70b9\u5206\u6790<\/h4>\n\n- \u4f18\u70b9<\/strong>\uff1a\u538b\u7f29\u7387\u9ad8\uff0c\u4e14\u80fd\u975e\u5e38\u597d\u5730\u4fdd\u7559\u8f68\u8ff9\u7684\u6574\u4f53\u8f6e\u5ed3\u548c\u5173\u952e\u62d0\u70b9\u3002\u8fd9\u662f\u5176\u6700\u5927\u7684\u4ef7\u503c\u6240\u5728\uff0c\u538b\u7f29\u540e\u7684\u8f68\u8ff9\u5728\u5730\u56fe\u4e0a\u89c6\u89c9\u6548\u679c\u975e\u5e38\u63a5\u8fd1\u539f\u59cb\u8f68\u8ff9\u3002<\/li>\n
- \u7f3a\u70b9<\/strong>\uff1a\u8ba1\u7b97\u76f8\u5bf9\u590d\u6742\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u4e3aO(n\u00b2)\uff0c\u5e73\u5747\u4e3aO(n log n)\u3002\u7b97\u6cd5\u5bf9\u8f68\u8ff9\u5e8f\u5217\u4e2d\u7684\u5c16\u9510\u201c\u6bdb\u523a\u201d\u70b9\uff08\u4f8b\u5982\u7531GPS\u4fe1\u53f7\u6f02\u79fb\u4ea7\u751f\u7684\u566a\u70b9\uff09\u975e\u5e38\u654f\u611f\uff0c\u53ef\u80fd\u4f1a\u5c06\u8fd9\u4e9b\u65e0\u610f\u4e49\u7684\u70b9\u4f5c\u4e3a\u5173\u952e\u70b9\u4fdd\u7559\u4e0b\u6765\u3002\u6b64\u5916\uff0c\u5b83\u662f\u4e00\u4e2a\u7eaf\u7cb9\u7684\u7a7a\u95f4\u7b97\u6cd5\uff0c\u5b8c\u5168\u5ffd\u7565\u4e86\u65f6\u95f4\u3001\u901f\u5ea6\u7b49\u975e\u7a7a\u95f4\u7ef4\u5ea6\u4fe1\u606f\u3002<\/li>\n<\/ul>\n
\u9002\u7528\u573a\u666f<\/h4>\n
DP\u7b97\u6cd5\u975e\u5e38\u9002\u5408\u5bf9\u8f68\u8ff9\u5f62\u6001\u4fdd\u771f\u5ea6\u8981\u6c42\u9ad8\u7684\u573a\u666f\uff0c\u4f8b\u5982\uff1a<\/p>\n
\n- \u5730\u56fe\u5e94\u7528\u4e2d\u7684\u8def\u5f84\u7ed8\u5236\u4e0e\u5c55\u793a\u3002<\/li>\n
- \u8f68\u8ff9\u76f8\u4f3c\u5ea6\u5206\u6790\u3001\u9a7e\u9a76\u884c\u4e3a\u5206\u6790\u7b49\u9700\u8981\u4fdd\u7559\u8def\u7ebf\u7279\u5f81\u7684\u7b97\u6cd5\u524d\u5e8f\u5904\u7406\u3002<\/li>\n
- \u7535\u5b50\u56f4\u680f\u7684\u5339\u914d\u5224\u65ad\uff0c\u5224\u65ad\u4e00\u6761\u8f68\u8ff9\u662f\u5426\u7a7f\u8d8a\u4e86\u67d0\u4e2a\u533a\u57df\u3002<\/li>\n<\/ul>\n
\u7b97\u6cd5\u4e8c\uff1a\u57fa\u4e8e\u65f6\u95f4\u4e0e\u8ddd\u79bb\u9608\u503c\u7684\u62bd\u7a00\u7b97\u6cd5<\/h3>\n
\u8fd9\u662f\u4e00\u79cd\u5b9e\u73b0\u8d77\u6765\u975e\u5e38\u7b80\u5355\u3001\u8ba1\u7b97\u6548\u7387\u6781\u9ad8\u7684\u538b\u7f29\u65b9\u6cd5\uff0c\u5728\u5f88\u591a\u5bf9\u5b9e\u65f6\u6027\u8981\u6c42\u9ad8\u7684\u573a\u666f\u4e2d\u88ab\u5e7f\u6cdb\u5e94\u7528\u3002<\/p>\n
\u539f\u7406\u4e0e\u6838\u5fc3\u601d\u60f3<\/h4>\n
\u8be5\u7b97\u6cd5\u7684\u903b\u8f91\u975e\u5e38\u76f4\u89c2\uff0c\u5b83\u6309\u987a\u5e8f\u904d\u5386\u6240\u6709\u8f68\u8ff9\u70b9\uff0c\u5e76\u6839\u636e\u4e0e\u4e0a\u4e00\u4e2a\u201c\u5df2\u4fdd\u7559\u70b9\u201d\u7684\u5173\u7cfb\u6765\u51b3\u5b9a\u5f53\u524d\u70b9\u662f\u5426\u8981\u88ab\u4fdd\u7559\u3002<\/p>\n
\n- \u987a\u5e8f\u904d\u5386<\/strong>\uff1a\u4ece\u8f68\u8ff9\u7684\u7b2c\u4e00\u4e2a\u70b9\u5f00\u59cb\uff08\u7b2c\u4e00\u4e2a\u70b9\u9ed8\u8ba4\u4fdd\u7559\uff09\uff0c\u4f9d\u6b21\u5411\u540e\u68c0\u67e5\u6bcf\u4e2a\u70b9\u3002<\/li>\n
- \u53cc\u91cd\u9608\u503c<\/strong>\uff1a\u5bf9\u4e8e\u5f53\u524d\u70b9\uff0c\u8ba1\u7b97\u5b83\u4e0e\u4e0a\u4e00\u4e2a\u88ab\u4fdd\u7559\u4e0b\u6765\u7684\u70b9\u4e4b\u95f4\u7684\u65f6\u95f4\u5dee\u548c\u7a7a\u95f4\u8ddd\u79bb\u3002<\/li>\n
- \u4fdd\u7559\u51b3\u7b56<\/strong>\uff1a\u53ea\u6709\u5f53\u65f6\u95f4\u5dee\u8d85\u8fc7\u4e86\u8bbe\u5b9a\u7684\u65f6\u95f4\u9608\u503c\uff08\u598230\u79d2\uff09\uff0c\u6216\u8005\u7a7a\u95f4\u8ddd\u79bb\u8d85\u8fc7\u4e86\u8bbe\u5b9a\u7684\u8ddd\u79bb\u9608\u503c\uff08\u598250\u7c73\uff09\u65f6\uff0c\u624d\u4fdd\u7559\u5f53\u524d\u70b9\u3002\u4e00\u65e6\u5f53\u524d\u70b9\u88ab\u4fdd\u7559\uff0c\u5b83\u5c31\u6210\u4e3a\u65b0\u7684\u201c\u4e0a\u4e00\u4e2a\u4fdd\u7559\u70b9\u201d\uff0c\u7528\u4e8e\u548c\u540e\u7eed\u7684\u70b9\u8fdb\u884c\u6bd4\u8f83\u3002<\/li>\n<\/ul>\n
Java\u4ee3\u7801\u5b9e\u73b0\u4e0e\u8be6\u89e3<\/h4>\n
\u8be5\u7b97\u6cd5\u7684\u5b9e\u73b0\u4e0d\u6d89\u53ca\u590d\u6742\u7684\u9012\u5f52\u6216\u6570\u5b66\u8ba1\u7b97\uff0c\u4ee3\u7801\u903b\u8f91\u6e05\u6670\u6613\u61c2\u3002<\/p>\n
import java.util.ArrayList;import java.util.List;\/\/ \u5047\u8bbePoint\u7c7b\u5df2\u5b9a\u4e49\uff0c\u5e76\u589e\u52a0\u4e86\u65f6\u95f4\u6233\u5c5e\u6027class TimedPoint extends Point { long timestamp; \/\/ a a a a a a a a a public TimedPoint(double x, double y, long timestamp) { super(x, y); this.timestamp = timestamp; }}public class TimeDistanceThinning { \/\/ \u7b80\u5316\u7684\u7ecf\u7eac\u5ea6\u8ddd\u79bb\u8ba1\u7b97\uff08\u5355\u4f4d\uff1a\u7c73\uff09\uff0c\u5b9e\u9645\u9879\u76ee\u4e2d\u5efa\u8bae\u4f7f\u7528\u66f4\u7cbe\u786e\u7684Haversine\u516c\u5f0f private double calculateDistance(Point p1, Point p2) { double R = 6371000; \/\/ \u5730\u7403\u534a\u5f84 double lat1Rad = Math.toRadians(p1.y); double lat2Rad = Math.toRadians(p2.y); double deltaLat = Math.toRadians(p2.y - p1.y); double deltaLon = Math.toRadians(p2.x - p1.x); double a = Math.sin(deltaLat \/ 2) * Math.sin(deltaLat \/ 2) + Math.cos(lat1Rad) * Math.cos(lat2Rad) * Math.sin(deltaLon \/ 2) * Math.sin(deltaLon \/ 2); double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a)); return R * c; } \/** * \u57fa\u4e8e\u65f6\u95f4\u548c\u8ddd\u79bb\u9608\u503c\u7684\u62bd\u7a00\u7b97\u6cd5 * @param points \u539f\u59cb\u8f68\u8ff9\u70b9\u5217\u8868 * @param timeThreshold \u65f6\u95f4\u9608\u503c\uff08\u79d2\uff09 * @param distanceThreshold \u8ddd\u79bb\u9608\u503c\uff08\u7c73\uff09 * @return \u538b\u7f29\u540e\u7684\u8f68\u8ff9\u70b9\u5217\u8868 *\/ public List compress(List points, long timeThreshold, double distanceThreshold) { if (points == null || points.size() < 2) { return points; } List compressedPoints = new ArrayList<>(); TimedPoint lastKeptPoint = points.get(0); compressedPoints.add(lastKeptPoint); for (int i = 1; i < points.size(); i++) { TimedPoint currentPoint = points.get(i); long timeDiff = (currentPoint.timestamp - lastKeptPoint.timestamp) \/ 1000; \/\/ \u8f6c\u6362\u4e3a\u79d2 double distance = calculateDistance(currentPoint, lastKeptPoint); if (timeDiff >= timeThreshold || distance >= distanceThreshold) { compressedPoints.add(currentPoint); lastKeptPoint = currentPoint; } } \/\/ \u786e\u4fdd\u6700\u540e\u4e00\u4e2a\u70b9\u603b\u662f\u88ab\u5305\u542b\uff0c\u4ee5\u5b8c\u6574\u8868\u793a\u8f68\u8ff9\u6bb5 TimedPoint lastOriginalPoint = points.get(points.size() - 1); if (compressedPoints.get(compressedPoints.size() - 1) != lastOriginalPoint) { compressedPoints.add(lastOriginalPoint); } return compressedPoints; }}<\/code><\/pre>\n\u4f18\u7f3a\u70b9\u5206\u6790<\/h4>\n\n- \u4f18\u70b9<\/strong>\uff1a\u7b97\u6cd5\u6781\u5176\u7b80\u5355\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n)\uff0c\u8ba1\u7b97\u901f\u5ea6\u98de\u5feb\uff0c\u5185\u5b58\u5360\u7528\u5c0f\u3002\u975e\u5e38\u9002\u5408\u5728\u8d44\u6e90\u53d7\u9650\u7684\u7ec8\u7aef\u8bbe\u5907\u4e0a\u6216\u9700\u8981\u9ad8\u541e\u5410\u91cf\u7684\u6d41\u5f0f\u5904\u7406\u573a\u666f\u4e2d\u4f7f\u7528\u3002<\/li>\n
- \u7f3a\u70b9<\/strong>\uff1a\u538b\u7f29\u6548\u679c\u4e25\u91cd\u4f9d\u8d56\u4e8e\u9608\u503c\u7684\u8bbe\u5b9a\uff0c\u4e14\u5bb9\u6613\u4e22\u5931\u8f68\u8ff9\u7684\u5c40\u90e8\u5f62\u72b6\u7ec6\u8282\u3002\u4f8b\u5982\uff0c\u8f66\u8f86\u5728\u4e00\u4e2a\u5c0f\u8303\u56f4\u5185\u8fde\u7eed\u8f6c\u5f2f\uff0c\u5982\u679c\u6bcf\u4e2a\u70b9\u4e0e\u4e0a\u4e00\u4e2a\u70b9\u7684\u65f6\u7a7a\u8ddd\u79bb\u90fd\u4e0d\u5927\uff0c\u8fd9\u4e9b\u5173\u952e\u7684\u8f6c\u5f2f\u70b9\u5c31\u53ef\u80fd\u88ab\u5168\u90e8\u820d\u5f03\uff0c\u5bfc\u81f4\u8f68\u8ff9\u88ab\u201c\u62c9\u76f4\u201d\u3002<\/li>\n<\/ul>\n
\u9002\u7528\u573a\u666f<\/h4>\n\n- \u5b9e\u65f6\u8f68\u8ff9\u4e0a\u4f20<\/strong>\uff1a\u5728\u8f66\u8f7d\u8bbe\u5907\u6216\u624b\u673aApp\u7aef\u8fdb\u884c\u521d\u6b65\u538b\u7f29\uff0c\u51cf\u5c11\u7f51\u7edc\u6d41\u91cf\u6d88\u8017\u3002<\/li>\n
- \u6570\u636e\u91cf\u6781\u5927\u7684\u573a\u666f\u7c97\u7b5b<\/strong>\uff1a\u4f5c\u4e3a\u6570\u636e\u5165\u5e93\u524d\u7684\u7b2c\u4e00\u9053\u6e05\u6d17\u5de5\u5e8f\uff0c\u53bb\u9664\u660e\u663e\u7684\u5197\u4f59\u70b9\u3002<\/li>\n
- \u5bf9\u8f68\u8ff9\u5f62\u72b6\u8981\u6c42\u4e0d\u9ad8\u7684\u4e1a\u52a1<\/strong>\uff1a\u5982\u4ec5\u9700\u7edf\u8ba1\u884c\u9a76\u91cc\u7a0b\u3001\u8ba1\u7b97\u8fd0\u884c\u65f6\u957f\u7b49\u3002<\/li>\n<\/ul>\n
\u7b97\u6cd5\u4e09\uff1aVisvalingam-Whyatt \u7b97\u6cd5<\/h3>\n
\u8fd9\u662f\u4e00\u79cd\u76f8\u5bf9\u4e8eDP\u7b97\u6cd5\u66f4\u4e3a\u73b0\u4ee3\u7684\u7ebf\u5316\u7b80\u7b97\u6cd5\uff0c\u5b83\u901a\u8fc7\u4e00\u79cd\u4e0d\u540c\u7684\u51e0\u4f55\u6807\u51c6\u6765\u5224\u65ad\u70b9\u7684\u91cd\u8981\u6027\u3002<\/p>\n
\u539f\u7406\u4e0e\u6838\u5fc3\u601d\u60f3<\/h4>\n
Visvalingam-Whyatt\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u201c\u6709\u6548\u9762\u79ef\u201d\uff08Effective Area\uff09\u3002\u5b83\u4e0d\u5173\u5fc3\u70b9\u5230\u7ebf\u6bb5\u7684\u8ddd\u79bb\uff0c\u800c\u662f\u5173\u5fc3\u4e00\u4e2a\u70b9\u88ab\u79fb\u9664\u540e\uff0c\u5bf9\u539f\u59cb\u5f62\u72b6\u9020\u6210\u7684\u201c\u89c6\u89c9\u5f71\u54cd\u201d\u6709\u591a\u5927\u3002<\/p>\n
\n- \u6709\u6548\u9762\u79ef<\/strong>\uff1a\u5bf9\u4e8e\u8f68\u8ff9\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u8fde\u7eed\u7684\u70b9\u4e09\u5143\u7ec4\uff08P_i-1, P_i, P_i+1\uff09\uff0c\u8fd9\u4e09\u4e2a\u70b9\u6784\u6210\u4e00\u4e2a\u4e09\u89d2\u5f62\u3002\u8fd9\u4e2a\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u5c31\u88ab\u5b9a\u4e49\u4e3a\u4e2d\u95f4\u70b9P_i\u7684\u6709\u6548\u9762\u79ef\u3002\u8fd9\u4e2a\u9762\u79ef\u76f4\u89c2\u5730\u53cd\u6620\u4e86P_i\u8fd9\u4e2a\u70b9\u7684\u201c\u5c16\u9510\u201d\u7a0b\u5ea6\u3002<\/li>\n
- \u8fed\u4ee3\u5220\u9664<\/strong>\uff1a\u7b97\u6cd5\u9996\u5148\u8ba1\u7b97\u51fa\u8f68\u8ff9\u4e2d\u9664\u9996\u5c3e\u70b9\u5916\u6240\u6709\u70b9\u7684\u6709\u6548\u9762\u79ef\u3002\u7136\u540e\uff0c\u5b83\u4f1a\u627e\u5230\u5177\u6709\u6700\u5c0f\u6709\u6548\u9762\u79ef\u7684\u90a3\u4e2a\u70b9\uff0c\u5e76\u68c0\u67e5\u8fd9\u4e2a\u9762\u79ef\u662f\u5426\u5c0f\u4e8e\u8bbe\u5b9a\u7684\u9608\u503c\u3002\n
\n- \u5982\u679c\u5c0f\u4e8e\u9608\u503c\uff0c\u5c31\u5c06\u8fd9\u4e2a\u70b9\u5220\u9664\u3002\u5220\u9664\u8be5\u70b9\u540e\uff0c\u5176\u76f8\u90bb\u7684\u4e24\u4e2a\u70b9\uff08P_i-1, P_i+1\uff09\u4f1a\u5f62\u6210\u65b0\u7684\u90bb\u5c45\u5173\u7cfb\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u70b9\u7684\u6709\u6548\u9762\u79ef\u5c31\u9700\u8981\u88ab\u91cd\u65b0\u8ba1\u7b97\u3002<\/li>\n
- \u8fd9\u4e2a\u201c\u5bfb\u627e\u6700\u5c0f\u9762\u79ef\u70b9 -> \u5224\u65ad -> \u5220\u9664 -> \u66f4\u65b0\u90bb\u5c45\u9762\u79ef\u201d\u7684\u8fc7\u7a0b\u4f1a\u4e00\u76f4\u8fed\u4ee3\u4e0b\u53bb\uff0c\u76f4\u5230\u8f68\u8ff9\u4e2d\u6240\u6709\u70b9\u7684\u6709\u6548\u9762\u79ef\u90fd\u5927\u4e8e\u8bbe\u5b9a\u7684\u9608\u503c\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n
[\u56fe\u7247\uff1aVisvalingam-Whyatt\u7b97\u6cd5\u539f\u7406\u793a\u610f\u56fe\uff0c\u5c55\u793a\u4e09\u89d2\u5f62\u9762\u79ef\u8ba1\u7b97\u548c\u70b9\u5220\u9664\u8fc7\u7a0b]<\/code><\/p>\nJava\u4ee3\u7801\u5b9e\u73b0\u4e0e\u8be6\u89e3<\/h4>\n
\u8be5\u7b97\u6cd5\u7684\u5b9e\u73b0\u6bd4DP\u8981\u590d\u6742\uff0c\u901a\u5e38\u9700\u8981\u4f7f\u7528\u4f18\u5148\u961f\u5217\uff08Min-Heap\uff09\u6765\u9ad8\u6548\u5730\u627e\u5230\u9762\u79ef\u6700\u5c0f\u7684\u70b9\u3002<\/p>\n
import java.util.ArrayList;import java.util.LinkedList;import java.util.List;import java.util.PriorityQueue;\/\/ \u5047\u8bbePoint\u7c7b\u5df2\u5b9a\u4e49class Triangle implements Comparable { int index; double area; Triangle prev, next; public Triangle(int index, double area) { this.index = index; this.area = area; } @Override public int compareTo(Triangle other) { return Double.compare(this.area, other.area); }}public class VisvalingamWhyatt { private double calculateTriangleArea(Point p1, Point p2, Point p3) { return Math.abs(p1.x * (p2.y - p3.y) + p2.x * (p3.y - p1.y) + p3.x * (p1.y - p2.y)) \/ 2.0; } public List compress(List points, double areaThreshold) { if (points == null || points.size() < 3) { return points; } List pointList = new LinkedList<>(points); boolean[] removed = new boolean[points.size()]; PriorityQueue heap = new PriorityQueue<>(); \/\/ \u521d\u59cb\u5316\uff0c\u8ba1\u7b97\u6240\u6709\u70b9\u7684\u6709\u6548\u9762\u79ef\u5e76\u653e\u5165\u4f18\u5148\u961f\u5217 for (int i = 1; i < points.size() - 1; i++) { double area = calculateTriangleArea(points.get(i - 1), points.get(i), points.get(i + 1)); \/\/ \u5b9e\u9645\u9879\u76ee\u4e2d\u9700\u8981\u66f4\u5065\u58ee\u7684\u7ed3\u6784\u6765\u5173\u8054\u70b9\u548c\u4e09\u89d2\u5f62 \/\/ \u8fd9\u91cc\u7528\u7d22\u5f15\u4f5c\u4e3a\u7b80\u5316\u793a\u4f8b heap.add(new Triangle(i, area)); } int removedCount = 0; int targetSize = points.size(); \/\/ Can be a parameter \/\/ \u8fed\u4ee3\u5220\u9664 while (!heap.isEmpty() && heap.peek().area < areaThreshold && (points.size() - removedCount) > 2) { Triangle smallest = heap.poll(); int indexToRemove = smallest.index; \/\/ \u8fd9\u662f\u4e00\u4e2a\u7b80\u5316\u7684\u903b\u8f91\uff0c\u5b9e\u9645\u5b9e\u73b0\u9700\u8981\u5904\u7406\u597d\u5220\u9664\u70b9\u540e\uff0c \/\/ \u5176\u524d\u540e\u90bb\u5c45\u7684\u6709\u6548\u9762\u79ef\u66f4\u65b0\u95ee\u9898\uff0c\u8fd9\u901a\u5e38\u9700\u8981\u4e00\u4e2a\u53cc\u5411\u94fe\u8868\u6765\u9ad8\u6548\u5b8c\u6210\u3002 \/\/ \u4f2a\u4ee3\u7801\u903b\u8f91: \/\/ 1. \u4ece\u53cc\u5411\u94fe\u8868\u4e2d\u627e\u5230\u8981\u5220\u9664\u7684\u70b9node_i \/\/ 2. \u83b7\u53d6\u5176\u524d\u9a71 node_prev \u548c\u540e\u7ee7 node_next \/\/ 3. \u5c06 node_i \u4ece\u94fe\u8868\u4e2d\u79fb\u9664 \/\/ 4. \u91cd\u65b0\u8ba1\u7b97 node_prev \u7684\u6709\u6548\u9762\u79ef\uff08\u5982\u679c\u5b83\u4e0d\u662f\u9996\u8282\u70b9\uff09 \/\/ 5. \u91cd\u65b0\u8ba1\u7b97 node_next \u7684\u6709\u6548\u9762\u79ef\uff08\u5982\u679c\u5b83\u4e0d\u662f\u5c3e\u8282\u70b9\uff09 \/\/ 6. \u5728\u4f18\u5148\u961f\u5217\u4e2d\u66f4\u65b0 node_prev \u548c node_next \u5bf9\u5e94\u4e09\u89d2\u5f62\u7684\u9762\u79ef removed[indexToRemove] = true; removedCount++; } List result = new ArrayList<>(); for (int i = 0; i < points.size(); i++) { if (!removed[i]) { result.add(points.get(i)); } } return result; }}<\/code><\/pre>\n\u6ce8\uff1a\u4e0a\u8ff0\u4ee3\u7801\u4e3a\u7b80\u5316\u793a\u4f8b\uff0c\u65e8\u5728\u9610\u8ff0\u6838\u5fc3\u601d\u60f3\u3002\u4e00\u4e2a\u5065\u58ee\u7684\u751f\u4ea7\u7ea7\u5b9e\u73b0\u9700\u8981\u4f7f\u7528\u53cc\u5411\u94fe\u8868\u6765\u9ad8\u6548\u5730\u7ba1\u7406\u70b9\u7684\u90bb\u63a5\u5173\u7cfb\u548c\u66f4\u65b0\u6709\u6548\u9762\u79ef\u3002<\/em><\/p>\n\u4f18\u7f3a\u70b9\u5206\u6790<\/h4>\n\n- \u4f18\u70b9<\/strong>\uff1a\u76f8\u6bd4DP\u7b97\u6cd5\uff0c\u5b83\u5728\u5904\u7406\u67d0\u4e9b\u7c7b\u578b\u7684\u66f2\u7ebf\u65f6\uff0c\u80fd\u66f4\u597d\u5730\u4fdd\u7559\u611f\u77e5\u4e0a\u66f4\u91cd\u8981\u7684\u7279\u5f81\u70b9\uff0c\u538b\u7f29\u7ed3\u679c\u5728\u89c6\u89c9\u4e0a\u53ef\u80fd\u66f4\u5e73\u6ed1\u3001\u66f4\u81ea\u7136\u3002<\/li>\n
- \u7f3a\u70b9<\/strong>\uff1a\u8ba1\u7b97\u590d\u6742\u5ea6\u901a\u5e38\u9ad8\u4e8eDP\u7b97\u6cd5\uff0c\u5b9e\u73b0\u4e5f\u66f4\u4e3a\u590d\u6742\u3002<\/li>\n<\/ul>\n
\u9002\u7528\u573a\u666f<\/h4>\n\n- \u5bf9\u89c6\u89c9\u6548\u679c\u548c\u7279\u5f81\u4fdd\u7559\u6709\u66f4\u9ad8\u8981\u6c42\u7684\u9886\u57df\uff0c\u5982\u5730\u7406\u4fe1\u606f\u53ef\u89c6\u5316\u3001\u5730\u56fe\u5236\u56fe\u3001\u5730\u5f62\u5efa\u6a21\u7b49\u3002\u5bf9\u4e8e\u5927\u591a\u6570Web\u540e\u7aef\u5e94\u7528\uff0c\u5176\u5e26\u6765\u7684\u89c6\u89c9\u63d0\u5347\u53ef\u80fd\u4e0d\u8db3\u4ee5\u62b5\u6d88\u5176\u5b9e\u73b0\u7684\u590d\u6742\u6027\u3002<\/li>\n<\/ul>\n
\u7b97\u6cd5\u56db\uff1a\u4e1a\u52a1\u9a71\u52a8\u7684\u590d\u5408\u538b\u7f29\u7b56\u7565<\/h3>\n
\u5728\u771f\u5b9e\u7684\u5de5\u7a0b\u5b9e\u8df5\u4e2d\uff0c\u5355\u4e00\u7684\u7b97\u6cd5\u5f80\u5f80\u96be\u4ee5\u5b8c\u7f8e\u5e94\u5bf9\u6240\u6709\u95ee\u9898\u3002\u4e00\u4e2a\u66f4\u6210\u719f\u7684\u65b9\u6848\u662f\u6839\u636e\u4e1a\u52a1\u903b\u8f91\uff0c\u5c06\u591a\u79cd\u65b9\u6cd5\u7ec4\u5408\u8d77\u6765\uff0c\u5f62\u6210\u4e00\u4e2a\u591a\u9636\u6bb5\u7684\u5904\u7406\u7ba1\u9053\u3002<\/p>\n
\u7ed3\u5408\u505c\u7559\u70b9\u4e0e\u901f\u5ea6\u5f02\u5e38\u70b9<\/h4>\n
\u5f88\u591a\u8f68\u8ff9\u6570\u636e\u538b\u7f29\u7684\u573a\u666f\uff0c\u4e0d\u4ec5\u4ec5\u662f\u4e3a\u4e86\u51cf\u5c11\u70b9\uff0c\u4e5f\u662f\u4e3a\u4e86\u6570\u636e\u6e05\u6d17\u3002<\/p>\n
\n- \u505c\u7559\u70b9\u538b\u7f29<\/strong>\uff1a\u901a\u8fc7\u5224\u65ad\u8fde\u7eed\u591a\u4e2a\u70b9\u662f\u5426\u5728\u6781\u5c0f\u7684\u7a7a\u95f4\u8303\u56f4\uff08\u5982\u534a\u5f8420\u7c73\uff09\u5185\u505c\u7559\u4e86\u8d85\u8fc7\u4e00\u5b9a\u65f6\u95f4\uff08\u59825\u5206\u949f\uff09\uff0c\u53ef\u4ee5\u5c06\u8fd9\u4e9b\u70b9\u5408\u5e76\u4e3a\u4e00\u4e2a\u201c\u505c\u7559\u70b9\u201d\uff0c\u5e76\u9644\u5e26\u505c\u7559\u65f6\u957f\u4fe1\u606f\u3002\u8fd9\u5bf9\u4e8e\u5206\u6790\u7528\u6237\u7684\u5174\u8da3\u70b9\uff08POI\uff09\u6216\u8f66\u8f86\u7684\u505c\u9760\u70b9\u975e\u5e38\u6709\u4ef7\u503c\u3002<\/li>\n
- \u901f\u5ea6\u8fc7\u6ee4<\/strong>\uff1aGPS\u4fe1\u53f7\u5076\u5c14\u4f1a\u53d1\u751f\u6f02\u79fb\uff0c\u5bfc\u81f4\u4e24\u4e2a\u8fde\u7eed\u7684\u70b9\u4e4b\u95f4\u8ba1\u7b97\u51fa\u5f02\u5e38\u9ad8\u7684\u77ac\u65f6\u901f\u5ea6\uff08\u5982\u65f6\u901f\u8d85\u8fc7300\u516c\u91cc\uff09\u3002\u8fd9\u4e9b\u660e\u663e\u662f\u566a\u58f0\u7684\u70b9\u5e94\u8be5\u88ab\u76f4\u63a5\u5254\u9664\u3002\u540c\u65f6\uff0c\u901f\u5ea6\u957f\u65f6\u95f4\u4e3a0\u7684\u70b9\u4e5f\u53ef\u4ee5\u88ab\u89c6\u4e3a\u505c\u7559\u70b9\u5904\u7406\u3002<\/li>\n<\/ul>\n
\u591a\u7b97\u6cd5\u7ec4\u5408\u5e94\u7528\uff08\u63a8\u8350\u5b9e\u8df5\uff09<\/h4>\n
\u4e00\u4e2a\u975e\u5e38\u9ad8\u6548\u4e14\u5b9e\u7528\u7684\u7ec4\u5408\u7b56\u7565\u6d41\u7a0b\u5982\u4e0b\uff1a<\/p>\n
\n- \u9884\u5904\u7406<\/strong>\uff1a\u5148\u5bf9\u539f\u59cb\u8f68\u8ff9\u8fdb\u884c\u901f\u5ea6\u5f02\u5e38\u70b9\u8fc7\u6ee4\uff0c\u5254\u9664\u660e\u663e\u7684\u566a\u58f0\u3002<\/li>\n
- \u7c97\u7b5b<\/strong>\uff1a\u4f7f\u7528\u8ba1\u7b97\u5f00\u9500\u6781\u4f4e\u7684\u201c\u57fa\u4e8e\u65f6\u95f4\u4e0e\u8ddd\u79bb\u9608\u503c\u7684\u62bd\u7a00\u7b97\u6cd5\u201d\u8fdb\u884c\u7b2c\u4e00\u8f6e\u538b\u7f29\u3002\u8fd9\u4e00\u6b65\u53ef\u4ee5\u5feb\u901f\u53bb\u9664\u5927\u91cf\u7684\u7ebf\u6027\u5197\u4f59\u70b9\uff0c\u5927\u5e45\u51cf\u5c11\u4e0b\u4e00\u9636\u6bb5\u7684\u8ba1\u7b97\u91cf\u3002<\/li>\n
- \u7cbe\u70bc<\/strong>\uff1a\u5bf9\u7c97\u7b5b\u540e\u7684\u8f68\u8ff9\u5e94\u7528\u201cDP\u7b97\u6cd5\u201d\uff0c\u8fdb\u884c\u7cbe\u7ec6\u7684\u5f62\u6001\u4f18\u5316\u538b\u7f29\uff0c\u4fdd\u7559\u5173\u952e\u7684\u62d0\u70b9\uff0c\u786e\u4fdd\u8f68\u8ff9\u8f6e\u5ed3\u7684\u4fdd\u771f\u5ea6\u3002<\/li>\n<\/ol>\n
\/\/ \u4f2a\u4ee3\u7801\u6216\u6d41\u7a0b\u4ee3\u7801public List compositeCompress(List rawPoints) { \/\/ \u6b65\u9aa41: \u4e1a\u52a1\u903b\u8f91\u8fc7\u6ee4\uff08\u901f\u5ea6\u3001\u505c\u7559\u7b49\uff09 List filteredPoints = businessLogicFilter(rawPoints); \/\/ \u6b65\u9aa42: \u65f6\u95f4\/\u8ddd\u79bb\u7c97\u7b5b TimeDistanceThinning thinner = new TimeDistanceThinning(); List thinnedPoints = thinner.compress(filteredPoints, 30, 50); \/\/ 30\u79d2, 50\u7c73 \/\/ \u6b65\u9aa43: DP\u7b97\u6cd5\u7cbe\u70bc DouglasPeucker dp = new DouglasPeucker(); \/\/ DP\u7b97\u6cd5\u9700\u8981Point\u5217\u8868\uff0c\u8fdb\u884c\u7c7b\u578b\u8f6c\u6362 List pointsForDp = new ArrayList<>(thinnedPoints); List finalCompressedPoints = dp.compress(pointsForDp, 10); \/\/ 10\u7c73\u9608\u503c return finalCompressedPoints;}private List businessLogicFilter(List points) { \/\/ \u6b64\u5904\u5b9e\u73b0\u901f\u5ea6\u5f02\u5e38\u70b9\u5254\u9664\u3001\u505c\u7559\u70b9\u5408\u5e76\u7b49\u903b\u8f91 return points; \/\/ \u8fd4\u56de\u5904\u7406\u540e\u7684\u70b9}<\/code><\/pre>\n\u8fd9\u79cd\u590d\u5408\u7b56\u7565\u517c\u987e\u4e86\u5904\u7406\u6548\u7387\u548c\u538b\u7f29\u8d28\u91cf\uff0c\u662f\u6784\u5efa\u9ad8\u6027\u80fd\u3001\u9ad8\u53ef\u7528\u4f4d\u7f6e\u6570\u636e\u670d\u52a1\u7684\u63a8\u8350\u5b9e\u8df5\u3002<\/p>\n
\u6027\u80fd\u5bf9\u6bd4\u4e0e\u6280\u672f\u9009\u578b\u6307\u5357<\/h2>\n
\u9009\u62e9\u54ea\u79cd\u7b97\u6cd5\u5e76\u975e\u4e00\u4e2a\u6709\u6807\u51c6\u7b54\u6848\u7684\u95ee\u9898\uff0c\u5b83\u672c\u8d28\u4e0a\u662f\u5728\u591a\u4e2a\u7ef4\u5ea6\u4e4b\u95f4\u8fdb\u884c\u6743\u8861\u3002<\/p>\n
\u6838\u5fc3\u8bc4\u4f30\u6307\u6807<\/h3>\n
\u5728\u8bc4\u4f30\u4e00\u4e2a\u538b\u7f29\u7b97\u6cd5\u7684\u6548\u679c\u65f6\uff0c\u6211\u4eec\u4e3b\u8981\u5173\u6ce8\u4ee5\u4e0b\u4e09\u4e2a\u6307\u6807\uff1a<\/p>\n
\n- \u538b\u7f29\u7387\uff08Compression Ratio\uff09<\/strong>\uff1a
(1 - \u538b\u7f29\u540e\u70b9\u6570 \/ \u539f\u59cb\u70b9\u6570) * 100%<\/code>\u3002\u8fd9\u662f\u8861\u91cf\u5b58\u50a8\u548c\u4f20\u8f93\u6210\u672c\u8282\u7701\u7a0b\u5ea6\u6700\u76f4\u63a5\u7684\u6307\u6807\u3002<\/li>\n- \u8ba1\u7b97\u6548\u7387\uff08Time Complexity\uff09<\/strong>\uff1a\u7b97\u6cd5\u6267\u884c\u6240\u9700\u7684\u65f6\u95f4\u3002\u5bf9\u4e8e\u5b9e\u65f6\u7cfb\u7edf\uff0c\u8fd9\u662f\u5173\u952e\u7684\u6027\u80fd\u74f6\u9888\u3002<\/li>\n
- \u4f4d\u7f6e\u7cbe\u5ea6\u635f\u5931\uff08Positional Accuracy Loss\uff09<\/strong>\uff1a\u538b\u7f29\u540e\u8f68\u8ff9\u4e0e\u539f\u59cb\u8f68\u8ff9\u4e4b\u95f4\u7684\u504f\u5dee\u3002\u901a\u5e38\u53ef\u4ee5\u7528\u5e73\u5747\u8ddd\u79bb\u8bef\u5dee\u6216\u6700\u5927\u8ddd\u79bb\u8bef\u5dee\u6765\u8861\u91cf\u3002<\/li>\n<\/ul>\n
\u4e0d\u540c\u7b97\u6cd5\u6548\u679c\u5bf9\u6bd4<\/h3>\n
\u4e3a\u4e86\u76f4\u89c2\u5c55\u793a\u5dee\u5f02\uff0c\u6211\u4eec\u901a\u5e38\u4f1a\u4f7f\u7528\u540c\u4e00\u7ec4\u771f\u5b9e\u7684\u8f68\u8ff9\u6570\u636e\uff0c\u5e94\u7528\u4e0d\u540c\u7684\u7b97\u6cd5\u548c\u53c2\u6570\uff0c\u7136\u540e\u8fdb\u884c\u53ef\u89c6\u5316\u548c\u6570\u636e\u5bf9\u6bd4\u3002<\/p>\n
[\u56fe\u8868\uff1a\u4f7f\u7528\u540c\u4e00\u7ec4\u8f68\u8ff9\u6570\u636e\uff0c\u5bf9\u6bd4\u5c55\u793a\u4e0d\u540c\u7b97\u6cd5\u5728\u4e0d\u540c\u9608\u503c\u4e0b\u7684\u538b\u7f29\u7387\u3001\u8017\u65f6\u548c\u8f68\u8ff9\u5f62\u6001\u5dee\u5f02]<\/code><\/p>\n[\u56fe\u7247\uff1a\u539f\u59cb\u8f68\u8ff9\u4e0e\u7ecf\u8fc7DP\u3001\u65f6\u95f4\u8ddd\u79bb\u3001Visvalingam\u7b97\u6cd5\u538b\u7f29\u540e\u7684\u8f68\u8ff9\u53e0\u52a0\u5bf9\u6bd4\u56fe]<\/code><\/p>\n\u4ece\u5bf9\u6bd4\u4e2d\u901a\u5e38\u53ef\u4ee5\u89c2\u5bdf\u5230\uff1a<\/p>\n
\n- \u65f6\u95f4\u8ddd\u79bb\u7b97\u6cd5<\/strong>\uff1a\u538b\u7f29\u7387\u53ef\u8c03\u8303\u56f4\u5927\uff0c\u4f46\u8f68\u8ff9\u5f62\u6001\u635f\u5931\u660e\u663e\uff0c\u5f88\u591a\u5f2f\u9053\u88ab\u201c\u6284\u4e86\u8fd1\u9053\u201d\u3002<\/li>\n
- DP\u7b97\u6cd5<\/strong>\uff1a\u80fd\u5728\u6781\u9ad8\u7684\u538b\u7f29\u7387\u4e0b\uff0c\u4f9d\u7136\u4fdd\u6301\u4e0e\u539f\u59cb\u8f68\u8ff9\u9ad8\u5ea6\u76f8\u4f3c\u7684\u8f6e\u5ed3\u3002<\/li>\n
- Visvalingam\u7b97\u6cd5<\/strong>\uff1a\u4e0eDP\u7b97\u6cd5\u6548\u679c\u63a5\u8fd1\uff0c\u5728\u67d0\u4e9b\u5c40\u90e8\u7ec6\u8282\u4e0a\u53ef\u80fd\u5904\u7406\u5f97\u66f4\u5e73\u6ed1\u3002<\/li>\n<\/ul>\n
\u5982\u4f55\u505a\u51fa\u6b63\u786e\u7684\u6280\u672f\u9009\u578b\uff1f<\/h3>\n
\u57fa\u4e8e\u4ee5\u4e0a\u5206\u6790\uff0c\u6211\u4eec\u53ef\u4ee5\u4e3a\u4e0d\u540c\u7684\u4e1a\u52a1\u573a\u666f\u5236\u5b9a\u6e05\u6670\u7684\u6280\u672f\u9009\u578b\u7b56\u7565\u3002<\/p>\n
\n- \n
\u573a\u666f\u4e00\uff1a\u5b9e\u65f6\u6570\u636e\u4e0a\u4f20\uff08\u5982\u7f51\u7ea6\u8f66\u3001\u5916\u5356\u9a91\u624b\u4f4d\u7f6e\u4e0a\u62a5\uff09<\/strong><\/p>\n\n- \u51b3\u7b56<\/strong>\uff1a\u4f18\u5148\u9009\u62e9 \u201c\u57fa\u4e8e\u65f6\u95f4\u4e0e\u8ddd\u79bb\u9608\u503c\u7684\u62bd\u7a00\u7b97\u6cd5\u201d<\/strong>\u3002<\/li>\n
- \u539f\u56e0<\/strong>\uff1a\u6b64\u573a\u666f\u5bf9\u5b9e\u65f6\u6027\u8981\u6c42\u6700\u9ad8\uff0c\u5bf9\u7f51\u7edc\u6d41\u91cf\u6700\u654f\u611f\u3002\u8be5\u7b97\u6cd5\u8ba1\u7b97\u91cf\u6781\u5c0f\uff0c\u53ef\u5728\u7ec8\u7aef\u8bbe\u5907\u4e0a\u8f7b\u677e\u5b8c\u6210\uff0c\u80fd\u6709\u6548\u964d\u4f4e\u529f\u8017\u548c\u6d41\u91cf\u6210\u672c\u3002\u8f68\u8ff9\u5f62\u6001\u7684\u8f7b\u5fae\u5931\u771f\u5728\u6b64\u573a\u666f\u4e0b\u53ef\u4ee5\u63a5\u53d7\u3002<\/li>\n<\/ul>\n<\/li>\n
- \n
\u573a\u666f\u4e8c\uff1a\u5386\u53f2\u8f68\u8ff9\u5b58\u50a8\u4e0e\u5c55\u793a\uff08\u5982\u8f66\u961f\u7ba1\u7406\u540e\u53f0\u3001\u4e2a\u4eba\u8fd0\u52a8\u8bb0\u5f55\u56de\u653e\uff09<\/strong><\/p>\n\n- \u51b3\u7b56<\/strong>\uff1a\u63a8\u8350\u4f7f\u7528 \u201cDP\u7b97\u6cd5\u201d<\/strong> \u6216 \u201c\u590d\u5408\u538b\u7f29\u7b56\u7565\u201d<\/strong>\u3002<\/li>\n
- \u539f\u56e0<\/strong>\uff1a\u6b64\u573a\u666f\u7684\u6838\u5fc3\u662f\u6570\u636e\u5206\u6790\u548c\u53ef\u89c6\u5316\uff0c\u5bf9\u8f68\u8ff9\u7684\u4fdd\u771f\u5ea6\u8981\u6c42\u9ad8\u3002DP\u7b97\u6cd5\u80fd\u5f88\u597d\u5730\u5e73\u8861\u538b\u7f29\u7387\u548c\u5f62\u6001\u4fdd\u7559\u3002\u91c7\u7528\u5148\u7c97\u7b5b\u540e\u7cbe\u70bc\u7684\u590d\u5408\u7b56\u7565\uff0c\u5219\u53ef\u4ee5\u5728\u5904\u7406\u6d77\u91cf\u5386\u53f2\u6570\u636e\u65f6\u83b7\u5f97\u66f4\u9ad8\u7684\u6548\u7387\u3002<\/li>\n<\/ul>\n<\/li>\n
- \n
\u573a\u666f\u4e09\uff1a\u9ad8\u7cbe\u5ea6\u5730\u56fe\u7ed8\u5236\u4e0e\u5730\u7406\u5206\u6790<\/strong><\/p>\n\n- \u51b3\u7b56<\/strong>\uff1a\u53ef\u4ee5\u8003\u8651 \u201cVisvalingam-Whyatt\u7b97\u6cd5\u201d<\/strong> \u6216\u7cbe\u8c03\u53c2\u6570\u7684 \u201cDP\u7b97\u6cd5\u201d<\/strong>\u3002<\/li>\n
- \u539f\u56e0<\/strong>\uff1a\u8fd9\u7c7b\u4e13\u4e1aGIS\u5e94\u7528\u5bf9\u7ebf\u6761\u7684\u5e73\u6ed1\u5ea6\u548c\u89c6\u89c9\u6548\u679c\u6709\u82db\u523b\u8981\u6c42\u3002Visvalingam\u7b97\u6cd5\u5728\u8fd9\u4e9b\u65b9\u9762\u6709\u5176\u72ec\u7279\u4f18\u52bf\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n
[\u56fe\u7247\uff1aGPS\u8f68\u8ff9\u538b\u7f29\u7b97\u6cd5\u9009\u578b\u51b3\u7b56\u6d41\u7a0b\u56fe]<\/code><\/p>\n\u5e38\u89c1\u95ee\u9898 (FAQ)<\/h2>\nQ1: \u54ea\u79cdGPS\u8f68\u8ff9\u538b\u7f29\u7b97\u6cd5\u662f\u6700\u597d\u7684\uff1f<\/h3>\n
\u4e0d\u5b58\u5728\u7edd\u5bf9\u201c\u6700\u597d\u201d\u7684\u7b97\u6cd5\u3002\u6700\u4f73\u9009\u62e9\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u4e1a\u52a1\u9700\u6c42\uff0c\u9700\u8981\u5728\u538b\u7f29\u7387\u3001\u6570\u636e\u4fdd\u771f\u5ea6\u548c\u8ba1\u7b97\u6210\u672c\u4e4b\u95f4\u8fdb\u884c\u6743\u8861\u3002\u5bf9\u4e8e\u5927\u591a\u6570Web\u5e94\u7528\uff0c\u201cDP\u7b97\u6cd5\u201d\u53ca\u5176\u53d8\u79cd\u662f\u6027\u4ef7\u6bd4\u6700\u9ad8\u7684\u9009\u62e9\uff0c\u56e0\u4e3a\u5b83\u5728\u4fdd\u7559\u8f68\u8ff9\u5f62\u6001\u65b9\u9762\u8868\u73b0\u51fa\u8272\uff0c\u4e14\u6709\u6210\u719f\u7684\u5b9e\u73b0\u65b9\u6848\u3002<\/p>\n
Q2: \u5982\u4f55\u79d1\u5b66\u5730\u8bc4\u4f30\u538b\u7f29\u7b97\u6cd5\u7684\u6548\u679c\uff1f<\/h3>\n
\u8bc4\u4f30\u5e94\u4ece\u5b9a\u91cf\u548c\u5b9a\u6027\u4e24\u4e2a\u65b9\u9762\u8fdb\u884c\uff1a<\/p>\n
\n- \u5b9a\u91cf\u8bc4\u4f30<\/strong>\uff1a\u8ba1\u7b97\u538b\u7f29\u7387\u3001\u7b97\u6cd5\u6267\u884c\u8017\u65f6\u3001\u5e73\u5747\u4f4d\u7f6e\u8bef\u5dee\u3001\u6700\u5927\u4f4d\u7f6e\u8bef\u5dee\u7b49\u786c\u6027\u6307\u6807\u3002\u5e73\u5747\u4f4d\u7f6e\u8bef\u5dee\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u539f\u59cb\u8f68\u8ff9\u4e0a\u88ab\u820d\u5f03\u7684\u70b9\u5230\u538b\u7f29\u540e\u8f68\u8ff9\u5bf9\u5e94\u7ebf\u6bb5\u7684\u5e73\u5747\u8ddd\u79bb\u6765\u5f97\u51fa\u3002<\/li>\n
- \u5b9a\u6027\u8bc4\u4f30<\/strong>\uff1a\u5c06\u539f\u59cb\u8f68\u8ff9\u4e0e\u538b\u7f29\u540e\u8f68\u8ff9\u5728\u5730\u56fe\u4e0a\u8fdb\u884c\u53ef\u89c6\u5316\u53e0\u52a0\u5bf9\u6bd4\u3002\u8fd9\u662f\u6700\u76f4\u89c2\u7684\u65b9\u5f0f\uff0c\u53ef\u4ee5\u68c0\u67e5\u5173\u952e\u7684\u7279\u5f81\uff08\u5982\u8f6c\u5f2f\u3001\u6389\u5934\u3001\u505c\u7559\uff09\u662f\u5426\u5728\u538b\u7f29\u540e\u4e22\u5931\u3002<\/li>\n<\/ul>\n
Q3: \u5728Java\u4e2d\u5b9e\u73b0\u8fd9\u4e9b\u7b97\u6cd5\u9700\u8981\u6ce8\u610f\u54ea\u4e9b\u6027\u80fd\u95ee\u9898\uff1f<\/h3>\n\n- \u907f\u514d\u5728\u5faa\u73af\u4e2d\u9891\u7e41\u521b\u5efa\u65b0\u5bf9\u8c61<\/strong>\uff1a\u5c24\u5176\u662f\u5728\u5904\u7406\u5927\u89c4\u6a21\u8f68\u8ff9\u6570\u636e\u65f6\uff0c\u9891\u7e41
new Point()<\/code> \u4f1a\u7ed9GC\u5e26\u6765\u538b\u529b\u3002\u53ef\u4ee5\u8003\u8651\u5bf9\u8c61\u590d\u7528\u6216\u4f7f\u7528\u66f4\u539f\u59cb\u7684\u6570\u636e\u7ed3\u6784\u3002<\/li>\n- \u6d41\u5f0f\u5904\u7406<\/strong>\uff1a\u5bf9\u4e8eTB\u7ea7\u522b\u7684\u8d85\u5927\u89c4\u6a21\u5386\u53f2\u8f68\u8ff9\u6570\u636e\uff0c\u4e00\u6b21\u6027\u52a0\u8f7d\u5230\u5185\u5b58\u4e2d\u662f\u4e0d\u73b0\u5b9e\u7684\u3002\u5e94\u8003\u8651\u4ece\u6570\u636e\u5e93\u6216\u6587\u4ef6\u4e2d\u6d41\u5f0f\u8bfb\u53d6\u6570\u636e\uff0c\u5206\u6bb5\u8fdb\u884c\u538b\u7f29\u5904\u7406\u3002<\/li>\n
- \u9ad8\u6548\u7684\u8ddd\u79bb\u8ba1\u7b97<\/strong>\uff1a\u7ecf\u7eac\u5ea6\u8ddd\u79bb\u8ba1\u7b97\u6d89\u53ca\u4e09\u89d2\u51fd\u6570\u548c\u5f00\u65b9\u8fd0\u7b97\uff0c\u662f\u6027\u80fd\u70ed\u70b9\u3002\u5bf9\u4e8e\u7cbe\u5ea6\u8981\u6c42\u4e0d\u9ad8\u7684\u573a\u666f\uff0c\u53ef\u4ee5\u4f7f\u7528\u7b80\u5316\u7684\u4f30\u7b97\u516c\u5f0f\u3002\u5bf9\u4e8e\u9ad8\u7cbe\u5ea6\u573a\u666f\uff0c\u53ef\u4ee5\u8003\u8651\u5f15\u5165\u6210\u719f\u7684GIS\u5e93\uff08\u5982JTS - Java Topology Suite\uff09\uff0c\u5b83\u4eec\u901a\u5e38\u63d0\u4f9b\u4e86\u7ecf\u8fc7\u4f18\u5316\u7684\u51e0\u4f55\u8fd0\u7b97\u65b9\u6cd5\u3002<\/li>\n<\/ul>\n
Q4: \u9664\u4e86\u6587\u4e2d\u63d0\u5230\u7684\u7b97\u6cd5\uff0c\u8fd8\u6709\u54ea\u4e9b\u66f4\u524d\u6cbf\u7684\u6280\u672f\uff1f<\/h3>\n\n- \u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u538b\u7f29\u65b9\u6cd5<\/strong>\uff1a\u4f8b\u5982\uff0c\u4f7f\u7528LSTM\uff08\u957f\u77ed\u671f\u8bb0\u5fc6\u7f51\u7edc\uff09\u7b49\u5e8f\u5217\u6a21\u578b\u6765\u5b66\u4e60\u8f68\u8ff9\u7684\u8fd0\u52a8\u6a21\u5f0f\uff0c\u7136\u540e\u53ea\u4fdd\u7559\u6a21\u578b\u9884\u6d4b\u5931\u8d25\u7684\u5173\u952e\u70b9\uff0c\u6216\u8005\u7528\u6a21\u578b\u6765\u91cd\u5efa\u548c\u63d2\u503c\u8f68\u8ff9\uff0c\u4ece\u800c\u5b9e\u73b0\u538b\u7f29\u3002<\/li>\n
- \u8003\u8651\u8bed\u4e49\u7684\u8f68\u8ff9\u538b\u7f29<\/strong>\uff1a\u8fd9\u79cd\u65b9\u6cd5\u8bd5\u56fe\u7406\u89e3\u8f68\u8ff9\u80cc\u540e\u7684\u201c\u610f\u56fe\u201d\u3002\u4f8b\u5982\uff0c\u8bc6\u522b\u51fa\u4e00\u6bb5\u8f68\u8ff9\u5c5e\u4e8e\u201c\u4e0a\u73ed\u901a\u52e4\u201d\uff0c\u53e6\u4e00\u6bb5\u5c5e\u4e8e\u201c\u5546\u573a\u8d2d\u7269\u201d\uff0c\u7136\u540e\u53ea\u4fdd\u7559\u4ee3\u8868\u8fd9\u4e9b\u8bed\u4e49\u6d3b\u52a8\u7684\u5173\u952e\u8282\u70b9\uff08\u5982\u5bb6\u3001\u516c\u53f8\u3001\u5546\u573a\uff09\uff0c\u800c\u4e0d\u662f\u7eaf\u7cb9\u7684\u51e0\u4f55\u62d0\u70b9\u3002\u8fd9\u7c7b\u6280\u672f\u76ee\u524d\u66f4\u591a\u5904\u4e8e\u5b66\u672f\u7814\u7a76\u9636\u6bb5\u3002<\/li>\n<\/ul>\n
\u603b\u7ed3<\/h2>\n
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