Region.IsVisible（PointF）对于大浮点值

Question

我遇到了一个奇怪的性能问题，对我正在经历的行为进行解释会很棒。

我正在使用System.Drawing.Region.IsVisible（PointF）来确定某个点是否在多边形内。这通常效果很好，但昨天我注意到，如果多边形很复杂并且由大的x和y值组成，则IsVisible方法的性能会变得非常慢。

下面是一些重现问题的代码（以及显示多边形形状的图像），对于较大的数组大小感到抱歉，但在问题出现之前，多边形需要非常复杂。

当在原始点上调用IsVisible时，我的机器需要460 651毫秒才能完成，而当我首先将所有点除以1000，然后调用该方法时，需要1毫秒。为什么我在时间上看到如此大的差异？我认为浮动的实际值不会影响性能。

using System;
using System.Diagnostics;
using System.Drawing;
using System.Drawing.Drawing2D;
using System.Linq;

namespace PerformanceTest
{
    class Program
    {
        static void Main(string[] args)
        {

            // Create complex polygon with large x and y values
            float[] xValues = {1.014498E+07f, 1.016254E+07f, 1.019764E+07f, 1.021519E+07f, 1.023274E+07f, 1.026785E+07f, 1.026785E+07f, 1.02854E+07f, 1.02854E+07f, 1.030295E+07f, 1.03205E+07f, 1.033805E+07f, 1.035561E+07f, 1.037316E+07f, 1.039071E+07f, 1.040826E+07f, 1.042581E+07f, 1.044337E+07f, 1.046092E+07f, 1.047847E+07f, 1.049602E+07f, 1.051357E+07f, 1.054868E+07f, 1.056623E+07f, 1.058378E+07f, 1.060133E+07f, 1.061888E+07f, 1.061888E+07f, 1.063644E+07f, 1.065399E+07f, 1.068909E+07f, 1.068909E+07f, 1.070664E+07f, 1.07242E+07f, 1.074175E+07f, 1.074175E+07f, 1.07593E+07f, 1.07593E+07f, 1.077685E+07f, 1.07944E+07f, 1.07944E+07f, 1.081196E+07f, 1.081196E+07f, 1.081196E+07f, 1.082951E+07f, 1.084706E+07f, 1.084706E+07f, 1.086461E+07f, 1.086461E+07f, 1.088216E+07f, 1.089971E+07f, 1.091727E+07f, 1.093482E+07f, 1.098747E+07f, 1.100503E+07f, 1.102258E+07f, 1.104013E+07f, 1.105768E+07f, 1.107523E+07f, 1.107523E+07f, 1.109279E+07f, 1.109279E+07f, 1.109279E+07f, 1.109279E+07f, 1.109279E+07f, 1.111034E+07f, 1.111034E+07f, 1.111034E+07f, 1.111034E+07f, 1.111034E+07f, 1.112789E+07f, 1.112789E+07f, 1.112789E+07f, 1.114544E+07f, 1.116299E+07f, 1.118054E+07f, 1.11981E+07f, 1.12332E+07f, 1.125075E+07f, 1.12683E+07f, 1.128586E+07f, 1.130341E+07f, 1.135606E+07f, 1.137361E+07f, 1.139117E+07f, 1.140872E+07f, 1.144382E+07f, 1.146137E+07f, 1.147893E+07f, 1.149648E+07f, 1.151403E+07f, 1.153158E+07f, 1.154913E+07f, 1.156669E+07f, 1.156669E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.158424E+07f, 1.156669E+07f, 1.156669E+07f, 1.151403E+07f, 1.149648E+07f, 1.149648E+07f, 1.149648E+07f, 1.149648E+07f, 1.149648E+07f, 1.149648E+07f, 1.149648E+07f, 1.149648E+07f, 1.149648E+07f, 1.153158E+07f, 1.154913E+07f, 1.156669E+07f, 1.156669E+07f, 1.158424E+07f, 1.160179E+07f, 1.160179E+07f, 1.161934E+07f, 1.165444E+07f, 1.1672E+07f, 1.168955E+07f, 1.17071E+07f, 1.172465E+07f, 1.17422E+07f, 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9793945f, 9776394f, 9741290f, 9723738f, 9688635f, 9653531f, 9653531f, 9618427f, 9618427f, 9600875f, 9600875f, 9600875f, 9583323f, 9565771f, 9565771f, 9530667f, 9530667f, 9530667f, 9530667f, 9530667f, 9530667f, 9530667f, 9530667f, 9548219f, 9565771f, 9583323f, 9618427f, 9653531f, 9671083f, 9688635f, 9706186f, 9741290f, 9758842f, 9811497f, 9829050f, 9864154f, 9881705f, 9916809f, 9934361f, 9951913f, 9987016f, 1.000457E+07f, 1.003967E+07f, 1.005722E+07f, 1.007478E+07f, 1.010988E+07f, 1.014498E+07f, 1.016254E+07f, 1.016254E+07f, 1.018009E+07f, 1.019764E+07f, 1.021519E+07f, 1.023274E+07f, 1.023274E+07f, 1.023274E+07f, 1.023274E+07f, 1.023274E+07f, 1.023274E+07f, 1.023274E+07f, 1.023274E+07f, 1.021519E+07f, 1.019764E+07f, 1.016254E+07f, 1.014498E+07f, 1.012743E+07f, 1.009233E+07f, 1.003967E+07f, 1.000457E+07f, 9951913f, 9934361f, 9899257f, 9881705f, 9864154f, 9846602f, 9829050f, 9793945f, 9758842f, 9723738f, 9688635f, 9653531f, 9635979f, 9618427f, 9583323f, 9565771f, 9530667f, 9513116f, 9495564f, 9478012f, 9460460f, 9460460f, 9442908f, 9425357f, 9425357f, 9407805f, 9390253f, 9390253f, 9372701f, 9372701f, 9372701f, 9372701f, 9372701f, 9372701f, 9372701f, 9372701f, 9372701f, 9372701f, 9372701f, 9372701f, 9390253f, 9407805f, 9425357f, 9460460f, 9495564f, 9513116f, 9583323f, 9600875f, 9635979f, 9653531f, 9688635f, 9706186f, 9723738f, 9758842f, 9793945f, 9811497f, 9846602f};
            float[] yValues = { 7286825f, 7286825f, 7269351f, 7269351f, 7269351f, 7269351f, 7251876f, 7251876f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7234401f, 7216927f, 7199453f, 7181979f, 7181979f, 7164504f, 7164504f, 7147029f, 7129555f, 7112081f, 7077132f, 7042183f, 7024709f, 7007235f, 6972285f, 6954811f, 6937337f, 6919863f, 6902388f, 6884913f, 6867439f, 6867439f, 6832491f, 6815016f, 6797541f, 6780067f, 6762593f, 6762593f, 6745119f, 6745119f, 6727644f, 6727644f, 6710169f, 6710169f, 6710169f, 6710169f, 6710169f, 6710169f, 6710169f, 6727644f, 6762593f, 6780067f, 6832491f, 6849965f, 6867439f, 6902388f, 6937337f, 6954811f, 6972285f, 6989760f, 7024709f, 7042183f, 7077132f, 7094607f, 7112081f, 7129555f, 7129555f, 7129555f, 7129555f, 7129555f, 7129555f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7147029f, 7129555f, 7112081f, 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6762593f, 6762593f, 6745119f, 6745119f, 6745119f, 6745119f, 6745119f, 6745119f, 6762593f, 6762593f, 6797541f, 6832491f, 6867439f, 6884913f, 6884913f, 6919863f, 6954811f, 6954811f, 6972285f, 6989760f, 7007235f, 7042183f, 7042183f, 7059657f, 7077132f, 7094607f, 7094607f, 7112081f, 7112081f, 7112081f, 7112081f, 7112081f, 7112081f, 7112081f, 7112081f, 7112081f, 7112081f, 7112081f, 7094607f, 7077132f, 7042183f, 7024709f, 7024709f, 7007235f, 6989760f, 6989760f, 6972285f, 6954811f, 6937337f, 6937337f, 6919863f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6902388f, 6919863f, 6919863f, 6954811f, 6972285f, 6972285f, 6989760f, 7024709f, 7042183f, 7059657f, 7094607f, 7112081f, 7129555f, 7164504f, 7181979f, 7199453f, 7234401f, 7251876f, 7269351f, 7286825f, 7321773f, 7321773f, 7339248f, 7339248f, 7356723f, 7374197f, 7374197f, 7374197f, 7374197f, 7374197f, 7391671f, 7391671f, 7409145f, 7409145f, 7426620f, 7426620f, 7426620f, 7444095f, 7444095f, 7461569f, 7479043f, 7496517f, 7513992f, 7513992f, 7513992f, 7531467f, 7548941f, 7548941f, 7566415f, 7601364f, 7618839f, 7636313f, 7653787f, 7671261f, 7688736f, 7706211f, 7741159f, 7793583f, 7828531f, 7846005f, 7880955f, 7880955f, 7898429f, 7898429f, 7915903f, 7933377f, 7933377f, 7950852f, 7950852f, 7950852f, 7950852f, 7950852f, 7950852f, 7950852f, 7968327f, 7985801f, 8003275f, 8020749f, 8038224f, 8055699f, 8073173f, 8090647f, 8108121f, 8125596f, 8160545f, 8178019f, 8195493f, 8212968f, 8212968f, 8230443f, 8247917f, 8265391f, 8282865f, 8282865f, 8282865f, 8282865f, 8282865f, 8282865f, 8282865f, 8282865f, 8265391f, 8230443f, 8212968f, 8195493f, 8178019f, 8160545f, 8160545f, 8143071f, 8143071f, 8125596f, 8108121f, 8108121f, 8090647f, 8090647f, 8073173f, 8038224f, 8038224f, 8020749f, 8020749f, 8003275f, 7985801f, 7985801f, 7968327f, 7950852f, 7950852f, 7933377f, 7933377f, 7933377f, 7933377f, 7915903f, 7898429f, 7898429f, 7898429f, 7898429f, 7898429f, 7898429f, 7880955f, 7880955f, 7880955f, 7880955f, 7880955f, 7880955f, 7880955f, 7880955f, 7880955f, 7880955f, 7880955f, 7898429f, 7898429f, 7933377f, 7968327f, 7985801f, 8003275f, 8020749f, 8055699f, 8073173f, 8108121f, 8108121f, 8143071f, 8178019f, 8178019f, 8212968f, 8212968f, 8230443f, 8247917f, 8265391f, 8282865f, 8282865f, 8317815f, 8335289f, 8352763f, 8387712f, 8405186f, 8422661f, 8440134f, 8457609f, 8475084f, 8510033f, 8527506f, 8544981f, 8562456f, 8614878f, 8632353f, 8667302f, 8684777f, 8737200f, 8772149f, 8789622f, 8824572f, 8842046f, 8859521f, 8876994f, 8894469f, 8929418f, 8929418f, 8946893f, 8946893f, 8946893f, 8946893f, 8946893f, 8946893f, 8946893f, 8946893f, 8946893f, 8946893f, 8911944f, 8894469f, 8859521f, 8824572f, 8789622f, 8772149f, 8702250f, 8684777f, 8667302f, 8632353f, 8614878f, 8597405f, 8562456f, 8544981f, 8510033f, 8492558f, 8475084f, 8457609f, 8440134f, 8422661f, 8405186f, 8387712f, 8370237f, 8352763f, 8352763f, 8352763f, 8352763f, 8352763f, 8352763f, 8352763f, 8352763f, 8352763f, 8352763f, 8370237f, 8370237f, 8387712f, 8387712f, 8405186f, 8422661f, 8422661f, 8440134f, 8457609f, 8492558f, 8527506f, 8544981f, 8562456f, 8579930f, 8597405f, 8614878f, 8632353f, 8649828f, 8667302f, 8702250f, 8719725f, 8737200f, 8772149f, 8789622f, 8807097f, 8824572f, 8842046f, 8876994f, 8894469f, 8911944f, 8929418f, 8946893f, 8964366f, 8964366f, 8981841f, 8999316f, 9016790f, 9034265f, 9034265f, 9051738f, 9051738f, 9051738f, 9051738f, 9051738f, 9051738f, 9051738f, 9016790f, 8999316f, 8964366f, 8946893f, 8929418f, 8911944f, 8876994f, 8859521f, 8842046f, 8824572f, 8807097f, 8789622f, 8772149f, 8754674f, 8702250f, 8667302f, 8649828f, 8632353f, 8614878f, 8597405f, 8579930f, 8562456f, 8544981f, 8510033f, 8492558f, 8492558f, 8492558f, 8492558f, 8492558f, 8492558f, 8492558f, 8492558f, 8492558f, 8492558f, 8492558f, 8492558f, 8510033f, 8544981f, 8544981f, 8562456f, 8562456f, 8597405f, 8614878f, 8632353f, 8667302f, 8702250f, 8719725f, 8754674f, 8789622f, 8824572f, 8842046f, 8859521f, 8876994f, 8911944f, 8929418f, 8964366f, 8964366f, 8999316f, 9016790f, 9034265f, 9086688f, 9104162f, 9139110f, 9156585f, 9174060f, 9209009f, 9243957f, 9261432f, 9261432f, 9261432f, 9261432f, 9261432f, 9261432f, 9261432f, 9261432f, 9261432f, 9261432f, 9261432f, 9243957f, 9226482f, 9191534f, 9174060f, 9156585f, 9086688f, 9051738f, 9034265f, 8999316f, 8981841f, 8964366f, 8929418f, 8894469f, 8876994f, 8842046f, 8824572f, 8807097f, 8789622f, 8772149f, 8754674f, 8702250f, 8684777f, 8667302f, 8667302f, 8649828f, 8614878f, 8597405f, 8579930f, 8562456f, 8562456f, 8527506f, 8510033f, 8492558f, 8475084f, 8440134f, 8422661f, 8422661f, 8387712f, 8370237f, 8370237f, 8370237f, 8370237f, 8370237f, 8335289f, 8335289f, 8335289f, 8335289f, 8335289f, 8335289f, 8335289f, 8335289f, 8335289f, 8335289f, 8335289f, 8352763f, 8370237f, 8405186f, 8440134f, 8457609f, 8492558f, 8510033f, 8527506f, 8562456f, 8579930f, 8597405f, 8597405f, 8632353f, 8632353f, 8667302f, 8702250f, 8719725f, 8754674f, 8754674f, 8754674f, 8754674f, 8754674f, 8754674f, 8754674f, 8754674f, 8737200f, 8719725f, 8702250f, 8684777f, 8667302f, 8649828f, 8632353f, 8614878f, 8562456f, 8527506f, 8440134f, 8422661f, 8387712f, 8352763f, 8317815f, 8300340f, 8282865f, 8265391f, 8247917f, 8212968f, 8212968f, 8160545f, 8143071f, 8125596f, 8108121f, 8108121f, 8090647f, 8090647f, 8073173f, 8073173f, 8055699f, 8055699f, 8055699f, 8038224f, 8038224f, 8038224f, 8038224f, 8038224f, 8020749f, 8020749f, 8003275f, 8003275f, 7985801f, 7950852f, 7933377f, 7915903f, 7915903f, 7880955f, 7863480f, 7846005f, 7828531f, 7793583f, 7776108f, 7758633f, 7741159f, 7723685f, 7706211f, 7706211f, 7706211f, 7706211f, 7706211f, 7706211f, 7706211f, 7706211f, 7706211f, 7706211f, 7706211f, 7706211f, 7723685f, 7723685f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7741159f, 7723685f, 7723685f, 7688736f, 7671261f, 7653787f, 7583889f, 7566415f, 7513992f, 7461569f, 7444095f, 7409145f, 7374197f, 7356723f, 7321773f, 7304299f, 7286825f, 7269351f, 7251876f, 7234401f, 7199453f, 7181979f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7164504f, 7181979f, 7199453f };

            PointF[] points = xValues.Zip(yValues, (x, y) => new PointF(x, y)).ToArray();


            // Create a region with the original values 
            GraphicsPath pathWithOriginalPoints = new GraphicsPath();
            pathWithOriginalPoints.AddPolygon(points);
            Region regionFromOriginalPoints = new Region(pathWithOriginalPoints);

            // Create a region with the values divided by 1000
            GraphicsPath pathDividedBy1000 = new GraphicsPath();
            pathDividedBy1000.AddPolygon(points.Select(p => new PointF(p.X/1000f, p.Y/1000f)).ToArray());
            Region regionDividedby1000 = new Region(pathDividedBy1000);


            // Time call to Region.IsVisible(PointF)
            var stopwatch = Stopwatch.StartNew();
            Console.WriteLine("Computing region.IsVisible for points divided by 1000:");
            regionDividedby1000.IsVisible(new PointF(0f, 0f));
            var dividedBy1000Timing = stopwatch.ElapsedMilliseconds;
            Console.WriteLine($"Elapsed time: {dividedBy1000Timing} ms");

            stopwatch.Restart();
            Console.WriteLine("Computing region.IsVisible for original points");
            regionFromOriginalPoints.IsVisible(new PointF(0f, 0f));
            var originalTiming = stopwatch.ElapsedMilliseconds;
            Console.WriteLine($"Elapsed time: {originalTiming} ms");
        }
    }
}

Answer 1

TLTR

进行一次Region.IsVisible(Point)通话所需的时间并不取决于点数。相反，它取决于完全和精确覆盖区域所需的矩形数。这取决于......：

• 这些点描述的形状，通常是
• 形状的大小。

示例1：矩形区域有四个点，它总是需要一个矩形来覆盖它。如果你想添加大量的点，只要它们都位于矩形的两侧，这就不会改变！

示例2：圆形区域（！）有四个点_（） 但是你需要完全覆盖它的矩形数量取决于该圆的直径。查看底部的图形！

全文

Region不是我所说的＆＃39;记录良好的＆＃39;类。

你可以看到内部工作似乎依赖RegionData，可以通过调用var RData = your Region.GetRegionData()来访问。{3}}。

这同样有道理：至少可以说没有详细记录。也许我无法找到它，但似乎没有关于这些字节结构的信息。

_{（下面的数字表明每个点需要1个字节作为类型指示符加上2 + 4个字节用于两个浮点坐标。这就像PathPoints&PathTypes中的GraphicsPath一样在你的924 + 1点和1 + 2 * 4字节的例子中，这组成8325个字节;另外27个字节存在; 8个可以保持缩放..）}

有一件事很有意思：调查RegionData的 的Regions可以很容易地看到他们的相同大小..：8352。这表明RegionData与额外时间没有直接关系..

但另一个，有些同样神秘，读到：记录错误的电话：GetRegionScans。 MSDN对此进行了说明：

  

返回与此Region近似的RectangleF结构数组   在应用指定的矩阵变换之后。

首先让我们看看如果我们撤出“扫描”会发生什么？对于您的两个地区：

Matrix M = new Matrix();

var scans1 = regionFromOriginalPoints.GetRegionScans(M);
var scans2 = regionDividedby1000.GetRegionScans(M);

我使用简单的单位矩阵（*），即没有变换，这些是结果：

scans1.Length = 5.960.690
scans2.Length = 5.956

所以它会创建 1000倍矩形来近似Region，并且，这样做也需要花费很多时间..：

这并不奇怪：未缩放的路径覆盖了一个巨大的区域并且近似它我会期望需要更多的矩形。我不知道近似是如何工作的，但它可能会决定，即使返回RectangleF，也不需要任何边长度小于1像素的矩形。

所以我得出结论，IsVisible调用内部需要创建那些近似矩形，并且它需要足够的覆盖区域内的每个完整像素。 （请注意，Region不支持部分/抗锯齿像素！）区域边界越大，像素越适合，扫描过程所需的时间越长。

我还假设扫描过程严格耗费时间。

下一步：执行RectangleF.Contains(Point)应该非常快，即使是一百万次通话也是如此。我们来看看;当我衡量这个：

int hits = 0;
PointF pt = new PointF(123.456f, 789.012f);
foreach (RectangleF r in scans1) if (r.Contains(pt)) hits++;

..只需42ms即可完成。因此，一旦你有缓存扫描矩形，就可以轻松地对它们进行大量的点击测试而不是进行单独的IsVisible调用..

以下是数字摘要：

  

您的原始路径：

     

多边形点数= 924
  regionData1.Length = 8.352
  scans1.Length = 5.960.690
  经过时间1：453.187毫秒

     

路径按比例缩小1000：

     

多边形点数= 924
  regionData2.Length = 8.352
  scans2.Length = 5.956
  经过时间2：2毫秒

     

全套扫描的经过时间：41毫秒

最后：为了更好地理解扫描矩形，我使用交替颜色近似了一个圆圈：

for (int i = 0; i < scans.Length; i++)
     g.FillRectangle(i%2 == 0 ? Brushes.ForestGreen : Brushes.Salmon, scans[i]);

你可以看到，每一行的顶部和底部都是一个矩形，因为这里曲线是平的，x坐标快速向外移动。我们越接近中间，矩形就越大（即......更高）...我们可以看到近似严格遵循行 ..

即使边界矩形高于宽度也是如此，使用列可以使用更少的矩形：

此处两个省略号（222x111和111x222）近似为85 水平条纹。由于曲率不同，这比圆圈小。

（*） - 我们已跳过Matrix ;但它可用于通过向上或向下缩放数据来修改结果。 该圈子有Height个222像素，需要135个扫描矩形来近似它。如果我们放大Matrix，（即用于表示Graphics}的Region对象：m.Scale(10,10);需要1315个扫描矩形来覆盖放大的圆圈。

因此，可以使用按0.001f缩小的矩阵，而不是缩放数据点;但它只测试按比例缩小的版本，可能会错过边框周围的像素或包含错误的像素。所以最好只使用你真正需要的正确比例..

_{（* *）请注意，广告GraphicsPath确实有 13 PathPoints;但这些只是四个真实点（加上第一个重复关闭图形）加上每对点之间的两个控制点;所以5 + 4 * 2 = 13.另请注意GraphicsPath中的任何行是直线还是贝塞尔曲线。这包括弧，椭圆和圆！}

Answer 2

我们一直在努力解决同样的问题：使用50k点多边形，在IsVisible（）方法后面构建矩形需要45秒。我们试图缓存这些数据，但最后我们有超过1百万个矩形;对于多个区域，我们有数百兆字节的数据要缓存。

最后我们转向PNPoly算法，只需几毫秒：

https://wrf.ecse.rpi.edu/Research/Short_Notes/pnpoly.html

这里是c＃版本：

    public bool IsVisible(Point p, List<Point> points)
    {
        int i, j = points.Count - 1;
        bool isVisible = false;
        for (i = 0; i < points.Count; i++)
        {
            if (points[i].Y < p.Y && points[j].Y >= p.Y 
                || points[j].Y < p.Y && points[i].Y >= p.Y)
            {
                if (points[i].X + (p.Y - points[i].Y) / (points[j].Y - points[i].Y) 
                    * (points[j].X - points[i].X) < p.X)
                {
                    isVisible = !isVisible;
                }
            }
            j = i;
        }
        return isVisible;
    }