c# - Region.IsVisible(PointF) 对于大浮点值的性能非常慢

Question

我遇到了一个奇怪的性能问题，如果能解释一下我正在经历的行为，那就太好了。

我正在使用 System.Drawing.Region.IsVisible(PointF) 来确定一个点是否在多边形内。这通常工作得很好，但昨天我注意到如果多边形很复杂并且它由大的 x 和 y 值组成，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），对于大数组大小感到抱歉，但在问题出现之前，多边形需要非常复杂。

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。为什么我看到时间上有这么大的差异？我不认为浮点数的实际值会影响性能。

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

打一个电话所需的时间Region.IsVisible(Point)根本不取决于点数。相反，它取决于完全准确地覆盖该区域所需的矩形数量。这取决于..：

• 这些点描述的形状，通常
• 形状的大小。

示例 1：一个矩形区域有四个点，并且总是需要一个矩形来覆盖它。如果您要添加大量点，只要它们都位于矩形的边上，这不会改变！

示例 2：一个圆形区域 (!) 也有四个点_{( )}，但您需要完全覆盖它的矩形数量**取决于该圆的直径。请参阅底部的图形！

---

全文

Region不是我所说的“有据可查”的课程。

可以看到内部工作似乎依赖于RegionData，可以通过调用var RData = your Region.GetRegionData().

这里也是一样的：至少可以说没有很好的记录。也许我只是找不到它，但似乎没有关于这些字节的结构的信息..

_{（下面的数字表明，所需的每个点都需要 1 个字节作为类型指示符，加上两个浮点坐标的 2+4 个字节。这就像.PathPoints&PathTypes在GraphicsPath您的示例中具有 924+1 个点和 1+2*4 个字节这构成了 8325 个字节；另外还有 27 个字节；8 个可以保持缩放比例..)}

不过有一件事很有趣：RegionData从你的两个Regions人身上看，很容易看出它们的大小是一样的..：8352。这表明RegionData无论如何与额外时间没有直接关系..

但是还有另一个同样神秘的，读作： ill-documented call: GetRegionScans。MSDN 是这么说的：

在应用指定的矩阵变换后，返回一个近似此 Region 的 RectangleF 结构数组。

首先让我们看看如果我们为您的两个区域提取那些“扫描”会发生什么：

Matrix M = new Matrix();

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

我使用简单的单位矩阵（*），即没有转换，这些是结果：

scans1.Length = 5.960.690
scans2.Length = 5.956

因此，它创建了1000 倍以上的矩形来近似Region，并且，你瞧，这样做也需要很多时间..：

这并不奇怪：未缩放的路径覆盖了一个巨大的区域，并且为了近似它，我预计需要更多的矩形。我不知道近似值是如何工作的，但它可能会决定，即使RectangleF返回，也不需要任何边小于 1 像素的矩形。

所以我得出结论，IsVisible内部调用需要创建那些近似矩形，并且需要足够的它们来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，适合的像素越多，扫描过程所需的时间就越长。

我还假设严格来说是扫描过程消耗了时间。

Next : 执行 aRectangleF.Contains(Point)应该非常快，即使是一百万次调用。让我们来看看; 当我测量这个时：

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

..它只 42ms需要完成。因此，一旦您缓存了扫描矩形，您就可以轻松地对它们进行大量命中测试，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
Elapsed time1：453.187 ms

路径缩小 1000：

多边形点数 = 924 regionData2.Length
= 8.352
scans2.Length = 5.956
Elapsed time2: 2 ms

全套扫描经过的时间：41 毫秒

---

最后：为了更好地理解扫描矩形，我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]);

您可以看到，在顶部和底部，每一行都是一个矩形，因为这里的曲线是平坦的，并且 x 坐标快速向外移动。我们越靠近中间，矩形就越大（即更高）......所以我们可以看到近似值严格遵循行......

即使边界矩形高于宽度，这也是正确的，并且使用列，可以使用更少的矩形：

这里两个椭圆 (222x111和111x222) 都近似为85 水平条纹。由于曲率不同，那小于圆..

---

(*) -我们跳过了Matrix; 但它可用于通过放大或缩小数据来修改结果。圆有一个Height像素222，它需要135扫描矩形来近似它。如果我们放大Matrix,（即Graphics用于表示 的对象Region）：m.Scale(10,10);它需要1315扫描矩形来覆盖放大的圆。

0.001f因此，可以使用按比例缩小的矩阵来代替缩放数据点；但它只会测试按比例缩小的版本，并且可能会错过边框周围的像素或包含错误的像素。所以最好只使用你实际需要的正确比例。

_{(* *) 请注意，该通知GraphicsPath确实有13 PathPoints；但这些实际上只是四个实际点（加上第一个重复以关闭图形）加上每对点之间的两个控制点；所以 5 + 4*2 = 13。还要注意， a 中的任何线要么GraphicsPath是直线，要么是贝塞尔曲线。这包括圆弧、椭圆和圆！}

Answer 2

我们一直在努力解决同样的问题：对于一个 50k 点的多边形，在 IsVisible() 方法后面构建矩形需要 45 秒。我们试图缓存这些数据，但最终我们有超过 100 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，它只需要几毫秒：

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;
    }