Region.IsVisible(PointF) 对于大浮点值的性能非常慢
Region.IsVisible(PointF) has very slow performance for large floating point values
我 运行 遇到了一个奇怪的性能问题，最好能解释一下我遇到的行为。
我正在使用 System.Drawing.Region.IsVisible(PointF) 来确定点是否在多边形内。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包含大的 x 和 y 值，IsVisible 方法的性能会变得非常慢。
下面是一些重现该问题的代码（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，但多边形需要非常复杂才能出现问题。
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？我不认为 float 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, 1.175976E+07f, 1.177731E+07f, 1.179486E+07f, 1.181241E+07f, 1.182996E+07f, 1.184752E+07f, 1.186507E+07f, 1.188262E+07f, 1.190017E+07f, 1.190017E+07f, 1.191772E+07f, 1.191772E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.195283E+07f, 1.197038E+07f, 1.198793E+07f, 1.200548E+07f, 1.202303E+07f, 1.204059E+07f, 1.205814E+07f, 1.207569E+07f, 1.209324E+07f, 1.211079E+07f, 1.212835E+07f, 1.21459E+07f, 1.216345E+07f, 1.2181E+07f, 1.219855E+07f, 1.221611E+07f, 1.221611E+07f, 1.223366E+07f, 1.225121E+07f, 1.226876E+07f, 1.226876E+07f, 1.228631E+07f, 1.230386E+07f, 1.230386E+07f, 1.230386E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.235652E+07f, 1.235652E+07f, 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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, 7077132f, 7059657f, 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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, 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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");
}
}
}
TLTR
进行一次 Region.IsVisible(Point) 调用所花费的时间根本不取决于点数。相反，它取决于完全和精确地 覆盖区域 所需的 矩形数量 。这取决于..:[=54=]
- 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，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：圆形区域也 (!) 有四个点 () 但是完全覆盖它需要的矩形数量 ** 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 'well-documented' class.
你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()来访问它。
同样的道理：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..
（下面的数字表明需要的每个点需要 1 个字节作为类型指示符加上 2+4 个字节作为两个浮点坐标。这就像 PathPoints&PathTypes GraphicsPath。在你的例子中有 924+1 个点和 1+2*4 个字节，这构成了 8325 个字节；还有 27 个字节；8 个可以保持缩放..)
有一件事很有趣：从 both 查看 Regions 的 RegionData 可以很容易地看到他们有 相同 大小..: 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 ，有点同样神秘，阅读：记录不完整的电话：GetRegionScans。 MSDN 是这样说的：
Returns an array of RectangleF structures that approximate this Region
after the specified matrix transformation is applied.
首先 让我们看看如果我们为你们的两个区域提取这些 'scans' 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，结果如下：
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，而且，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很大的区域，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，即使返回 RectangleF，也不需要任何边小于 1 像素的矩形。
所以我得出结论，IsVisible 调用在内部需要创建那些近似矩形，并且它需要足够多的矩形来覆盖每个完整像素区域内。 （请注意 Region 不支持 partial/anti-aliased 像素！）区域边界越大，适合的像素越多，扫描过程所需的时间也越长。
我还假设完全是扫描过程耗尽了时间。
Next：执行 RectangleF.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++;
..只需 42ms 即可完成。因此，一旦您 缓存 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：
Your original path:
number of polygon points = 924
regionData1.Length = 8.352
scans1.Length = 5.960.690
Elapsed time1: 453.187 ms
The path scaled down by 1000:
number of polygon points = 924
regionData2.Length = 8.352
scans2.Length= 5.956
Elapsed time2: 2 ms
Elapsed time for full set of scans: 41 ms
最后：为了更好地理解扫描矩形，我用交替颜色近似为一个圆：
for (int i = 0; i < scans.Length; i++)
g.FillRectangle(i%2 == 0 ? Brushes.ForestGreen : Brushes.Salmon, scans[i]);
可以看到上下每一行都是一个矩形，因为这里曲线是平的，x坐标向外移动很快。我们越靠近中间，矩形就越大（即越高）...所以我们可以看到近似值严格遵循 rows..
即使边界矩形比宽度高并且使用列，也可以使用更少的矩形，这也是正确的：
此处两个椭圆（222x111和111x222）近似为85水平条纹。因为曲率不同所以小于圆..
(*) - 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。 圆形有 Height 个 222 像素，它需要 135 个扫描矩形来近似它。 如果我们放大 Matrix ，（即用于表示 Region 的 Graphics 对象）：m.Scale(10,10); 它需要 1315 个扫描矩形来覆盖放大的圆。
因此可以使用按比例缩小 0.001f 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，并且可能会错过边界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..
(* *)注意循环GraphicsPath确实有13PathPoints；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 GraphicsPath 中的 任何 线是 直线或贝塞尔曲线。 这包括圆弧、椭圆和圆！
我们一直在为同一个问题而苦苦挣扎：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。
最后我们转向了 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;
}
我 运行 遇到了一个奇怪的性能问题，最好能解释一下我遇到的行为。
我正在使用 System.Drawing.Region.IsVisible(PointF) 来确定点是否在多边形内。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包含大的 x 和 y 值，IsVisible 方法的性能会变得非常慢。
下面是一些重现该问题的代码（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，但多边形需要非常复杂才能出现问题。
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？我不认为 float 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, 1.175976E+07f, 1.177731E+07f, 1.179486E+07f, 1.181241E+07f, 1.182996E+07f, 1.184752E+07f, 1.186507E+07f, 1.188262E+07f, 1.190017E+07f, 1.190017E+07f, 1.191772E+07f, 1.191772E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.193528E+07f, 1.195283E+07f, 1.197038E+07f, 1.198793E+07f, 1.200548E+07f, 1.202303E+07f, 1.204059E+07f, 1.205814E+07f, 1.207569E+07f, 1.209324E+07f, 1.211079E+07f, 1.212835E+07f, 1.21459E+07f, 1.216345E+07f, 1.2181E+07f, 1.219855E+07f, 1.221611E+07f, 1.221611E+07f, 1.223366E+07f, 1.225121E+07f, 1.226876E+07f, 1.226876E+07f, 1.228631E+07f, 1.230386E+07f, 1.230386E+07f, 1.230386E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.232142E+07f, 1.235652E+07f, 1.235652E+07f, 1.237407E+07f, 1.237407E+07f, 1.239162E+07f, 1.239162E+07f, 1.240918E+07f, 1.242673E+07f, 1.242673E+07f, 1.244428E+07f, 1.247938E+07f, 1.249694E+07f, 1.251449E+07f, 1.253204E+07f, 1.254959E+07f, 1.256714E+07f, 1.258469E+07f, 1.260225E+07f, 1.263735E+07f, 1.26549E+07f, 1.267245E+07f, 1.269001E+07f, 1.270756E+07f, 1.272511E+07f, 1.272511E+07f, 1.274266E+07f, 1.274266E+07f, 1.276021E+07f, 1.276021E+07f, 1.277776E+07f, 1.277776E+07f, 1.277776E+07f, 1.277776E+07f, 1.279532E+07f, 1.279532E+07f, 1.279532E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.281287E+07f, 1.279532E+07f, 1.277776E+07f, 1.276021E+07f, 1.276021E+07f, 1.274266E+07f, 1.274266E+07f, 1.272511E+07f, 1.272511E+07f, 1.272511E+07f, 1.274266E+07f, 1.276021E+07f, 1.279532E+07f, 1.281287E+07f, 1.283042E+07f, 1.284797E+07f, 1.286552E+07f, 1.288308E+07f, 1.290063E+07f, 1.291818E+07f, 1.293573E+07f, 1.295328E+07f, 1.295328E+07f, 1.297084E+07f, 1.297084E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.298839E+07f, 1.300594E+07f, 1.300594E+07f, 1.302349E+07f, 1.304104E+07f, 1.305859E+07f, 1.30937E+07f, 1.311125E+07f, 1.31288E+07f, 1.314635E+07f, 1.316391E+07f, 1.318146E+07f, 1.319901E+07f, 1.321656E+07f, 1.323411E+07f, 1.325167E+07f, 1.325167E+07f, 1.326922E+07f, 1.326922E+07f, 1.328677E+07f, 1.330432E+07f, 1.330432E+07f, 1.330432E+07f, 1.332187E+07f, 1.333943E+07f, 1.335698E+07f, 1.335698E+07f, 1.337453E+07f, 1.339208E+07f, 1.340963E+07f, 1.340963E+07f, 1.342718E+07f, 1.344474E+07f, 1.346229E+07f, 1.347984E+07f, 1.349739E+07f, 1.351494E+07f, 1.355005E+07f, 1.35676E+07f, 1.36027E+07f, 1.363781E+07f, 1.367291E+07f, 1.367291E+07f, 1.370801E+07f, 1.372557E+07f, 1.376067E+07f, 1.377822E+07f, 1.381333E+07f, 1.383088E+07f, 1.384843E+07f, 1.386598E+07f, 1.390109E+07f, 1.391864E+07f, 1.391864E+07f, 1.393619E+07f, 1.395374E+07f, 1.397129E+07f, 1.398884E+07f, 1.40064E+07f, 1.402395E+07f, 1.405905E+07f, 1.409416E+07f, 1.412926E+07f, 1.414681E+07f, 1.418191E+07f, 1.419947E+07f, 1.421702E+07f, 1.423457E+07f, 1.426967E+07f, 1.430478E+07f, 1.433988E+07f, 1.435743E+07f, 1.437499E+07f, 1.439254E+07f, 1.439254E+07f, 1.442764E+07f, 1.442764E+07f, 1.444519E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.446274E+07f, 1.444519E+07f, 1.442764E+07f, 1.441009E+07f, 1.439254E+07f, 1.437499E+07f, 1.435743E+07f, 1.433988E+07f, 1.432233E+07f, 1.430478E+07f, 1.430478E+07f, 1.426967E+07f, 1.426967E+07f, 1.423457E+07f, 1.421702E+07f, 1.418191E+07f, 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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");
}
}
}
TLTR
进行一次 Region.IsVisible(Point) 调用所花费的时间根本不取决于点数。相反，它取决于完全和精确地 覆盖区域 所需的 矩形数量 。这取决于..:[=54=]
- 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，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：圆形区域也 (!) 有四个点 () 但是完全覆盖它需要的矩形数量 ** 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 'well-documented' class.
你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()来访问它。
同样的道理：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..
（下面的数字表明需要的每个点需要 1 个字节作为类型指示符加上 2+4 个字节作为两个浮点坐标。这就像 PathPoints&PathTypes GraphicsPath。在你的例子中有 924+1 个点和 1+2*4 个字节，这构成了 8325 个字节；还有 27 个字节；8 个可以保持缩放..)
有一件事很有趣：从 both 查看 Regions 的 RegionData 可以很容易地看到他们有 相同 大小..: 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 ，有点同样神秘，阅读：记录不完整的电话：GetRegionScans。 MSDN 是这样说的：
Returns an array of RectangleF structures that approximate this Region after the specified matrix transformation is applied.
首先 让我们看看如果我们为你们的两个区域提取这些 'scans' 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，结果如下：
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，而且，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很大的区域，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，即使返回 RectangleF，也不需要任何边小于 1 像素的矩形。
所以我得出结论，IsVisible 调用在内部需要创建那些近似矩形，并且它需要足够多的矩形来覆盖每个完整像素区域内。 （请注意 Region 不支持 partial/anti-aliased 像素！）区域边界越大，适合的像素越多，扫描过程所需的时间也越长。
我还假设完全是扫描过程耗尽了时间。
Next：执行 RectangleF.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++;
..只需 42ms 即可完成。因此，一旦您 缓存 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：
Your original path:
number of polygon points = 924
regionData1.Length = 8.352
scans1.Length = 5.960.690
Elapsed time1: 453.187 msThe path scaled down by 1000:
number of polygon points = 924
regionData2.Length = 8.352
scans2.Length= 5.956
Elapsed time2: 2 msElapsed time for full set of scans: 41 ms
最后：为了更好地理解扫描矩形，我用交替颜色近似为一个圆：
for (int i = 0; i < scans.Length; i++)
g.FillRectangle(i%2 == 0 ? Brushes.ForestGreen : Brushes.Salmon, scans[i]);
可以看到上下每一行都是一个矩形，因为这里曲线是平的，x坐标向外移动很快。我们越靠近中间，矩形就越大（即越高）...所以我们可以看到近似值严格遵循 rows..
即使边界矩形比宽度高并且使用列，也可以使用更少的矩形，这也是正确的：
此处两个椭圆（222x111和111x222）近似为85水平条纹。因为曲率不同所以小于圆..
(*) - 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。 圆形有 Height 个 222 像素，它需要 135 个扫描矩形来近似它。 如果我们放大 Matrix ，（即用于表示 Region 的 Graphics 对象）：m.Scale(10,10); 它需要 1315 个扫描矩形来覆盖放大的圆。
因此可以使用按比例缩小 0.001f 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，并且可能会错过边界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..
(* *)注意循环GraphicsPath确实有13PathPoints；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 GraphicsPath 中的 任何 线是 直线或贝塞尔曲线。 这包括圆弧、椭圆和圆！
我们一直在为同一个问题而苦苦挣扎：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。
最后我们转向了 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;
}