Region.IsVisible(PointF)对于大浮点值的性能非常慢
lar*_*sjr 5 c# gdi+ region winforms graphicspath
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好.
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而言很抱歉,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,它需要1毫秒.为什么我在时间上看到如此大的差异？我不认为浮动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, 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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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6727644f, 6710169f, 6692695f, 6675221f, 6657747f, 6657747f, 6640272f, 6622797f, 6622797f, 6622797f, 6622797f, 6622797f, 6622797f, 6622797f, 6622797f, 6622797f, 6622797f, 6640272f, 6657747f, 6692695f, 6692695f, 6710169f, 6727644f, 6745119f, 6762593f, 6780067f, 6780067f, 6797541f, 6815016f, 6832491f, 6849965f, 6867439f, 6884913f, 6902388f, 6919863f, 6937337f, 6954811f, 6972285f, 6989760f, 7007235f, 7024709f, 7042183f, 7059657f, 7077132f, 7094607f, 7112081f, 7129555f, 7147029f, 7164504f, 7181979f, 7199453f, 7234401f, 7234401f, 7251876f, 7251876f, 7269351f, 7286825f, 7304299f, 7321773f, 7321773f, 7321773f, 7321773f, 7321773f, 7321773f, 7321773f, 7321773f, 7321773f, 7321773f, 7321773f, 7304299f, 7286825f, 7269351f, 7251876f, 7234401f, 7216927f, 7199453f, 7181979f, 7164504f, 7147029f, 7129555f, 7112081f, 7094607f, 7077132f, 7042183f, 7024709f, 7007235f, 6989760f, 6954811f, 6937337f, 6919863f, 6902388f, 6849965f, 6832491f, 6815016f, 6797541f, 6780067f, 6780067f, 6762593f, 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");
}
}
}
TLTR
Region.IsVisible(Point)拨打一个电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该区域所需的矩形数量.这取决于..:
- 这些点描述的形状和通常
- 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(!)也有四个点(),但是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 不是我称之为"记录良好"的课程.
你可以看到内部工作似乎依赖于RegionData,可以通过调用访问var RData = your Region.GetRegionData().
在这里也是如此:至少可以说没有详细记录.也许我只是找不到它,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在GraphicsPath.在你的例子中有924 + 1个点和1 + 2*4个字节这组成了8325个字节;另外还有27个字节; 8个可以保存缩放...)
有一件事很有意思:RegionData从你们两个人的角度Regions来看,可以很容易地发现它们的尺寸相同 ......:8352.这表明这RegionData与额外的时间没有直接关系.
但另一个有点同样神秘的内容是:记录错误的电话:GetRegionScans.MSDN对此说了这样的话:
返回应用指定矩阵变换后近似此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进行'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
所以它创造了1000倍以上的矩形来近似Region,并且,并且看到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希望还需要更多的矩形.我不知道近似是如何工作的,但它可能会决定,即使RectangleF返回,也不需要任何边长度小于1像素的矩形.
因此我得出结论,IsVisible内部调用需要创建这些近似矩形,并且需要足够的内容来覆盖区域内的每个完整像素.(注意,Region它不支持部分/消除锯齿的像素!)区域边界越大,像素越适合,扫描过程所需的时间越长.
我还假设严格来说,扫描过程耗费时间.
下一步:做一个RectangleF.Contains(Point)应该非常快,即使是一百万个电话.让我们来看看; 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 42ms需要完成.因此,一旦缓存了扫描矩形,您就可以轻松地对它们进行大量的命中测试,而不是单独IsVisible调用.
以下是数字摘要:
你的原始路径:
的多边形点的数量= 924
regionData1.Length = 8.352
scans1.Length = 5.960.690
经过的时间1:453.187毫秒路径缩小1000:
多边形点数= 924 regionData2.Length = 8.352次
扫描
2.Length = 5.956
经过时间2:2 ms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,我用交替的颜色近似了一个圆:
for (int i = 0; i < scans.Length; i++)
g.FillRectangle(i%2 == 0 ? Brushes.ForestGreen : Brushes.Salmon, scans[i]);
您可以看到在每个行的顶部和底部是一个矩形,因为此处曲线是平的,x坐标快速向外移动.我们越接近中间,矩形就越大(即......更高)......所以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:
这里两个椭圆(222x111和111x222)都用85 水平条纹近似.由于曲率不同,这比圆圈小..
(*) - 我们跳过了Matrix ; 但它可用于通过向上或向下缩放数据来修改结果.圆具有Height的222像素,它需要135扫描的矩形接近它.如果我们按比例放大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.
因此,0.001f可以使用按比例缩小的矩阵,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..
(**)注意圆形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,还要注意的是任何在一条线GraphicsPath是直的或Bezier曲线.这包括弧形,椭圆形和圆形!
- 但您需要遵循曲线并包含每个完整像素！尝试想象对一个圆进行扫描过程：如果它小到 3x3，那么您需要的矩形数量可以低至 1-3 个；不要让它变大，比如说 30x30 并用矩形近似它：每行或每隔一行至少需要一个，因此需要 15-30 个矩形。我尝试过，对于一个圆 __ 它确实每行需要一个矩形排__。 (2认同)
- 请参阅我附上的插图! (2认同)
我们一直在努力解决同样的问题：对于 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，我们需要缓存数百兆字节的数据。
最后我们转向 PNPoly 算法，该算法只需要几毫秒：
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;
}
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