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，如果能对我所遇到的行为做出解释，那就太好了。

我正在使用System.Drawing.Region.IsVisible(PointF)确定某个点是否在多边形内。这通常效果很好，但是昨天我注意到，如果多边形很复杂并且包含较大的x和y值，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，但是在问题出现之前，多边形必须非常复杂。

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，则需要1毫秒。为什么我看到时间有如此大的差异？我认为 float 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, 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, 1.414681E+07f, 1.412926E+07f, 1.409416E+07f, 1.405905E+07f, 1.402395E+07f, 1.40064E+07f, 1.395374E+07f, 1.393619E+07f, 1.391864E+07f, 1.390109E+07f, 1.390109E+07f, 1.388353E+07f, 1.388353E+07f, 1.388353E+07f, 1.388353E+07f, 1.388353E+07f, 1.388353E+07f, 1.388353E+07f, 1.388353E+07f, 1.388353E+07f, 1.388353E+07f, 1.390109E+07f, 1.391864E+07f, 1.393619E+07f, 1.395374E+07f, 1.398884E+07f, 1.398884E+07f, 1.40064E+07f, 1.402395E+07f, 1.402395E+07f, 1.40415E+07f, 1.405905E+07f, 1.40766E+07f, 1.412926E+07f, 1.414681E+07f, 1.416436E+07f, 1.418191E+07f, 1.419947E+07f, 1.421702E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.423457E+07f, 1.421702E+07f, 1.419947E+07f, 1.418191E+07f, 1.416436E+07f, 1.416436E+07f, 1.412926E+07f, 1.411171E+07f, 1.409416E+07f, 1.40766E+07f, 1.405905E+07f, 1.40415E+07f, 1.402395E+07f, 1.40064E+07f, 1.397129E+07f, 1.397129E+07f, 1.395374E+07f, 1.393619E+07f, 1.393619E+07f, 1.391864E+07f, 1.391864E+07f, 1.390109E+07f, 1.388353E+07f, 1.388353E+07f, 1.386598E+07f, 1.384843E+07f, 1.383088E+07f, 1.379577E+07f, 1.376067E+07f, 1.372557E+07f, 1.370801E+07f, 1.369046E+07f, 1.365536E+07f, 1.363781E+07f, 1.362026E+07f, 1.36027E+07f, 1.358515E+07f, 1.35676E+07f, 1.35325E+07f, 1.351494E+07f, 1.349739E+07f, 1.347984E+07f, 1.346229E+07f, 1.344474E+07f, 1.339208E+07f, 1.337453E+07f, 1.335698E+07f, 1.333943E+07f, 1.332187E+07f, 1.332187E+07f, 1.330432E+07f, 1.326922E+07f, 1.325167E+07f, 1.323411E+07f, 1.321656E+07f, 1.319901E+07f, 1.316391E+07f, 1.314635E+07f, 1.31288E+07f, 1.311125E+07f, 1.307615E+07f, 1.304104E+07f, 1.302349E+07f, 1.300594E+07f, 1.300594E+07f, 1.300594E+07f, 1.300594E+07f, 1.300594E+07f, 1.300594E+07f, 1.300594E+07f, 1.302349E+07f, 1.304104E+07f, 1.307615E+07f, 1.30937E+07f, 1.311125E+07f, 1.314635E+07f, 1.316391E+07f, 1.318146E+07f, 1.319901E+07f, 1.321656E+07f, 1.323411E+07f, 1.323411E+07f, 1.323411E+07f, 1.323411E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.325167E+07f, 1.323411E+07f, 1.323411E+07f, 1.321656E+07f, 1.319901E+07f, 1.318146E+07f, 1.316391E+07f, 1.314635E+07f, 1.31288E+07f, 1.305859E+07f, 1.304104E+07f, 1.298839E+07f, 1.295328E+07f, 1.291818E+07f, 1.288308E+07f, 1.286552E+07f, 1.284797E+07f, 1.283042E+07f, 1.279532E+07f, 1.277776E+07f, 1.276021E+07f, 1.272511E+07f, 1.270756E+07f, 1.269001E+07f, 1.26549E+07f, 1.263735E+07f, 1.260225E+07f, 1.258469E+07f, 1.256714E+07f, 1.256714E+07f, 1.254959E+07f, 1.253204E+07f, 1.253204E+07f, 1.253204E+07f, 1.251449E+07f, 1.251449E+07f, 1.251449E+07f, 1.251449E+07f, 1.251449E+07f, 1.249694E+07f, 1.249694E+07f, 1.249694E+07f, 1.249694E+07f, 1.247938E+07f, 1.247938E+07f, 1.246183E+07f, 1.244428E+07f, 1.240918E+07f, 1.239162E+07f, 1.235652E+07f, 1.233897E+07f, 1.230386E+07f, 1.226876E+07f, 1.225121E+07f, 1.221611E+07f, 1.219855E+07f, 1.219855E+07f, 1.2181E+07f, 1.216345E+07f, 1.216345E+07f, 1.21459E+07f, 1.21459E+07f, 1.212835E+07f, 1.212835E+07f, 1.212835E+07f, 1.212835E+07f, 1.212835E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.211079E+07f, 1.209324E+07f, 1.207569E+07f, 1.207569E+07f, 1.204059E+07f, 1.202303E+07f, 1.200548E+07f, 1.198793E+07f, 1.197038E+07f, 1.195283E+07f, 1.193528E+07f, 1.191772E+07f, 1.190017E+07f, 1.188262E+07f, 1.186507E+07f, 1.181241E+07f, 1.181241E+07f, 1.179486E+07f, 1.177731E+07f, 1.177731E+07f, 1.177731E+07f, 1.175976E+07f, 1.175976E+07f, 1.17422E+07f, 1.17422E+07f, 1.17422E+07f, 1.17422E+07f, 1.17422E+07f, 1.17422E+07f, 1.172465E+07f, 1.172465E+07f, 1.172465E+07f, 1.172465E+07f, 1.172465E+07f, 1.172465E+07f, 1.172465E+07f, 1.172465E+07f, 1.172465E+07f, 1.172465E+07f, 1.17071E+07f, 1.168955E+07f, 1.1672E+07f, 1.163689E+07f, 1.161934E+07f, 1.160179E+07f, 1.156669E+07f, 1.154913E+07f, 1.151403E+07f, 1.149648E+07f, 1.147893E+07f, 1.146137E+07f, 1.144382E+07f, 1.144382E+07f, 1.139117E+07f, 1.139117E+07f, 1.137361E+07f, 1.137361E+07f, 1.137361E+07f, 1.137361E+07f, 1.137361E+07f, 1.137361E+07f, 1.135606E+07f, 1.135606E+07f, 1.135606E+07f, 1.135606E+07f, 1.135606E+07f, 1.135606E+07f, 1.135606E+07f, 1.135606E+07f, 1.135606E+07f, 1.135606E+07f, 1.133851E+07f, 1.133851E+07f, 1.133851E+07f, 1.133851E+07f, 1.133851E+07f, 1.130341E+07f, 1.130341E+07f, 1.128586E+07f, 1.12683E+07f, 1.125075E+07f, 1.121565E+07f, 1.116299E+07f, 1.112789E+07f, 1.107523E+07f, 1.105768E+07f, 1.102258E+07f, 1.098747E+07f, 1.095237E+07f, 1.091727E+07f, 1.089971E+07f, 1.088216E+07f, 1.086461E+07f, 1.082951E+07f, 1.081196E+07f, 1.081196E+07f, 1.07944E+07f, 1.07944E+07f, 1.077685E+07f, 1.07593E+07f, 1.07593E+07f, 1.074175E+07f, 1.074175E+07f, 1.074175E+07f, 1.074175E+07f, 1.074175E+07f, 1.074175E+07f, 1.074175E+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, 1.082951E+07f, 1.082951E+07f, 1.086461E+07f, 1.088216E+07f, 1.089971E+07f, 1.089971E+07f, 1.091727E+07f, 1.091727E+07f, 1.091727E+07f, 1.091727E+07f, 1.091727E+07f, 1.091727E+07f, 1.089971E+07f, 1.088216E+07f, 1.082951E+07f, 1.07944E+07f, 1.07593E+07f, 1.070664E+07f, 1.068909E+07f, 1.067154E+07f, 1.065399E+07f, 1.063644E+07f, 1.061888E+07f, 1.060133E+07f, 1.058378E+07f, 1.056623E+07f, 1.054868E+07f, 1.051357E+07f, 1.049602E+07f, 1.047847E+07f, 1.046092E+07f, 1.042581E+07f, 1.039071E+07f, 1.030295E+07f, 1.026785E+07f, 1.023274E+07f, 1.019764E+07f, 1.018009E+07f, 1.016254E+07f, 1.014498E+07f, 1.010988E+07f, 1.009233E+07f, 1.007478E+07f, 1.005722E+07f, 1.003967E+07f, 1.002212E+07f, 9969464f, 9916809f, 9881705f, 9864154f, 9846602f, 9829050f, 9811497f, 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, 7077132f, 7059657f, 7007235f, 6972285f, 6954811f, 6937337f, 6902388f, 6867439f, 6832491f, 6815016f, 6797541f, 6780067f, 6710169f, 6710169f, 6692695f, 6675221f, 6640272f, 6622797f, 6605323f, 6587849f, 6570375f, 6535425f, 6517951f, 6500477f, 6483003f, 6465528f, 6448053f, 6448053f, 6430579f, 6430579f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6413105f, 6430579f, 6448053f, 6483003f, 6500477f, 6552900f, 6570375f, 6622797f, 6640272f, 6657747f, 6675221f, 6692695f, 6710169f, 6745119f, 6762593f, 6780067f, 6797541f, 6849965f, 6867439f, 6902388f, 6954811f, 6972285f, 6989760f, 7007235f, 7042183f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7059657f, 7042183f, 7042183f, 7024709f, 7007235f, 6989760f, 6989760f, 6972285f, 6954811f, 6937337f, 6919863f, 6902388f, 6867439f, 6832491f, 6815016f, 6797541f, 6780067f, 6762593f, 6745119f, 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");
        }
    }
}

Answer 1

TLTR

进行一次Region.IsVisible(Point)调用所需的时间根本不取决于点数。取而代之的是，它取决于矩形的数目，该数目足以完全准确地覆盖区域。这取决于..:

这些点描述的形状，通常是

形状的大小。

示例1:一个矩形区域有四个点，并且始终需要 一个矩形来覆盖它。如果您要添加大量的点，只要它们都位于矩形的边上，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的数量**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”的类。

您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。

这里也是如此:至少可以说，没有充分的文件证明。也许我只是找不到它，但是似乎没有有关这些字节的结构信息。

(下面的数字表明，每个需要的点都需要1个字节作为类型指示符，再加上两个浮点坐标的2 + 4个字节。这类似于 PathPoints&PathTypes中的 GraphicsPath。在您的示例中为924 + 1个点和1 + 2 * 4个字节组成了8325个字节；另外还有27个字节； 8个可以保持缩放比例。)

不过有一件很有趣的事情:从 中查看RegionData，您的Regions的都可以轻松地看到它们的 的大小相同。这表明 8352在额外的时间中并不直接相关。

但还有 ，另一个，虽然有点神秘，但请阅读:记录不良的电话: RegionData。 MSDN对此表示:

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对您的两个地区都进行了“扫描”，会发生什么情况:

Matrix M = new Matrix();

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

我使用简单的身份矩阵(*)，即不进行任何转换，而得出的结果是:

scans1.Length = 5.960.690
scans2.Length = 5.956

因此，它会创建更多矩形的 1000倍，以近似GetRegionScans，并且瞧瞧这样做也要花费很多时间。.:

这并不令人感到意外:未缩放的路径覆盖了一个很大的区域，要对其进行近似估计，我希望需要更多的矩形。我不知道这种近似的工作原理，但它可能决定即使返回Region，也不需要任何边小于1像素的矩形。

因此，我得出的结论是，RectangleF调用内部需要创建这些近似矩形，并且需要足够的矩形才能覆盖区域内每个完整像素。 (请注意IsVisible不支持部分/抗锯齿像素!)区域的边界越大，适合的像素就越多，扫描过程所需的时间也越长。

我还认为，严格来说，扫描过程会浪费时间。

下一个:即使要进行一百万次调用，执行Region也应该非常快。让我们来看看;当我测量这个:

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

..只需完成RectangleF.Contains(Point)。因此，一旦缓存了扫描矩形，您就可以轻松地对它们进行很多 HitTest 而不是来进行单独的42ms调用。

这是数字的摘要:

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]);

您可以看到每行的顶部和底部是一个矩形，因为此处的曲线是平坦的，并且x坐标快速向外移动。我们越靠近中间，矩形就可以越大(即越高)...因此，我们可以看到近似值严格遵循行 ..

即使边界矩形的高度大于宽度，也是如此，使用列可以减少矩形的数量:



这里和两个椭圆(IsVisible和222x111)都用111x222 水平条纹近似。由于曲率不同，该值小于圆。

(*)-我们已跳过85 ；但可以通过按比例放大或缩小数据来修改结果。 该圆的Matrix为Height像素，并且需要222扫描矩形才能对其进行近似。 如果我们按比例放大135(即用于表示Matrix的Graphics对象):Region，则需要m.Scale(10,10);扫描矩形覆盖放大的圆。

因此，可以使用按1315缩放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，并且可能会丢失边框周围的像素或包含错误的像素。因此，最好只使用您实际需要的正确比例。

(* *)请注意，圆形0.001f确实具有 13 GraphicsPath；但是这些实际上只是四个实点(再加上第一个实点来关闭图形)，以及，每对点之间有两个控制点；因此5 + 4 * 2 =13。另外请注意，PathPoints中的任何线 均为直线或贝塞尔曲线的。 这包括弧，椭圆和圆!