feat: 过弯检测工具（纯解析几何公式）

NavisworksTransport.UnitTests.csproj

@@ -62,6 +62,7 @@
   <ItemGroup>
     <Compile Include="UnitTests\Core\AliasTreeTests.cs" />
     <Compile Include="UnitTests\Core\PathHelperTests.cs" />
+    <Compile Include="UnitTests\Core\CornerTurnCheckHelperTests.cs" />
     <Compile Include="UnitTests\Core\SelectionClipBoxLockStateTests.cs" />
     <Compile Include="UnitTests\Core\PathPlanningManagerHoistingCompletionTests.cs" />
     <Compile Include="UnitTests\Core\PathPersistenceTests.cs" />

TransportPlugin.csproj

@@ -278,6 +278,9 @@
     <Compile Include="src\UI\WPF\Views\EditCoordinatesWindow.xaml.cs">
       <DependentUpon>EditCoordinatesWindow.xaml</DependentUpon>
     </Compile>
+    <Compile Include="src\UI\WPF\Views\CornerTurnCheckDialog.xaml.cs">
+      <DependentUpon>CornerTurnCheckDialog.xaml</DependentUpon>
+    </Compile>
     <Compile Include="src\UI\WPF\Views\ModelItemBoundsWindow.xaml.cs">
       <DependentUpon>ModelItemBoundsWindow.xaml</DependentUpon>
     </Compile>
@@ -342,6 +345,7 @@
     <Compile Include="src\Utils\NavisworksSelectionHelper.cs" />
     <Compile Include="src\Utils\NavisworksToDMesh3Converter.cs" />
     <Compile Include="src\Utils\UnitsConverter.cs" />
+    <Compile Include="src\Utils\CornerTurnCheckHelper.cs" />
     <Compile Include="src\Utils\VersionInfo.cs" />
     <!-- Coordinate System -->
     <Compile Include="src\Utils\CoordinateSystem\AlignToGroundMinCrossSectionYawSearcher.cs" />
@@ -407,6 +411,10 @@
       <SubType>Designer</SubType>
       <Generator>MSBuild:Compile</Generator>
     </Page>
+    <Page Include="src\UI\WPF\Views\CornerTurnCheckDialog.xaml">
+      <SubType>Designer</SubType>
+      <Generator>MSBuild:Compile</Generator>
+    </Page>
     <Page Include="src\UI\WPF\Views\ModelItemBoundsWindow.xaml">
       <SubType>Designer</SubType>
       <Generator>MSBuild:Compile</Generator>

UnitTests/Core/CornerTurnCheckHelperTests.cs

@@ -0,0 +1,99 @@
+using System;
+using Microsoft.VisualStudio.TestTools.UnitTesting;
+using NavisworksTransport.Utils;
+
+namespace NavisworksTransport.UnitTests.Core
+{
+    [TestClass]
+    public class CornerTurnCheckHelperTests
+    {
+        [TestMethod]
+        public void EqualWidth_MaxLength_ShouldPass()
+        {
+            var L = 3.0 * Math.Sqrt(2) - 1.5 - 0.01;
+            Assert.IsTrue(CornerTurnCheckHelper.CanPass(L, 1.5, 3.0, 3.0, out _, out _));
+        }
+
+        [TestMethod]
+        public void EqualWidth_TooLong_ShouldNotPass()
+        {
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(2.5, 1.0, 2.0, 2.0, out _, out _));
+        }
+
+        [TestMethod]
+        public void EqualWidth_Short_ShouldPass()
+        {
+            Assert.IsTrue(CornerTurnCheckHelper.CanPass(1.0, 0.5, 2.0, 2.0, out _, out _));
+        }
+
+        [TestMethod]
+        public void StraightPass_ShouldPass()
+        {
+            Assert.IsTrue(CornerTurnCheckHelper.CanPass(2.5, 0.3, 2.5, 3.0, out _, out _));
+        }
+
+        [TestMethod]
+        public void WidthExceedsBoth_ShouldNotPass()
+        {
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(3.0, 4.0, 2.0, 2.5, out _, out _));
+        }
+
+        [TestMethod]
+        public void ZeroOrNegativeInput_ShouldReturnFalse()
+        {
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(0, 1, 2, 2, out _, out _));
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(2, 0, 2, 2, out _, out _));
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(2, 1, 0, 2, out _, out _));
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(2, 1, 2, 0, out _, out _));
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(-1, 1, 2, 2, out _, out _));
+        }
+
+        [TestMethod]
+        public void UnequalWidth_Fits_ShouldPass()
+        {
+            Assert.IsTrue(CornerTurnCheckHelper.CanPass(0.8, 0.5, 3.0, 1.5, out _, out _));
+        }
+
+        [TestMethod]
+        public void VeryDifferentWidths_ShouldUseNarrower()
+        {
+            Assert.IsTrue(CornerTurnCheckHelper.CanPass(0.1, 0.55, 10.0, 0.6, out _, out _));
+        }
+
+        [TestMethod]
+        public void HugeModule_ShouldNotPass()
+        {
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(20.0, 5.0, 2.0, 2.0, out _, out _));
+        }
+
+        [TestMethod]
+        public void UserCase_LongerThanEntry_ShouldNotPass()
+        {
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(4.9, 2.0, 4.8, 2.75, out _, out _));
+        }
+
+        [TestMethod]
+        public void UserCase_WiderThanExit_ShouldNotPass()
+        {
+            Assert.IsFalse(CornerTurnCheckHelper.CanPass(4.8, 2.8, 3.0, 2.75, out _, out _));
+        }
+
+        [TestMethod]
+        public void EqualWidth_Square_ShouldPass()
+        {
+            Assert.IsTrue(CornerTurnCheckHelper.CanPass(1.0, 1.0, 2.0, 2.0, out _, out _));
+        }
+
+        [TestMethod]
+        public void EntryExact_ShouldPass()
+        {
+            Assert.IsTrue(CornerTurnCheckHelper.CanPass(2.75, 2.0, 5.0, 2.75, out _, out _));
+        }
+
+        [TestMethod]
+        public void Square_WidthEqualsCorridor_ShouldPass()
+        {
+            Assert.IsTrue(CornerTurnCheckHelper.CanPass(2.0, 2.0, 3.0, 2.75, out _, out _));
+        }
+    }
+}

src/UI/WPF/Resources/NavisworksStyles.xaml

@@ -209,6 +209,9 @@ NavisworksTransport 共享样式资源字典 - Navisworks 2026风格
         M17.65,6.35C16.2,4.9 14.21,4 12,4C7.58,4 4.01,7.58 4.01,12C4.01,16.42 7.58,20 12,20C15.73,20 18.84,17.45 19.73,14H17.65C16.83,16.33 14.61,18 12,18C8.69,18 6,15.31 6,12C6,8.69 8.69,6 12,6C13.66,6 15.14,6.69 16.22,7.78L13,11H20V4L17.65,6.35Z
     </Geometry>
 
+    <!-- L形转角图标 (过弯检测) -->
+    <Geometry x:Key="CornerCheckIconGeometry">M3,17 L17,17 L17,3</Geometry>
+
     <!-- 靶心/准心图标 (测量工具) -->
     <Geometry x:Key="TargetIconGeometry">
         M12,2C6.48,2 2,6.48 2,12C2,17.52 6.48,22 12,22C17.52,22 22,17.52 22,12C22,6.48 17.52,2 12,2ZM12,20C7.59,20 4,16.41 4,12C4,7.59 7.59,4 12,4C16.41,4 20,7.59 20,12C20,16.41 16.41,20 12,20ZM12,6C8.69,6 6,8.69 6,12C6,15.31 8.69,18 12,18C15.31,18 18,15.31 18,12C18,8.69 15.31,6 12,6ZM12,16C9.79,16 8,14.21 8,12C8,9.79 9.79,8 12,8C14.21,8 16,9.79 16,12C16,14.21 14.21,16 12,16Z

src/UI/WPF/Views/CornerTurnCheckDialog.xaml

@@ -0,0 +1,123 @@
+<Window x:Class="NavisworksTransport.UI.WPF.Views.CornerTurnCheckDialog"
+        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
+        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
+        xmlns:converters="clr-namespace:NavisworksTransport.UI.WPF.Converters"
+        Title="过弯检测" Height="520" Width="420"
+        WindowStartupLocation="CenterScreen"
+        ResizeMode="NoResize"
+        ShowInTaskbar="False"
+        Topmost="True"
+        Background="White">
+    <Window.Resources>
+        <ResourceDictionary>
+            <ResourceDictionary.MergedDictionaries>
+                <ResourceDictionary Source="pack://application:,,,/TransportPlugin;component/src/UI/WPF/Resources/NavisworksStyles.xaml"/>
+            </ResourceDictionary.MergedDictionaries>
+            <converters:EditableNumberConverter x:Key="EditableNumberConverter"/>
+        </ResourceDictionary>
+    </Window.Resources>
+
+    <Grid>
+        <Grid.RowDefinitions>
+            <RowDefinition Height="Auto"/>
+            <RowDefinition Height="*"/>
+            <RowDefinition Height="Auto"/>
+        </Grid.RowDefinitions>
+
+        <!-- 标题栏 -->
+        <Border Grid.Row="0" Background="#FFF8FBFF" BorderBrush="#FFD4E7FF" BorderThickness="0,0,0,1" Padding="20,15">
+            <StackPanel>
+                <TextBlock Text="过弯检测" FontWeight="SemiBold" FontSize="14" Foreground="#FF2B579A"/>
+                <TextBlock Text="检查矩形模块能否通过 L 形通道" FontSize="10" Foreground="#FF666666" Margin="0,3,0,0"/>
+            </StackPanel>
+        </Border>
+
+        <!-- 输入区域 -->
+        <Border Grid.Row="1" Padding="20,15">
+            <StackPanel>
+                <Border Background="#FFF0F7FF" BorderBrush="#FFD4E7FF" BorderThickness="1" Padding="12,10" Margin="0,0,0,15">
+                    <TextBlock Text="模块在转角处的投影宽度不能超过通道宽度，输入尺寸后计算最优化角度下的通过性。" 
+                               FontSize="10" Foreground="#FF666666" TextWrapping="Wrap"/>
+                </Border>
+
+                <!-- 入口通道宽度 -->
+                <Grid Margin="0,0,0,12">
+                    <Grid.ColumnDefinitions>
+                        <ColumnDefinition Width="100"/>
+                        <ColumnDefinition Width="*"/>
+                        <ColumnDefinition Width="30"/>
+                    </Grid.ColumnDefinitions>
+                    <TextBlock Text="入口通道宽度 C₁:" VerticalAlignment="Center" FontSize="11" Foreground="#FF333333"/>
+                    <TextBox Grid.Column="1" x:Name="EntryWidthBox" Height="28"
+                             VerticalContentAlignment="Center" Padding="8,0" FontSize="11"
+                             BorderBrush="#FFCCCCCC" BorderThickness="1"/>
+                    <TextBlock Grid.Column="2" Text="米" VerticalAlignment="Center" FontSize="11" Foreground="#FF666666" Margin="5,0,0,0"/>
+                </Grid>
+
+                <!-- 出口通道宽度 -->
+                <Grid Margin="0,0,0,12">
+                    <Grid.ColumnDefinitions>
+                        <ColumnDefinition Width="100"/>
+                        <ColumnDefinition Width="*"/>
+                        <ColumnDefinition Width="30"/>
+                    </Grid.ColumnDefinitions>
+                    <TextBlock Text="出口通道宽度 C₂:" VerticalAlignment="Center" FontSize="11" Foreground="#FF333333"/>
+                    <TextBox Grid.Column="1" x:Name="ExitWidthBox" Height="28"
+                             VerticalContentAlignment="Center" Padding="8,0" FontSize="11"
+                             BorderBrush="#FFCCCCCC" BorderThickness="1"/>
+                    <TextBlock Grid.Column="2" Text="米" VerticalAlignment="Center" FontSize="11" Foreground="#FF666666" Margin="5,0,0,0"/>
+                </Grid>
+
+                <!-- 分隔线 -->
+                <Border Height="1" Background="#FFEEEEEE" Margin="0,0,0,12"/>
+
+                <!-- 模块长度 -->
+                <Grid Margin="0,0,0,12">
+                    <Grid.ColumnDefinitions>
+                        <ColumnDefinition Width="100"/>
+                        <ColumnDefinition Width="*"/>
+                        <ColumnDefinition Width="30"/>
+                    </Grid.ColumnDefinitions>
+                    <TextBlock Text="模块长度 L:" VerticalAlignment="Center" FontSize="11" Foreground="#FF333333"/>
+                    <TextBox Grid.Column="1" x:Name="LengthBox" Height="28"
+                             VerticalContentAlignment="Center" Padding="8,0" FontSize="11"
+                             BorderBrush="#FFCCCCCC" BorderThickness="1"/>
+                    <TextBlock Grid.Column="2" Text="米" VerticalAlignment="Center" FontSize="11" Foreground="#FF666666" Margin="5,0,0,0"/>
+                </Grid>
+
+                <!-- 模块宽度 -->
+                <Grid Margin="0,0,0,12">
+                    <Grid.ColumnDefinitions>
+                        <ColumnDefinition Width="100"/>
+                        <ColumnDefinition Width="*"/>
+                        <ColumnDefinition Width="30"/>
+                    </Grid.ColumnDefinitions>
+                    <TextBlock Text="模块宽度 W:" VerticalAlignment="Center" FontSize="11" Foreground="#FF333333"/>
+                    <TextBox Grid.Column="1" x:Name="WidthBox" Height="28"
+                             VerticalContentAlignment="Center" Padding="8,0" FontSize="11"
+                             BorderBrush="#FFCCCCCC" BorderThickness="1"/>
+                    <TextBlock Grid.Column="2" Text="米" VerticalAlignment="Center" FontSize="11" Foreground="#FF666666" Margin="5,0,0,0"/>
+                </Grid>
+
+                <!-- 结果区 -->
+                <Border x:Name="ResultBorder" Background="#FFF0FFF0" BorderBrush="#FF4CAF50" BorderThickness="1" Padding="12,10" Margin="0,5,0,0"
+                        Visibility="Collapsed">
+                    <StackPanel>
+                        <TextBlock x:Name="ResultTitle" FontWeight="SemiBold" FontSize="12" Foreground="#FF2E7D32"/>
+                        <TextBlock x:Name="ResultDetail" FontSize="10" Foreground="#FF666666" Margin="0,3,0,0"/>
+                    </StackPanel>
+                </Border>
+            </StackPanel>
+        </Border>
+
+        <!-- 按钮栏 -->
+        <Border Grid.Row="2" Background="#FFF8FBFF" BorderBrush="#FFD4E7FF" BorderThickness="0,1,0,0" Padding="20,12">
+            <StackPanel Orientation="Horizontal" HorizontalAlignment="Right">
+                <Button Content="计算" Click="OnCalculateClick"
+                        Style="{StaticResource ActionButtonStyle}" Width="90" Height="32" Margin="0,0,10,0"/>
+                <Button Content="关闭" Click="OnCloseClick"
+                        Style="{StaticResource SecondaryButtonStyle}" Width="90" Height="32"/>
+            </StackPanel>
+        </Border>
+    </Grid>
+</Window>

src/UI/WPF/Views/CornerTurnCheckDialog.xaml.cs

@@ -0,0 +1,80 @@
+using System;
+using System.Windows;
+using System.Windows.Media;
+using NavisworksTransport.Utils;
+
+namespace NavisworksTransport.UI.WPF.Views
+{
+    public partial class CornerTurnCheckDialog : Window
+    {
+        public CornerTurnCheckDialog()
+        {
+            InitializeComponent();
+        }
+
+        private void OnCalculateClick(object sender, RoutedEventArgs e)
+        {
+            if (!TryParseInputs(out var c1, out var c2, out var length, out var width))
+                return;
+
+            var pass = CornerTurnCheckHelper.CanPass(length, width, c1, c2,
+                out var margin, out var maxLength);
+
+            ResultBorder.Visibility = Visibility.Visible;
+
+            if (pass)
+            {
+                ResultBorder.Background = new SolidColorBrush(Color.FromRgb(240, 255, 240));
+                ResultBorder.BorderBrush = new SolidColorBrush(Color.FromRgb(76, 175, 80));
+                ResultTitle.Text = "✅ 可通过";
+                ResultTitle.Foreground = new SolidColorBrush(Color.FromRgb(46, 125, 50));
+                ResultDetail.Text = $"余量: {margin:F2} 米\n最大可通过长度: {maxLength:F2} 米";
+            }
+            else
+            {
+                ResultBorder.Background = new SolidColorBrush(Color.FromRgb(255, 240, 240));
+                ResultBorder.BorderBrush = new SolidColorBrush(Color.FromRgb(244, 67, 54));
+                ResultTitle.Text = "❌ 不可通过";
+                ResultTitle.Foreground = new SolidColorBrush(Color.FromRgb(183, 28, 28));
+                ResultDetail.Text = $"超出: {-margin:F2} 米\n当前条件下最大可通过长度: {maxLength:F2} 米";
+            }
+        }
+
+        private void OnCloseClick(object sender, RoutedEventArgs e)
+        {
+            Close();
+        }
+
+        private bool TryParseInputs(out double c1, out double c2, out double length, out double width)
+        {
+            c1 = c2 = length = width = 0;
+
+            if (!TryParseTextBox(EntryWidthBox, out c1, "入口通道宽度")) return false;
+            if (!TryParseTextBox(ExitWidthBox, out c2, "出口通道宽度")) return false;
+            if (!TryParseTextBox(LengthBox, out length, "模块长度")) return false;
+            if (!TryParseTextBox(WidthBox, out width, "模块宽度")) return false;
+
+            return true;
+        }
+
+        private static bool TryParseTextBox(System.Windows.Controls.TextBox box, out double value, string name)
+        {
+            value = 0;
+            var text = box.Text.Trim();
+            if (string.IsNullOrEmpty(text))
+            {
+                MessageBox.Show($"请输入{name}。", "输入错误", MessageBoxButton.OK, MessageBoxImage.Warning);
+                box.Focus();
+                return false;
+            }
+            if (!double.TryParse(text, out value) || value <= 0)
+            {
+                MessageBox.Show($"请输入有效的{name}（正数）。", "输入错误", MessageBoxButton.OK, MessageBoxImage.Warning);
+                box.Focus();
+                box.SelectAll();
+                return false;
+            }
+            return true;
+        }
+    }
+}

src/UI/WPF/Views/PathEditingView.xaml

@@ -311,6 +311,7 @@ NavisworksTransport 路径编辑页签视图 - 采用与动画控制和分层管
                         <Grid.ColumnDefinitions>
                             <ColumnDefinition Width="*"/>
                             <ColumnDefinition Width="Auto"/>
+                            <ColumnDefinition Width="Auto"/>
                         </Grid.ColumnDefinitions>
                         <TextBlock Grid.Column="0" Text="路径点列表" VerticalAlignment="Center" FontSize="11" Foreground="#FF666666"/>
                         <Button Grid.Column="1" 
@@ -318,11 +319,22 @@ NavisworksTransport 路径编辑页签视图 - 采用与动画控制和分层管
                                 Click="OnMeasureBoundsButtonClick"
                                 Style="{StaticResource IconButtonStyle}"
                                 Width="24"
-                                Height="24">
+                                Height="24"
+                                Margin="0,0,2,0">
                             <Path Data="{StaticResource TargetIconGeometry}" 
                                   Fill="{StaticResource NavisworksPrimaryBrush}" 
                                   Width="16" Height="16" Stretch="Uniform"/>
                         </Button>
+                        <Button Grid.Column="2"
+                                ToolTip="过弯检测 — 检查模块能否通过 L 形通道"
+                                Click="OnCornerTurnCheckClick"
+                                Style="{StaticResource IconButtonStyle}"
+                                Width="24"
+                                Height="24">
+                            <Path Data="{StaticResource CornerCheckIconGeometry}" 
+                                  Fill="{StaticResource NavisworksPrimaryBrush}" 
+                                  Width="16" Height="16" Stretch="Uniform"/>
+                        </Button>
                     </Grid>
                     
                     <!-- 路径点列表 -->

src/UI/WPF/Views/PathEditingView.xaml.cs

@@ -286,6 +286,19 @@ namespace NavisworksTransport.UI.WPF.Views
             }
         }
 
+        private void OnCornerTurnCheckClick(object sender, RoutedEventArgs e)
+        {
+            try
+            {
+                var dialog = new CornerTurnCheckDialog();
+                dialog.ShowDialog();
+            }
+            catch (Exception ex)
+            {
+                LogManager.Error($"打开过弯检测对话框失败: {ex.Message}");
+            }
+        }
+
         /// <summary>
         /// 包围盒信息窗口实例(保持引用以防止被GC回收)
         /// </summary>

src/Utils/CornerTurnCheckHelper.cs

@@ -0,0 +1,98 @@
+using System;
+
+namespace NavisworksTransport.Utils
+{
+    public static class CornerTurnCheckHelper
+    {
+        public static bool CanPass(double length, double width, double entryWidth, double exitWidth,
+            out double margin, out double maxLength)
+        {
+            margin = 0;
+            maxLength = 0;
+
+            if (length <= 0 || width <= 0 || entryWidth <= 0 || exitWidth <= 0)
+                return false;
+
+            // 模块最短边必须能同时通过两条通道
+            var minDim = Math.Min(length, width);
+            if (minDim > entryWidth || minDim > exitWidth)
+                return false;
+
+            // 转角通过性解析判断
+            var r = Math.Sqrt(length * length + width * width);
+            var phi = Math.Atan2(width, length);
+
+            var sinEntryRatio = entryWidth / r;
+            var cosExitRatio = exitWidth / r;
+
+            // 入口侧：最大 θ 满足 Y_span ≤ C₁
+            var thetaYmax = double.NaN;
+            if (sinEntryRatio >= 1)
+                thetaYmax = Math.PI / 2; // 从不超出
+            else
+            {
+                thetaYmax = Math.Asin(sinEntryRatio) - phi;
+                if (thetaYmax < 0) thetaYmax = 0;
+                if (thetaYmax > Math.PI / 2) thetaYmax = Math.PI / 2;
+            }
+
+            // 出口侧：最小 θ 满足 X_span ≤ C₂
+            var thetaXmin = double.NaN;
+            if (cosExitRatio >= 1)
+                thetaXmin = 0; // 从不超出
+            else
+            {
+                thetaXmin = Math.Acos(cosExitRatio) + phi;
+                if (thetaXmin < 0) thetaXmin = 0;
+                if (thetaXmin > Math.PI / 2) thetaXmin = Math.PI / 2;
+            }
+
+            // 需要同时满足两条约束的区间有交集
+            var canPass = thetaYmax >= thetaXmin;
+
+            if (canPass)
+            {
+                // 余量 = 在交集中心处两个约束的最小剩余量
+                var thetaMid = (thetaYmax + thetaXmin) / 2;
+                var cos = Math.Cos(thetaMid);
+                var sin = Math.Sin(thetaMid);
+                var xSpan = length * cos + width * sin;
+                var ySpan = length * sin + width * cos;
+                margin = Math.Min(exitWidth - xSpan, entryWidth - ySpan);
+
+                maxLength = FindMaxLength(width, entryWidth, exitWidth);
+            }
+
+            return canPass;
+        }
+
+        /// <summary> 二分法求最大可通过长度，使用相同的解析条件 </summary>
+        private static double FindMaxLength(double width, double c1, double c2)
+        {
+            double lo = 0, hi = Math.Max(c1, c2) * 4;
+            for (int i = 0; i < 50; i++)
+            {
+                var mid = (lo + hi) / 2;
+                if (CheckLengthFeasible(mid, width, c1, c2))
+                    lo = mid;
+                else
+                    hi = mid;
+            }
+            return (lo + hi) / 2;
+        }
+
+        private static bool CheckLengthFeasible(double length, double width, double c1, double c2)
+        {
+            var r = Math.Sqrt(length * length + width * width);
+            var phi = Math.Atan2(width, length);
+
+            var thetaYmax = c1 >= r ? Math.PI / 2
+                : Math.Min(Math.Max(Math.Asin(c1 / r) - phi, 0), Math.PI / 2);
+
+            var thetaXmin = c2 >= r ? 0
+                : Math.Min(Math.Max(Math.Acos(c2 / r) + phi, 0), Math.PI / 2);
+
+            return thetaYmax >= thetaXmin;
+        }
+    }
+}