C# WinForm中的极坐标系实现与应用

极坐标系统在许多工程应用中具有重要作用，特别是在处理圆周运动、角度定位和雷达显示等场景。本文将详细介绍如何在C# WinForm中实现一个完整的极坐标系统，并展示其在实际应用中的使用场景。

应用场景

工业自动化
- 旋转工作台位置控制
- 圆周加工轨迹规划
- 机械臂角度控制
测量与检测
- 雷达扫描显示
- 声纳信号显示
- 角度传感器数据可视化
科学计算
- 极坐标函数绘制
- 圆周运动分析
- 扇形统计图表

完整代码实现

极坐标系控件类

C#
using System;
using System.Drawing;
using System.Windows.Forms;
using System.Collections.Generic;

public class PolarCoordinateControl : Control
{
    private float scale = 1.0f;          // 缩放比例
    private Point origin;                 // 原点位置
    private Point mouseDownLocation;      // 鼠标按下位置
    private bool isPanning = false;       // 是否正在平移
    private const int CIRCLE_COUNT = 5;   // 同心圆数量
    private const int ANGLE_STEP = 15;    // 角度刻度步进（度）

    public PolarCoordinateControl()
    {
        // 设置控件属性
        this.DoubleBuffered = true;
        this.BackColor = Color.White;
        this.Resize += PolarCoordinateControl_Resize;
        this.MouseDown += PolarCoordinateControl_MouseDown;
        this.MouseMove += PolarCoordinateControl_MouseMove;
        this.MouseUp += PolarCoordinateControl_MouseUp;
        this.MouseWheel += PolarCoordinateControl_MouseWheel;

        // 初始化原点位置
        UpdateOrigin();
    }

    private void UpdateOrigin()
    {
        origin = new Point(Width / 2, Height / 2);
    }

    private void PolarCoordinateControl_Resize(object sender, EventArgs e)
    {
        UpdateOrigin();
        Invalidate();
    }

    private void PolarCoordinateControl_MouseDown(object sender, MouseEventArgs e)
    {
        if (e.Button == MouseButtons.Left)
        {
            isPanning = true;
            mouseDownLocation = e.Location;
            Cursor = Cursors.Hand;
        }
    }

    private void PolarCoordinateControl_MouseMove(object sender, MouseEventArgs e)
    {
        if (isPanning)
        {
            int dx = e.X - mouseDownLocation.X;
            int dy = e.Y - mouseDownLocation.Y;
            origin.X += dx;
            origin.Y += dy;
            mouseDownLocation = e.Location;
            Invalidate();
        }
    }

    private void PolarCoordinateControl_MouseUp(object sender, MouseEventArgs e)
    {
        isPanning = false;
        Cursor = Cursors.Default;
    }

    private void PolarCoordinateControl_MouseWheel(object sender, MouseEventArgs e)
    {
        float oldScale = scale;
        if (e.Delta > 0)
            scale *= 1.1f;
        else
            scale /= 1.1f;

        // 限制缩放范围
        scale = Math.Max(0.1f, Math.Min(5.0f, scale));
        Invalidate();
    }

    protected override void OnPaint(PaintEventArgs e)
    {
        base.OnPaint(e);
        Graphics g = e.Graphics;
        g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.AntiAlias;

        // 绘制同心圆
        DrawConcentricCircles(g);

        // 绘制角度线
        DrawAngleLines(g);

        // 绘制刻度
        DrawScale(g);
    }

    private void DrawConcentricCircles(Graphics g)
    {
        using (Pen circlePen = new Pen(Color.LightGray, 1))
        {
            int baseRadius = Math.Min(Width, Height) / 3;
            float radiusStep = baseRadius / CIRCLE_COUNT;

            for (int i = 1; i <= CIRCLE_COUNT; i++)
            {
                float radius = i * radiusStep * scale;
                g.DrawEllipse(circlePen,
                    origin.X - radius,
                    origin.Y - radius,
                    radius * 2,
                    radius * 2);

                // 绘制半径值
                using (Font font = new Font("Arial", 8))
                using (Brush brush = new SolidBrush(Color.Black))
                {
                    string radiusText = (i * radiusStep).ToString("F1");
                    g.DrawString(radiusText, font, brush,
                        origin.X + 5,
                        origin.Y - radius);
                }
            }
        }
    }

    private void DrawAngleLines(Graphics g)
    {
        using (Pen anglePen = new Pen(Color.LightGray, 1))
        {
            int radius = (int)(Math.Min(Width, Height) / 2 * scale);

            for (int angle = 0; angle < 360; angle += ANGLE_STEP)
            {
                double radians = angle * Math.PI / 180;
                Point endPoint = new Point(
                    (int)(origin.X + radius * Math.Cos(radians)),
                    (int)(origin.Y + radius * Math.Sin(radians))
                );
                g.DrawLine(anglePen, origin, endPoint);

                // 绘制角度值
                if (angle % 30 == 0)
                {
                    using (Font font = new Font("Arial", 8))
                    using (Brush brush = new SolidBrush(Color.Black))
                    {
                        Point textPoint = new Point(
                            (int)(origin.X + (radius + 20) * Math.Cos(radians)),
                            (int)(origin.Y + (radius + 20) * Math.Sin(radians))
                        );
                        g.DrawString(angle.ToString() + "°", font, brush, textPoint);
                    }
                }
            }
        }
    }

    private void DrawScale(Graphics g)
    {
        // 绘制坐标轴
        using (Pen axisPen = new Pen(Color.Black, 2))
        {
            int radius = (int)(Math.Min(Width, Height) / 2 * scale);
            // X轴
            g.DrawLine(axisPen, origin.X - radius, origin.Y, origin.X + radius, origin.Y);
            // Y轴
            g.DrawLine(axisPen, origin.X, origin.Y - radius, origin.X, origin.Y + radius);
        }
    }

    // 坐标转换：极坐标到笛卡尔坐标
    public PointF PolarToCartesian(float r, float theta)
    {
        float x = r * (float)Math.Cos(theta);
        float y = r * (float)Math.Sin(theta);
        return new PointF(x, y);
    }

    // 坐标转换：笛卡尔坐标到极坐标
    public (float r, float theta) CartesianToPolar(float x, float y)
    {
        float r = (float)Math.Sqrt(x * x + y * y);
        float theta = (float)Math.Atan2(y, x);
        return (r, theta);
    }

    // 屏幕坐标到极坐标
    public (float r, float theta) ScreenToPolar(Point screenPoint)
    {
        float x = (screenPoint.X - origin.X) / scale;
        float y = (screenPoint.Y - origin.Y) / scale;
        return CartesianToPolar(x, y);
    }

    // 极坐标到屏幕坐标
    public Point PolarToScreen(float r, float theta)
    {
        PointF cartesian = PolarToCartesian(r, theta);
        return new Point(
            (int)(origin.X + cartesian.X * scale),
            (int)(origin.Y + cartesian.Y * scale)
        );
    }
}

实际应用示例

雷达扫描效果

C#
using System;
using System.Collections.Generic;
using System.Drawing.Drawing2D;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using Timer = System.Windows.Forms.Timer;

namespace AppMotionControl
{
    public class PolarCoordinateControl : Control
    {
        private float scale = 1.0f;          // 缩放比例
        private Point origin;                 // 原点位置
        private Point mouseDownLocation;      // 鼠标按下位置
        private bool isPanning = false;       // 是否正在平移
        private const int CIRCLE_COUNT = 5;   // 同心圆数量
        private const int ANGLE_STEP = 15;    // 角度刻度步进（度）

        private Timer _scanTimer;
        private float _scanAngle = 0f; // 扫描线当前角度
        public bool isRadarEnabled {get;set;}=false; // 雷达扫描开关

        public PolarCoordinateControl()
        {
            // 设置控件属性
            this.DoubleBuffered = true;
            this.BackColor = Color.White;
            this.Resize += PolarCoordinateControl_Resize;
            this.MouseDown += PolarCoordinateControl_MouseDown;
            this.MouseMove += PolarCoordinateControl_MouseMove;
            this.MouseUp += PolarCoordinateControl_MouseUp;
            this.MouseWheel += PolarCoordinateControl_MouseWheel;

            // 初始化原点位置
            UpdateOrigin();

            _scanTimer = new Timer();
            _scanTimer.Interval = 50; // 扫描速度，可根据需要调节  
            _scanTimer.Tick += (s, e) =>
            {
                // 让扫描角度在 0～360 度间循环  
                _scanAngle = (_scanAngle + 5) % 360f;
                Invalidate();
            };
            _scanTimer.Start();
        }

        private void UpdateOrigin()
        {
            origin = new Point(Width / 2, Height / 2);
        }

        private void PolarCoordinateControl_Resize(object sender, EventArgs e)
        {
            UpdateOrigin();
            Invalidate();
        }

        private void PolarCoordinateControl_MouseDown(object sender, MouseEventArgs e)
        {
            if (e.Button == MouseButtons.Left)
            {
                isPanning = true;
                mouseDownLocation = e.Location;
                Cursor = Cursors.Hand;
            }
        }

        private void PolarCoordinateControl_MouseMove(object sender, MouseEventArgs e)
        {
            if (isPanning)
            {
                int dx = e.X - mouseDownLocation.X;
                int dy = e.Y - mouseDownLocation.Y;
                origin.X += dx;
                origin.Y += dy;
                mouseDownLocation = e.Location;
                Invalidate();
            }
        }

        private void PolarCoordinateControl_MouseUp(object sender, MouseEventArgs e)
        {
            isPanning = false;
            Cursor = Cursors.Default;
        }

        private void PolarCoordinateControl_MouseWheel(object sender, MouseEventArgs e)
        {
            float oldScale = scale;
            if (e.Delta > 0)
                scale *= 1.1f;
            else
                scale /= 1.1f;

            // 限制缩放范围
            scale = Math.Max(0.1f, Math.Min(5.0f, scale));
            Invalidate();
        }

        protected override void OnPaint(PaintEventArgs e)
        {
            base.OnPaint(e);
            Graphics g = e.Graphics;
            g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.AntiAlias;

            // 绘制同心圆
            DrawConcentricCircles(g);

            // 绘制角度线
            DrawAngleLines(g);

            // 绘制刻度
            DrawScale(g);

            if (isRadarEnabled)
            {
                DrawRadarScan(g);
            }
        }

        private void DrawRadarScan(Graphics g)
        {
            int radius = (int)(Math.Min(Width, Height) / 2 * scale);
            double radians = _scanAngle * Math.PI / 180;

            // 绘制扫描扇形  
            using (LinearGradientBrush brush = new LinearGradientBrush(
                new Point(origin.X, origin.Y),
                new Point(
                    (int)(origin.X + radius * Math.Cos(radians)),
                    (int)(origin.Y + radius * Math.Sin(radians))
                ),
                Color.FromArgb(80, 0, 255, 0),  // 半透明绿色  
                Color.FromArgb(0, 0, 255, 0)))   // 完全透明  
            {
                g.FillPie(brush,
                    origin.X - radius,
                    origin.Y - radius,
                    radius * 2,
                    radius * 2,
                    _scanAngle - 30,
                    30);
            }

            // 绘制扫描线  
            using (Pen scanPen = new Pen(Color.Green, 2))
            {
                Point endPoint = new Point(
                    (int)(origin.X + radius * Math.Cos(radians)),
                    (int)(origin.Y + radius * Math.Sin(radians))
                );
                g.DrawLine(scanPen, origin, endPoint);
            }
        }

        private void DrawConcentricCircles(Graphics g)
        {
            using (Pen circlePen = new Pen(Color.LightGray, 1))
            {
                int baseRadius = Math.Min(Width, Height) / 3;
                float radiusStep = baseRadius / CIRCLE_COUNT;

                for (int i = 1; i <= CIRCLE_COUNT; i++)
                {
                    float radius = i * radiusStep * scale;
                    g.DrawEllipse(circlePen,
                        origin.X - radius,
                        origin.Y - radius,
                        radius * 2,
                        radius * 2);

                    // 绘制半径值
                    using (Font font = new Font("Arial", 8))
                    using (Brush brush = new SolidBrush(Color.Black))
                    {
                        string radiusText = (i * radiusStep).ToString("F1");
                        g.DrawString(radiusText, font, brush,
                            origin.X + 5,
                            origin.Y - radius);
                    }
                }
            }
        }

        private void DrawAngleLines(Graphics g)
        {
            using (Pen anglePen = new Pen(Color.LightGray, 1))
            {
                int radius = (int)(Math.Min(Width, Height) / 2 * scale);

                for (int angle = 0; angle < 360; angle += ANGLE_STEP)
                {
                    double radians = angle * Math.PI / 180;
                    Point endPoint = new Point(
                        (int)(origin.X + radius * Math.Cos(radians)),
                        (int)(origin.Y + radius * Math.Sin(radians))
                    );
                    g.DrawLine(anglePen, origin, endPoint);

                    // 绘制角度值
                    if (angle % 30 == 0)
                    {
                        using (Font font = new Font("Arial", 8))
                        using (Brush brush = new SolidBrush(Color.Black))
                        {
                            Point textPoint = new Point(
                                (int)(origin.X + (radius + 20) * Math.Cos(radians)),
                                (int)(origin.Y + (radius + 20) * Math.Sin(radians))
                            );
                            g.DrawString(angle.ToString() + "°", font, brush, textPoint);
                        }
                    }
                }
            }
        }

        private void DrawScale(Graphics g)
        {
            // 绘制坐标轴
            using (Pen axisPen = new Pen(Color.Black, 2))
            {
                int radius = (int)(Math.Min(Width, Height) / 2 * scale);
                // X轴
                g.DrawLine(axisPen, origin.X - radius, origin.Y, origin.X + radius, origin.Y);
                // Y轴
                g.DrawLine(axisPen, origin.X, origin.Y - radius, origin.X, origin.Y + radius);
            }
        }

        // 坐标转换：极坐标到笛卡尔坐标
        public PointF PolarToCartesian(float r, float theta)
        {
            float x = r * (float)Math.Cos(theta);
            float y = r * (float)Math.Sin(theta);
            return new PointF(x, y);
        }

        // 坐标转换：笛卡尔坐标到极坐标
        public (float r, float theta) CartesianToPolar(float x, float y)
        {
            float r = (float)Math.Sqrt(x * x + y * y);
            float theta = (float)Math.Atan2(y, x);
            return (r, theta);
        }

        // 屏幕坐标到极坐标
        public (float r, float theta) ScreenToPolar(Point screenPoint)
        {
            float x = (screenPoint.X - origin.X) / scale;
            float y = (screenPoint.Y - origin.Y) / scale;
            return CartesianToPolar(x, y);
        }

        // 极坐标到屏幕坐标
        public Point PolarToScreen(float r, float theta)
        {
            PointF cartesian = PolarToCartesian(r, theta);
            return new Point(
                (int)(origin.X + cartesian.X * scale),
                (int)(origin.Y + cartesian.Y * scale)
            );
        }

        protected override void Dispose(bool disposing)
        {
            if (disposing)
            {
                _scanTimer.Stop();
                _scanTimer.Dispose();
            }
            base.Dispose(disposing);
        }
    }
}

总结

本文详细介绍了在C# WinForm环境下实现极坐标系的完整方案。该实现适用于各种需要极坐标显示的场景，特别是在工业自动化、测量系统等领域。代码结构清晰，易于扩展，可以根据具体需求进行定制化开发。通过提供的功能和示例，开发者可以快速构建基于极坐标系的应用程序。

目录

应用场景

完整代码实现

极坐标系控件类

实际应用示例

雷达扫描效果

总结