等加速运动原理

等加速运动是最基础的加速模式，其特点是加速度恒定，速度随时间线性变化。。在工业自动化、游戏开发、动画制作等领域都有广泛应用。本文将详细介绍如何使用C#的GDI+来实现和可视化等加速运动。

基本公式

Markdown
- v = v0 + at       (速度方程)
- s = v0t + (1/2)at² (位移方程)
- v² = v0² + 2as    (速度-位移方程)

其中：
v0: 初始速度
v: 当前速度
a: 加速度
t: 时间
s: 位移

实现代码

运动参数类

C#
public class MotionParameters
{
    public double InitialVelocity { get; set; } // 初始速度
    public double Acceleration { get; set; }     // 加速度
    public double MaxVelocity { get; set; }      // 最大速度
    public double Distance { get; set; }         // 总距离
    public Point StartPoint { get; set; }        // 起点
    public Point EndPoint { get; set; }          // 终点

    public MotionParameters()
    {
        InitialVelocity = 0;
        Acceleration = 100;     // 像素/秒²
        MaxVelocity = 300;     // 像素/秒
        StartPoint = new Point(0, 0);
        EndPoint = new Point(0, 0);
    }
}

运动控制类

C#
public class MotionControl
{
    // 私有成员变量  
    private readonly MotionParameters _parameters;        // 运动参数  
    private double _currentTime;                         // 当前运动时间  
    private double _currentVelocity;                     // 当前速度  
    private Point _currentPosition;                      // 当前位置  
    private bool _isAccelerating;                       // 是否处于加速阶段  
    private double _totalDistance;                      // 总运动距离  
    private double _currentDistance;                    // 当前已运动距离  

    // 添加公共属性访问  
    public double CurrentVelocity => _currentVelocity;
    public bool IsCompleted => _currentDistance >= _totalDistance;
    public Point StartPoint => _parameters.StartPoint;
    public Point EndPoint => _parameters.EndPoint;

    public MotionControl(MotionParameters parameters)
    {
        _parameters = parameters;
        Initialize();
    }

    private void Initialize()
    {
        _currentTime = 0;
        _currentVelocity = _parameters.InitialVelocity;
        _currentPosition = _parameters.StartPoint;
        _isAccelerating = true;
        _currentDistance = 0;

        // 计算总距离  
        _totalDistance = Math.Sqrt(
            Math.Pow(_parameters.EndPoint.X - _parameters.StartPoint.X, 2) +
            Math.Pow(_parameters.EndPoint.Y - _parameters.StartPoint.Y, 2));
    }

    public Point CalculatePosition(double deltaTime)
    {
        if (IsCompleted) return _currentPosition;

        _currentTime += deltaTime;

        // 更新速度  
        if (_isAccelerating)
        {
            _currentVelocity += _parameters.Acceleration * deltaTime;
            if (_currentVelocity >= _parameters.MaxVelocity)
            {
                _currentVelocity = _parameters.MaxVelocity;
                _isAccelerating = false;
            }
        }

        // 计算这一帧移动的距离  
        double frameDistance = _currentVelocity * deltaTime;
        _currentDistance += frameDistance;

        // 确保不超过总距离  
        if (_currentDistance >= _totalDistance)
        {
            _currentDistance = _totalDistance;
            _currentPosition = _parameters.EndPoint;
            return _currentPosition;
        }

        // 计算当前位置  
        double ratio = _currentDistance / _totalDistance;
        _currentPosition.X = (int)(_parameters.StartPoint.X +
            (_parameters.EndPoint.X - _parameters.StartPoint.X) * ratio);
        _currentPosition.Y = (int)(_parameters.StartPoint.Y +
            (_parameters.EndPoint.Y - _parameters.StartPoint.Y) * ratio);

        return _currentPosition;
    }

    public void Reset()
    {
        Initialize();
    }
}

GDI+实现示例

主窗体类

C#
public partial class Form1 : Form
{
    private MotionControl _motionControl;
    private Timer _animationTimer;
    private Point _objectPosition;
    private bool _isMoving;
    private List<Point> _trajectoryPoints;
    public Form1()
    {
        InitializeComponent();
        this.DoubleBuffered = true;
        _trajectoryPoints = new List<Point>();
        InitializeComponents();
        SetupMotionControl();

    }
    private void InitializeComponents()
    {
        _animationTimer = new Timer();
        _animationTimer.Interval = 16; // ~60fps  
        _animationTimer.Tick += AnimationTimer_Tick;

        this.Paint += MotionSimulationForm_Paint;
        this.MouseClick += MotionSimulationForm_MouseClick;
    }

    private void SetupMotionControl()
    {
        var parameters = new MotionParameters
        {
            InitialVelocity = 0,
            Acceleration = 200,
            MaxVelocity = 400,
            StartPoint = new Point(100, 300),
        };

        _motionControl = new MotionControl(parameters);
        _objectPosition = parameters.StartPoint;
    }

    private void MotionSimulationForm_Paint(object sender, PaintEventArgs e)
    {
        Graphics g = e.Graphics;
        g.SmoothingMode = SmoothingMode.AntiAlias;

        // 绘制轨迹  
        if (_trajectoryPoints.Count > 1)
        {
            using (Pen pen = new Pen(Color.LightBlue, 2))
            {
                for (int i = 1; i < _trajectoryPoints.Count; i++)
                {
                    g.DrawLine(pen, _trajectoryPoints[i - 1], _trajectoryPoints[i]);
                }
            }
        }

        // 绘制起点和终点  
        if (_isMoving)
        {
            using (Pen pen = new Pen(Color.Gray, 1))
            {
                g.DrawLine(pen, _motionControl.StartPoint, _motionControl.EndPoint);
            }
        }

        // 绘制运动物体  
        using (SolidBrush brush = new SolidBrush(Color.Blue))
        {
            g.FillEllipse(brush,
                _objectPosition.X - 15,
                _objectPosition.Y - 15,
                30, 30);
        }

        // 绘制信息  
        using (Font font = new Font("Arial", 10))
        using (SolidBrush brush = new SolidBrush(Color.Black))
        {
            string info = $"速度: {_motionControl.CurrentVelocity:F2} 像素/秒";
            g.DrawString(info, font, brush, 10, 10);
        }
    }

    private void AnimationTimer_Tick(object sender, EventArgs e)
    {
        if (_isMoving)
        {
            _objectPosition = _motionControl.CalculatePosition(0.016);
            _trajectoryPoints.Add(_objectPosition);

            if (_motionControl.IsCompleted)
            {
                _isMoving = false;
                _animationTimer.Stop();
            }

            Invalidate();
        }
    }

    private void MotionSimulationForm_MouseClick(object sender, MouseEventArgs e)
    {
        if (!_isMoving)
        {
            var parameters = new MotionParameters
            {
                InitialVelocity = 0,
                Acceleration = 200,
                MaxVelocity = 400,
                StartPoint = _objectPosition,
                EndPoint = e.Location
            };

            _motionControl = new MotionControl(parameters);
            _trajectoryPoints.Clear();
            _trajectoryPoints.Add(_objectPosition);
            _isMoving = true;
            _animationTimer.Start();
        }
    }
}

总结

在本文中，我们展示了如何通过使用GDI+提供的优秀绘图支持、清晰的代码结构，实现了基础的加速运动模式。这个基础实现可以作为更复杂运动控制系统的基础，使得后续的开发更加简单、稳定和流畅。