Graham算法

关于凸包的定义和和重要性，已经有很多论文都有所论述，而对于求解平面给定的n个点的凸包，比较有效的算法之一是Graham算法，这个算法简洁优美且高效，具体的算法我就不再赘述了，根据这一算法编写了一个演示程序，自我感觉良好，做了一个GIF的动图，如下图：
C#中的坐标系和常规的坐标系有些不同，因此部分对算法中部分判定做了调整。

代码洋洋洒洒200-300行（自动生成的没有计算）。

而且大部分代码都是用于显示和绘图的，实际实现Graham算法的部分非常少
namespace HullDemo
{
public partial class Form1 : Form
{
const int DotRadius = 4;
bool hasStarted;
Stack<Point>sp;//stack for points
List<Point>lp,clp;//points
List<Point>slp,cslp;//sorted points
Bitmap bmp;
private int GlobalIndex;
public Form1()
{
InitializeComponent();
}
private void Form1_Load(object sender, EventArgs e)
{
hasStarted = false;
timer1.Enabled = false;
tssLabel.Text = "点击窗口，添加点，至少5个";
btn_Next.Enabled = false;
}
private void pictureBox1_MouseClick(object sender, MouseEventArgs e)
{
if (hasStarted)
return;
if(lp==null)
lp = new System.Collections.Generic.List<Point>();
lp.Add(new Point(e.X, e.Y));
Graphics g = pictureBox1.CreateGraphics();
g.FillEllipse(new SolidBrush(Color.Red), new Rectangle(e.X - DotRadius, e.Y - DotRadius, 2 * DotRadius, 2 * DotRadius));
g.Dispose();
tssLabel.Text=string.Format("点({0},{1})添加完成。

", e.X, e.Y); }
private void pictureBox1_MouseMove(object sender, MouseEventArgs e)
{
tsslocal.Text = string.Format("当前位置：({0},{1})", e.X, e.Y); }
private void btn_Start_Click(object sender, EventArgs e)
{
if (lp==null||lp.Count < 5)
return;
clp=new List<Point>(lp.ToArray());
btn_Next.Enabled = true;
btn_Start.Enabled = false;
hasStarted = true;
tssLabel.Text = "开始构造";
SortPoints();
cslp = new List<Point>(slp.ToArray());
Redraw();
timer1.Enabled = true;
}
private void MarkPoints(Bitmap b,List<Point>mps)
{
Graphics g = Graphics.FromImage(b);
int i = 0;
foreach (Point p in mps)
{
g.DrawString("p" + i.ToString(), this.Font, new
SolidBrush(Color.Orange), p);
i++;
}
g.Dispose();
}
/// <summary>
/// Y值最大的点，Y相同情况下，X值最小
/// </summary>
private Point FindBasePoint(List<Point>_lp)
{
Point p = _lp[0];
for (int i = 1; i <_lp.Count; i++)
{
if (p.Y <_lp[i].Y)//Y值应最大
p = _lp[i];
if ((p.Y == _lp[i].Y)&&(p.X >_lp[i].X))//Y值相等的情况下X值最小p = _lp[i];
}
return p;
}
/// <summary>
/// 让指定的点闪动
/// </summary>
/// <param name="p">指定的点</param>
private void FlashPoint(Point p)
{
Graphics g = pictureBox1.CreateGraphics();
for (int i = 0; i < 3; i++)
{
g.FillEllipse(new SolidBrush(Color.Yellow), new Rectangle(p.X - DotRadius, p.Y - DotRadius, 2 * DotRadius, 2 * DotRadius)); System.Threading.Thread.Sleep(80);
g.FillEllipse(new SolidBrush(Color.Red), new Rectangle(p.X - DotRadius, p.Y - DotRadius, 2 * DotRadius, 2 * DotRadius)); System.Threading.Thread.Sleep(80);
}
g.Dispose();
}
private void timer1_Tick(object sender, EventArgs e)
{
if (sp == null)
sp = new Stack<Point>();
if (sp.Count == 0)//将p0,p1,p2放入其中
{
for (int i = 0; i < 3; i++)
{
sp.Push(slp[0]);
slp.Remove(slp[0]);
}
listBox1.Items.Add("初始三点p0,p1,p2入栈");
listBox1.SelectedIndex = listBox1.Items.Count - 1;
GlobalIndex = 3;
Redraw();
timer1.Enabled = false;
return;
}
if(slp.Count != 0)
{
sp.Push(slp[0]);
listBox1.Items.Add("p"+GlobalIndex.ToString()+"入栈"); FlashPoint(sp.Peek());
listBox1.SelectedIndex = listBox1.Items.Count - 1; GlobalIndex++;
slp.Remove(slp[0]);
Point p0, p1, p2;
p2 = sp.Pop();
p1 = sp.Pop();
p0 = sp.Peek();
sp.Push(p1);
sp.Push(p2);
int sb = 1;
while (!IsTurnLeft(p0, p1, p2))
{
p2 = sp.Pop();
FlashPoint(sp.Pop());
listBox1.Items.Add("p" + (GlobalIndex - 1 - sb).ToString() + "出栈");
listBox1.SelectedIndex = listBox1.Items.Count - 1;
sb++;
p1 = sp.Pop();
p0 = sp.Peek();
sp.Push(p1);
sp.Push(p2);
}
Redraw();
timer1.Enabled = false;
}
else
{
timer1.Enabled = false;
btn_Next.Enabled = false;
listBox1.Items.Add("演示完成！");
listBox1.SelectedIndex = listBox1.Items.Count - 1;
Graphics g = pictureBox1.CreateGraphics();
g.DrawLine(new Pen(Color.Green), FindBasePoint(clp), sp.Peek());
g.Dispose();
}
}
private void Redraw()
{
bmp = new Bitmap(pictureBox1.Width, pictureBox1.Height); Graphics g = Graphics.FromImage(bmp);
g.Clear(Color.Black);
MarkPoints(bmp,cslp);
foreach (Point p in clp)
{
g.FillEllipse(new SolidBrush(Color.Red), new Rectangle(p.X - DotRadius, p.Y - DotRadius, 2 * DotRadius, 2 * DotRadius));
}
if(sp!=null)
g.DrawLines(new Pen(Color.Green),sp.ToArray());
g.Dispose();
pictureBox1.Image = bmp;
}
//value Range [0,Pi)
private double GetAngleToXAxis(Point basePoint, Point askPoint)
{
//once base point has been found, b is large than d
int a, b, c, d;
a=basePoint.X ;
b=basePoint.Y;
c= askPoint.X;
d= askPoint.Y;
double dist = Math.Sqrt((c - a) * (c - a) + (d - b) * (d - b)); return Math.Acos((c-a) / dist);
}
private bool IsTurnLeft(Point p0, Point p1, Point p2)
{
int t=(p1.X - p0.X) * (p0.Y - p2.Y) - (p2.X - p0.X) * (p0.Y - p1.Y); return (t >= 0);
}
private void SortPoints()
{
//remove base point
slp = new List<Point>(lp.Count);
Point bp = FindBasePoint(lp);
slp.Add(bp);
lp.Remove(bp);
Point[] pArr = lp.ToArray();
int i,j,n=lp.Count;
for (i = 0; i <n-1; i++)
{
for (j = i + 1; j <n; j++)
{
if (GetAngleToXAxis(bp, pArr[i]) >GetAngleToXAxis(bp, pArr[j])) {
Point tp = pArr[i];
pArr[i] = pArr[j];
pArr[j] = tp;
}
}
}
slp.AddRange(pArr);
}
private void btn_Clear_Click(object sender, EventArgs e) {
Graphics g = pictureBox1.CreateGraphics();
g.Clear(Color.Black);
g.Dispose();
lp = null;
clp = null;
slp = null;
cslp = null;
sp = null;
hasStarted = false;
btn_Start.Enabled = true;
GlobalIndex = 0;
listBox1.Items.Clear();
}
private void btn_Next_Click(object sender, EventArgs e) {
timer1.Enabled = true;
}
}
}。