This program is used to show how to generate an oval.
The moon's orbit around the sun is an oval two.
锘縰sing System;
using System.Windows.Forms;
using System.Drawing;
using System.Collections.Generic;
class Haha : Form
{
Haha()
{
WindowState = FormWindowState.Maximized;
Paint += draw;
Timer t = new Timer();
t.Tick += delegate
{
Invalidate();
};
init();
t.Interval = 200;
t.Start();
Activated += delegate
{
t.Start();
};
SizeChanged += delegate
{
if (WindowState == FormWindowState.Minimized) t.Stop();
};
}
const int period=100;
int now=0;
Bitmap[] bit=new Bitmap[period];
void init()
{
double the=Math.PI*2/period;
LinkedList<Point> mark = new LinkedList<Point>();
var p = new Pen(new SolidBrush(Color.Tomato), 1);
for (int i = 0; i < bit.Length; i++)
{
bit[i] = new Bitmap(200,200);
var g = Graphics.FromImage(bit[i]);
int R = Math.Min(bit[i].Width, bit[i].Height) >> 1;
int x = bit[i].Width >> 1;
int y = bit[i].Height >> 1;
g.DrawEllipse(p, x - R, y - R, R << 1, R << 1);
int RR = R >> 1;
double xx = x + RR * Math.Cos(the * i);
double yy = y + RR * Math.Sin(the * i);
g.DrawEllipse(p, (float)(xx - RR), (float)(yy - RR), RR << 1, RR << 1);
double r = RR * 0.5;
double xxx = xx + r * Math.Cos(-the * i);
double yyy = yy + r * Math.Sin(-the * i);
mark.AddLast(new Point((int)xxx, (int)yyy));
g.DrawEllipse(p, (float)(xxx - r), (float)(yyy - r), (float)r * 2, (float)r * 2);
foreach (var point in mark)
{
g.FillEllipse(new SolidBrush(Color.Tomato), point.X, point.Y, 2, 2);
}
g.DrawLine(p, (float)xxx, (float)yyy, (float)xx, (float)yy);
g.DrawLine(p, (float)xx, (float)yy, (float)x, (float)y);
}
}
void draw(object o,PaintEventArgs e)
{
now = (now + 1) % period;
int w = Math.Min(ClientSize.Width, ClientSize.Height);
e.Graphics.DrawImage(bit[now],0,0,w,w);
}
static void Main()
{
Application.Run(new Haha());
}
}
The oval rotates around its own corner.
1 using System; 2 using System.Windows.Forms; 3 using System.Drawing; 4 class Haha : Form 5 { 6 Haha() 7 { 8 Text = "椭圆焦点极坐标方程:顺时针旋转减去旋转角,逆时针旋转加上旋转角"; 9 Paint += draw; 10 WindowState = FormWindowState.Maximized; 11 } 12 double a, b, w, h; 13 double c, e, k; 14 double fx(double the, double phi) 15 { 16 return k / (1 + e * Math.Cos(the - phi)) * Math.Cos(the); 17 } 18 double fy(double the, double phi) 19 { 20 return k / (1 + e * Math.Cos(the - phi)) * Math.Sin(the); 21 } 22 Point mix, miy, corner; 23 double minX(double phi) 24 { 25 double l = Math.PI / 2, r = Math.PI / 2 * 3; 26 while (r - l > 1e-8) 27 { 28 double d = (r - l) / 3; 29 double lm = l + d; 30 double rm = r - d; 31 if (fx(lm, phi) > fx(rm, phi)) l = lm; 32 else r = rm; 33 } 34 mix.X = (int)fx(l, phi); 35 miy.Y = (int)fy(l, phi); 36 return fx(l, phi); 37 } 38 double minY(double phi) 39 { 40 double l = -Math.PI, r = 0; 41 while (r - l > 1e-8) 42 { 43 double d = (r - l) / 3; 44 double lm = l + d; 45 double rm = r - d; 46 if (fy(lm, phi) > fy(rm, phi)) l = lm; 47 else r = rm; 48 } 49 miy.X = (int)fx(l, phi); 50 miy.Y = (int)fy(l, phi); 51 return fy(l, phi); 52 } 53 void draw(object o, PaintEventArgs pe) 54 { 55 double phi = Math.PI*44/180; 56 Text = "" + phi / Math.PI * 180; 57 pe.Graphics.Clear(Color.Wheat); 58 var pen = new Pen(new SolidBrush(Color.Aqua), 3); 59 double the = 2 * Math.PI / 5000; 60 a=Math.Min(ClientSize.Width,ClientSize.Height)>>2; 61 b=0.618*a; 62 k=b*b/a; 63 c=Math.Sqrt(a*a-b*b); 64 e=c/a; 65 int centerX = ClientSize.Width >> 1; 66 int centerY = ClientSize.Height >> 1; 67 for (double i = 0; i< 2 * Math.PI; i += the) 68 { 69 double x=k/(1+e*Math.Cos(i-phi))*Math.Cos(i); 70 double y = k / (1 + e * Math.Cos(i-phi)) * Math.Sin(i); 71 pe.Graphics.FillEllipse(new SolidBrush(Color.Tomato),(int)(x+centerX),(int)(y+centerY),2,2); 72 } 73 pe.Graphics.FillEllipse(new SolidBrush(Color.Tomato), centerX, centerY,8,8); 74 minX(phi); 75 minY(phi); 76 corner.X=mix.X; 77 corner.Y=miy.Y; 78 mix.X += centerX; 79 mix.Y += centerY; 80 miy.X += centerX; 81 miy.Y += centerY; 82 corner.X += centerX; 83 corner.Y += centerY; 84 pen.Color = Color.Black; 85 pe.Graphics.DrawLine(pen, mix, corner); 86 pen.Color = Color.Blue; 87 pe.Graphics.DrawLine(pen, miy, corner); 88 pe.Graphics.FillEllipse(new SolidBrush(Color.Blue), miy.X, miy.Y, 8, 8); 89 } 90 static void Main() 91 { 92 Application.Run(new Haha()); 93 } 94 }