超急!!跪求˙FORTRAN高手大人解題!!小弟我痛哭流涕!

Question

利用這三個點算出圓的公式。

圖片參考：http://2.bp.blogspot.com/_rl4Ib9jDesQ/SRt1YrYS-aI/AAAAAAAAAM0/ZnaoJt4CJdA/s200/threee_pt_circle.png
假設讀取點為 P1、P2、P3，在這裡的算法是求出兩條分別垂直於P1P2連線與P1P3連線的直線方程式，L12與L13，如上圖所示。

求L12時，先求出P1P2連線的中點，再求出L12的斜率。

中點座標分別為 C12x = (P1x+P2x)/2, C12y = (P1y+P2y)/2，

斜率為 m12 = -(P2x-P1x)/(P2y-P1y)。

所以 L12 的直線公式為 y = m12 * (x - C12x) + C12y

L13 的計算方式類似，L13 的直線公式為 y = m13 * (x - C13x) + C13y

這時就可以求L12與L13兩條線的交點，這個交點 C 就是圓心。

求解L12與L13 聯立方程式，得圓心座標(x, y)

x = (C13y-C12y-m13*C13x+m12*C12x) / (m12-m13)
y = m12 * (x-C12x) + C12y

http://using-c.blogspot.com/2008/11/problem-190-circle-through-three-points.html   <----原始題目

搞了很久~打不出來QQ~~拜託大大解惑><(有詳解佳)

Jack · Accepted Answer

程式如下： program main
 implicit none
 character*1 signx, signy
 real*4 x1, y1, x2, y2, x3, y3, m12, m13, temp, c12x, c12y, c13x, c13y, cx, cy, r2
1  write (*, "(/' Enter x1, y1: ', $)")
 read (*, *) x1, y1
 write (*, "(' Enter x2, y2: ', $)")
 read (*, *) x2, y2
 write (*, "(' Enter x3, y3: ', $)")
 read (*, *) x3, y3
 if (y2 == y1) then
 temp = x1
 x1 = x3
 x3 = temp
 temp = y1
 y1 = y3
 y3 = temp
 else if (y3 == y1) then
 temp = x1
 x1 = x2
 x2 = temp
 temp = y1
 y1 = y2
 y2 = temp
 end if
 m12 = -(x2-x1)/(y2-y1)
 m13 = -(x3-x1)/(y3-y1)
 c12x = (x1+x2)/2.
 c12y = (y1+y2)/2.
 c13x = (x1+x3)/2.
 c13y = (y1+y3)/2.
 cx = (c13y-c12y-m13*c13x+m12*c12x)/(m12-m13)
 cy = m12*(cx-c12x)+c12y
 r2 = (cx-x1)**2 + (cy-y1)**2
 if (cx >= 0.) then
 signx = '-'
 else
 signx = '+'
 end if
 if (cy >= 0.) then
 signy = '-'
 else
 signy = '+'
 end if
 write (*, *) '方程式:  ( x ', signx,  abs(cx), ')^2 + ( y ', signy, abs(cy), ')^2 =', r2
 write (*, "(' 驗算:')")
 write (*, *), 'x1, y1:', (x1-cx)**2 + (y1-cy)**2
 write (*, *), 'x2, y2:', (x2-cx)**2 + (y2-cy)**2
 write (*, *), 'x3, y3:', (x3-cx)**2 + (y3-cy)**2
 go to 1
 end執行結果： Enter x1, y1: 1 0
 Enter x2, y2: -1 0
 Enter x3, y3: 0 1
 方程式:  ( x - 0. )^2 + ( y - 0. )^2 = 1.
 驗算:
 x1, y1: 1.
 x2, y2: 1.
 x3, y3: 1. Enter x1, y1: -7 4
 Enter x2, y2: 1 8
 Enter x3, y3: 3 4
 方程式:  ( x + 2. )^2 + ( y - 4. )^2 = 25.
 驗算:
 x1, y1: 25.
 x2, y2: 25.
 x3, y3: 25. Enter x1, y1: 1 2
 Enter x2, y2: -3 4
 Enter x3, y3: 0 8
 方程式:  ( x + 0.045454547 )^2 + ( y - 4.909091 )^2 = 9.555785
 驗算:
 x1, y1: 9.555785
 x2, y2: 9.555785
 x3, y3: 9.555784 Enter x1, y1: 1 2
 Enter x2, y2: 5 2
 Enter x3, y3: 6 0
 方程式:  ( x - 3. )^2 + ( y + 0.25 )^2 = 9.0625
 驗算:
 x1, y1: 9.0625
 x2, y2: 9.0625
 x3, y3: 9.0625 Enter x1, y1: ^C
（打 Ctrl/C 結束程式執行）

超急!!跪求˙FORTRAN高手大人解題!!小弟我痛哭流涕!

1 個解答