如何求空间两条直线的夹角啊！！！

qjchen

如gu_xl版主所说，两根不相交的空间直线要投影到某个平面上才可以求夹角，立体几何中是这么定义的
下面的代码利用矢量点乘的方法，计算空间（也可以是平面上的）两直线间的交角，没有太多的容错
较短的写法如下

2. 
   
3. ;;;Two line angle
   
4. (defun q:geo:2line:ang2(p1 p2 p3 p4)
   
5.   ((lambda(x) (atan (sqrt (- 1.0 (* x x))) x))
   
6.      (/ (apply '+ (mapcar '* (mapcar '- p2 p1) (mapcar '- p4 p3))) (distance p1 p2) (distance p3 p4))
   
7.   )
   
8. )
   
9. ;;;test
   
10. (q:geo:2line:ang2 (setq p1 (list 0 0 0)) (setq p2 (list 1 1 1))(setq p3 (list 0 1 0))(setq p4 (list 1 0 0)))
    

<br /> ;;;Two line angle<br /> (defun q:geo:2line:ang2(p1 p2 p3 p4)<br />   ((lambda(x) (atan (sqrt (- 1.0 (* x x))) x))<br />      (/ (apply '+ (mapcar '* (mapcar '- p2 p1) (mapcar '- p4 p3))) (distance p1 p2) (distance p3 p4))<br />   )<br /> )<br /> ;;;test<br /> (q:geo:2line:ang2 (setq p1 (list 0 0 0)) (setq p2 (list 1 1 1))(setq p3 (list 0 1 0))(setq p4 (list 1 0 0)))<br />

比较清晰的写法如下(都一样的)

2. 
   
3. ;;;Arccos
   
4. (defun acos(z)
   
5. (atan (sqrt (- 1.0 (* z z))) z)
   
6. )
   
7. ;;;;vec dot product
   
8. (defun q:vec:dot*(v1 v2)
   
9.   (apply '+ (mapcar '* v1 v2))
   
10. )
    
11. ;;; Two line angle
    
12. (defun q:geo:2line:ang(p1 p2 p3 p4)
    
13.   (acos (/ (q:vec:dot* (mapcar '- p2 p1) (mapcar '- p4 p3)) (distance p1 p2) (distance p3 p4)) )
    
14. )
    
15. ;;;test
    
16. (q:geo:2line:ang (setq p1 (list 0 0 0)) (setq p2 (list 1 1 1))(setq p3 (list 0 1 0))(setq p4 (list 1 0 0)))
    

<br /> ;;;Arccos<br /> (defun acos(z)<br /> (atan (sqrt (- 1.0 (* z z))) z)<br /> )<br /> ;;;;vec dot product<br /> (defun q:vec:dot*(v1 v2)<br />   (apply '+ (mapcar '* v1 v2))<br /> )<br /> ;;; Two line angle<br /> (defun q:geo:2line:ang(p1 p2 p3 p4)<br />   (acos (/ (q:vec:dot* (mapcar '- p2 p1) (mapcar '- p4 p3)) (distance p1 p2) (distance p3 p4)) )<br /> )<br /> ;;;test<br /> (q:geo:2line:ang (setq p1 (list 0 0 0)) (setq p2 (list 1 1 1))(setq p3 (list 0 1 0))(setq p4 (list 1 0 0)))<br />