求助数学问题，如何判断三维点在另外三个三维点构成的平面上的投影点，是否在三角形内

lijiao

2. (setq A '(0 0 0)
   
3.       B '(10 0 -7)
   
4.       C '(5 10 15)
   
5.       P '(5 5 3)
   
6.       )
   
7. 
   
8. (command "ucs" "")
   
9. (command "ucs" a b c)
   
10. (setq a1 (trans a 0 1))
    
11. (setq b1 (trans b 0 1))
    
12. (setq c1 (trans c 0 1))
    
13. (setq p1 (trans p 0 1))
    
14. (setq a1 (list (car a1) (cadr a1))
    
15.       b1 (list (car b1) (cadr b1))
    
16.       c1 (list (car c1) (cadr c1))
    
17.       p1 (list (car p1) (cadr p1))
    
18.       )
    
19. (command "ucs" "")
    
20. (command "pline" a1 b1 c1 "c")
    
21. (setq plent (vlax-ename->vla-object (entlast)))
    
22. (setq e0 (vla-get-Area plent))
    
23. (vlax-put plent 'Coordinates (append a1 b1 p1))
    
24. (setq e1 (vla-get-Area plent))
    
25. (vlax-put plent 'Coordinates (append c1 b1 p1))
    
26. (setq e2 (vla-get-Area plent))
    
27. (vlax-put plent 'Coordinates (append a1 c1 p1))
    
28. (setq e3 (vla-get-Area plent))
    
29. (vla-delete plent)
    
30. (command "ucs" "p")
    
31. (command "ucs" "p")
    
32. (command "ucs" "p")
    
33. (>= e0 (+ e1 e2 e3))

(setq A '(0 0 0)<br />       B '(10 0 -7)<br />       C '(5 10 15)<br />       P '(5 5 3)<br />       )<br /> <br /> (command "ucs" "")<br /> (command "ucs" a b c)<br /> (setq a1 (trans a 0 1))<br /> (setq b1 (trans b 0 1))<br /> (setq c1 (trans c 0 1))<br /> (setq p1 (trans p 0 1))<br /> (setq a1 (list (car a1) (cadr a1))<br />       b1 (list (car b1) (cadr b1))<br />       c1 (list (car c1) (cadr c1))<br />       p1 (list (car p1) (cadr p1))<br />       )<br /> (command "ucs" "")<br /> (command "pline" a1 b1 c1 "c")<br /> (setq plent (vlax-ename->vla-object (entlast)))<br /> (setq e0 (vla-get-Area plent))<br /> (vlax-put plent 'Coordinates (append a1 b1 p1))<br /> (setq e1 (vla-get-Area plent))<br /> (vlax-put plent 'Coordinates (append c1 b1 p1))<br /> (setq e2 (vla-get-Area plent))<br /> (vlax-put plent 'Coordinates (append a1 c1 p1))<br /> (setq e3 (vla-get-Area plent))<br /> (vla-delete plent)<br /> (command "ucs" "p")<br /> (command "ucs" "p")<br /> (command "ucs" "p")<br /> (>= e0 (+ e1 e2 e3))

jj2098

假设AC是三角形ABC的最长边，求P点在直线AC上的垂足P’，如果P'在直线AC外面则P点投影在三角形外；
否则再计算角PP'B，若角PP'B大于90度，则P点投影在三角形ABC外。

革天明

先求出点在面上的投影点，剩下的就是判断是否在三角形内了

mahuan1279

距离关系应该能判断吧？

纵横八方

直接用向量法，求总面积= 3个三角形面积和，如果一个面积为0就是点落在某边上