Re: ...

From

Alexei Ivanov ()

To

All ()

Date

2000-02-23T17:06:53Z

Area

RU.ALGORITHMS

From: Alexei Ivanov <A.Ivanov@tu-bs.de>

Hi,

Victor Anikeev wrote:
>  AI> A(x1,y1), B(x2,y2), C(x3,y3) P(x,y)
>  AI> xx1 = x1+x2-x-x;
>  AI> yy1 = y1+y2-y-y;
>  AI> xx2 = x3-x;
>  AI> yy2 = y3-y;
>  AI> if((abs(xx1+xx2) <= (abs(xx1) + abs(xx2))) && (abs(yy1+yy2) <=
>  AI> (abs(yy1) + abs(yy2)))) { puts("There is a inner point of the
>  AI> triangle."); // the bounds include (=) } else { puts("There is not
>  AI> inner point of the triangle."); }
> 
>  Можно переделать для трехмерного случая?
Yes.

I make some mistakes. Right version will be not so easy. :-)

2 dimensional version.

1. A(x1',y1'), B(x2',y2'), C(x3',y3') P(x,y)

2. A(x1 = x1' - x, y1 = y1' - y),
   B(x2 = x2' - x, y2 = y2' - y),
   C(x3 = x3' - x, y3 = y3' - y)
   P(0,0)

3. c1 = (x1*x2 + y1*y2)/sqrt((x1*x1 + y1*y1)*(x2*x2 + y2*y2));
   c2 = (x2*x3 + y2*y3)/sqrt((x2*x2 + y2*y2)*(x3*x3 + y3*y3));
   c3 = (x3*x1 + y3*y1)/sqrt((x3*x3 + y3*y3)*(x1*x1 + y1*y1));

4. if(c1 > c2)  { cc1 = c1; cc2 = c2;}
   else         { cc1 = c2; cc2 = c1;}
   if(c3 > cc2) cc2 = c3;

5. if((cc1 + cc2) <= 0) puts("There is a inner point of the triangle.");
   else                 puts("There is not inner point of the triangle."); 


3 dimensional version.

1. A(x1',y1',z1'), B(x2',y2',z2'), C(x3',y3',z3') P(x,y,z)

2. A(x1 = x1' - x, y1 = y1' - y, z1 = z1' - z),
   B(x2 = x2' - x, y2 = y2' - y, z2 = z2' - z),
   C(x3 = x3' - x, y3 = y3' - y, z3 = z3' - z),
   P(0,0,0)

3. determinant || x1 y1 z1 ||
               || x2 y2 z2 ||
               || x3 y3 z3 || 
   if(determinant != 0) puts("There is not inner point of the triangle."); 

4. c1 = (x1*x2 + y1*y2 + z1*z2)/sqrt((x1*x1 + y1*y1 + z1*z1)*(x2*x2 + y2*y2 + z2*z2));
   c2 = (x2*x3 + y2*y3 + z2*z3)/sqrt((x2*x2 + y2*y2 + z2*z2)*(x3*x3 + y3*y3 + z3*z3));
   c3 = (x3*x1 + y3*y1 + z3*z1)/sqrt((x3*x3 + y3*y3 + z3*z3)*(x1*x1 + y1*y1 + z1*z1));

4. if(c1 > c2)  { cc1 = c1; cc2 = c2;}
   else         { cc1 = c2; cc2 = c1;}
   if(c3 > cc2) cc2 = c3;

5. if((cc1 + cc2) <= 0) puts("There is a inner point of the triangle.");
   else                 puts("There is not inner point of the triangle."); 

-- 
Alexey Ivanov, Braunschweig-Germany
--- ifmail v.2.15dev4
 * Origin: Institut fuer Halbleitertechnik (2:5020/400)