(28S) three points are collinear ?

(28S) three points are collinear ? - Printable Version

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(28S) three points are collinear ? - Damien - 12-14-2013 07:20 PM

FIRST METHOD:

Code:

« C→R 1 

   4 ROLL C→R 1 

   7 ROLL C→R 1 

   {3 3} →ARRY DET 

   ABS 1E-10 <

 »

'ALIG'

A(a,a'), B(b,B'), C(c,c') are lined up if the determinant = 0
|a a' 1|
|b b' 1| = 0
|c c' 1|

SECOND METHOD: (added 26/12/2013)
A(a,a'), B(b,B'), C(c,c') are lined up if the angle (AB,AC) = 0 modulo π (in radians)

Lets find the angle (AB,AC) first

Code:

«  3 PICK - 

   ARG 

   SWAP ROT -

   ARG -

   1 SWAP R→C

   P→R ARG

 »

'ANGL'

then

Code:

«  ANGL 

   2 *

   1 SWAP R→C

   P→R ARG

   ABS 1E-10 <

 »

'ALIG'

Examples:

3: (2,2)
2: (4,1)
1: (5,3)
ALIG
1: 0 (false)

3: (2,-3)
2: (4,1)
1: (5,3)
ALIG
1: 1 (true)