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(50g) interception of two lines
10-25-2015, 05:10 PM
Post: #1
(50g) interception of two lines
Hello folks,

This program calculates the resultes of interception and give them back with exact values. The program uses the command LINSOLVE that is the fastes way because the numerical MSLV needs a lot of more time even for linear systems. And if there is no solution (parallel or skew lines) it will take a lot of more time to come to an end.

But the LINSOLVE only works correct in exact mode. So if you have an input with real vector componets you have them to convert into exact ones (the program does it automatically).

The program recognizes the 2D or 3D input by itself.

A line (2D or 3D) can be represented in the form:

\[ \vec{x} = \vec{t} + \alpha\cdot\vec{r} \].

ti an ri are 2D or 3D vectors

stack 4: ta
stack 3: ra
stack 2: tb
stack 1: rb

Here we go:

%%HP: T(3)A(R)F(,);
\<< 1, 4,                                                          @@convert the vectors in
      START \->Q\pi 4, ROLL                                        @@vectors with exact components
      NEXT                                                         @@\->Q doesn't work on vectors, so you have to use \->Q\pi
      \-> TA RA TB RB
      \<< TA TB - 'A' RA * 'B' RB * - +                            @@ preparing input for LINSOLVE 
            OBJ\-> OBJ\-> DROP \-> N     
            \<< N
                  IF 2, ==
                  THEN 0 = SWAP 0 = SWAP N \->ARRY              @@input for 2D vector equation
                  ELSE 0 = ROT 0 = ROT 0 = ROT N \->ARRY        @@input for 3D vector equation
                  END [ 'A' 'B' ]                               @@output variables
                  ROT DROP 
                  SWAP DROP 
                  DUP SIZE OBJ\-> DROP \-> LV NL                @@preparing output from LINSOLVE for analysing
                  \<< LV NL GET 
                       EXLR  \-> LEQ REQ                     
                       \<<  IF LEQ 'B' SAME
                              THEN TB RB REQ * + 
                                      REQ LV NL 1, - GET 
                                      EXLR SWAP DROP SWAP 3, \->LIST 1, @@ output for interception point
                                      IF LEQ 'A' SAME
                                      THEN TA 'A' RA * + 2,             @@ output for identical lines
                                      ELSE { } 0,                       @@ output for parallel or skew lines

output has for all three cases the same two stack form:

stack 2: {[x y (z)] A B} (for interception point for 2D or 3D, coordinates of the point and parameter values for the line representations )
stack 1: 1,
stack 2: 'ta + A*ra' (for identical lines)
stack 1: 2,
stack 2: {} (for no interception)
stack 1: 0
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