7.66 Bug in geom3d-package in Maple V.5 (15.3.99)

7.66.1 Arnold Zitterbart

Bug in the geom3d-package ! intersection(s,p1,p2) fails, if s is parallet to x1_x2_plane

> restart; 
> with(geom3d): 
> point(A,[4,9,3]):A=coordinates(A); 
 
                            A = [4, 9, 3] 
 
> point(B,[-2,5,3]):B=coordinates(B); 
 
                            B = [-2, 5, 3] 
 
> line(g,[A,B]); 
                                  g
 

g is obviously parallel to the x1_x2_plane

p1:= any plane containing g: 
 
> point(C1,[2,6,7]):plane(p1,[A,B,C1]); 
 
                                  p1 
p2:= any other plane containing g too: 
 
> point(C2,[-3,6,9]):plane(p2,[A,B,C2]); 
 
                                  p2 
 
> intersection(s,p1,p2); 
                                  s
 

but s is not the intersection-line:

> F:=FixedPoint(s):'F'=coordinates(F); 
 
                          F = [0, 19/3, -3] 
 
> IsOnObject(F,g); 
 
                                false 
 
> IsOnObject(F,p1); 
 
                                false 
 
> IsOnObject(F,p2); 
 
                                false
 

The sign of the x3-coord has to be changed:

> point(F_new,[xcoord(F),ycoord(F),-zcoord(F)]); 
 
                                F_new 
 
> IsOnObject(F_new,g); 
 
                                 true 
 
> IsOnObject(F_new,p1); 
 
                                 true 
 
> IsOnObject(F_new,p2); 
 
                                 true
 

therefore: a new intersection-procedure has to be defined:

> intersection_pp:=proc(g::symbol,p1::symbol,p2::symbol) 
>    local P; 
>    intersection(g,p1,p2); 
> 
point(P,[xcoord(FixedPoint(g)),ycoord(FixedPoint(g)),-zcoord(FixedPoint(g))]): 
 
>    line(g,[P,ParallelVector(g)]); 
> end;
 

Are there any other solutions to this problem ?

It is corrected with Maple 6. (U. Klein)