Re: LOGO-L> Substitute for "setorientation towardsxyz"

[George Mills <mills@softronix.com>]

Nice work again.

I could not think of a good rule to define the roll to.
You may of come with a good rule, let me chew on it a bit.

Regarding the machine that jammed up the output window, which flavor
of MSWLogo was it running and which Windows OS what it running on.

Did you find your orange peel glitch yet?

Tom Lynn wrote:
> 
> Hi.
> 
> After a few hours of pushing vectors around a piece of paper, moving
> protractors around at funny angles in the air and finally actually doing
> some coding, I've come up with this substitute for "setorientation
> towardsxyz".
> 
> The reason I think it's necessary is that after doing "setorientation
> towardsxyz [100 100 100]", the turtle ends up pointing towards [100 100
> 100], but if you follow this with "rt 90", you can't be sure where it's
> pointing.  So we need some rule which will fix the turtle's final position.
> 
> With the new procedure "settowardsxyz" given here, the new orientation of
> the turtle depends on the initial position.  To orientate itself towards a
> point, the turtle turns left or right until it is "above" or "below" the
> point and then pitches its nose up or down accordingly.  I find this rule
> makes visualising the final orientation of the turtle relatively easy.
> 
> The other procedures given here are just to test settowardsxyz to see that
> it works.  Totally off-subject: A strange problem I had was that when I was
> flooding the commander with output (uncomment the "print ..." lines) it
> occasionally clicked and output blank lines on one computer I tried it on.
> 
> George did say he was going to look at this problem too, so he may well
> have come up with another solution.
> 
> Tom
> 
> ---
> Begin "settowardsxyz.lgo"
> I don't trust my email program with attachments any more. :(
> ---
> to _test :p :q
> ; Test that settowardsxyz works between points :p and :q
>   pu setposxyz :p pd settowardsxyz :q fd distancexyz :q
> ; (print "Result: posxyz)
> end
> 
> to aaa
> ; Draws some axes (pretty pointless :) and then plots points at random
> ; directions and checks that the turtle has actually reached the correct
> ; point.
> 
>   cs perspective ht
>   ask -1 [setposxyz [1000 1000 1000]]
>   drawaxes
> 
>   ; Comment out the next line to keep record of maxerror between tests
>   localmake "maxerror 0
> 
>   repeat 1000 [
>     localmake "x 100 * (3 - random 6)
>     localmake "y 100 * (3 - random 6)
>     localmake "z 100 * (3 - random 6)
> 
>     localmake "px 300 - random 600
>     localmake "py 300 - random 600
>     localmake "pz 300 - random 600
> 
>     ; print (combine "From: (list :px :py :pz))
>     ; print (combine "To: (list :x :y :z))
>     _test (list :px :py :pz) (list :x :y :z)
> 
>     if :maxerror < abs ((first posxyz) - :x) [
>       make "maxerror abs ((first posxyz) - :x)
>     ]
> 
>     if :maxerror < abs ((first butfirst posxyz) - :y) [
>       make "maxerror abs ((first butfirst posxyz) - :y)
>     ]
> 
>     if :maxerror < abs ((first butfirst butfirst posxyz) - :z) [
>       make "maxerror abs ((first butfirst butfirst posxyz) - :z)
>     ]
>   ]
>   print (list "Maximum "error: :maxerror)
> end
> 
> to dotprod :a :b
> ; Returns the dot product of vectors :a and :b.
>   output apply "sum (map [?1 * ?2] :a :b)
> end
> 
> to drawaxes
> ; Draws the positive parts of the grid axes
>   pu home pd settowardsxyz [1000 0 0] fd distancexyz [1000 0 0]
>   pu home pd settowardsxyz [0 1000 0] fd distancexyz [0 1000 0]
>   pu home pd settowardsxyz [0 0 1000] fd distancexyz [0 0 1000]
> end
> 
> to settowardsxyz :F
> ; setorientation towardsxyz does not completely define the new orientation
> ; of the turtle. settowardsxyz defines the new orientation of the turtle by
> ; these rules:
> ;
> ; 1. Turns right until the target position is in the same pitch plane (sets
> ; yaw).
> ;
> ; 2. Pitch up or down until headed towards the target (sets pitch).
> ;
> ; I haven't found a situation where this gives an inappropriate
> ; orientation, but there probably is one, seeing as this is a hard problem.
> ; There are another three complementary functions which could be defined,
> ; which set pitch then yaw, roll then pitch and roll then yaw.  It might be
> ; useful to have these as well, but someone else can do them :)
> 
>   localmake "InitialPenState pendownp
>   localmake "T posxyz
>   localmake "fvec vecsub :F :T
>   pu fd 1 localmake "cvec vecsub posxyz :T bk 1
>   rt 90 fd 1 localmake "rvec vecsub posxyz :T bk 1 lt 90
>   down 90 fd 1 localmake "nvec vecsub posxyz :T bk 1 up 90
>   localmake "avec vecscale (dotprod :fvec :cvec) :cvec
>   localmake "bvec vecscale (dotprod :fvec :rvec) :rvec
>   localmake "svec vecadd :avec :bvec
> 
>   ifelse (veclen :svec) = 0 [
>     ifelse (dotprod :fvec :nvec) < 0 [up 90] [down 90]
>   ] [
>     localmake "costheta (dotprod :svec :cvec) / veclen :svec
>     if (abs :costheta) > 1 [  ; May happen due to numerical errors
>       ifelse :costheta < 0 [localmake "costheta -1][localmake "costheta 1]
>     ]
>     localmake "theta arccos :costheta
>     ifelse (dotprod :fvec :rvec) < 0 [lt :theta] [rt :theta]
> 
>     if not ((veclen :fvec) = 0) [
>       localmake "cosalpha ((dotprod :svec :fvec) / ((veclen :svec) * ~
>         (veclen :fvec)))
>       if (abs :cosalpha) > 1 [  ; May happen due to numerical errors
>         ifelse :cosalpha < 0 [localmake "cosalpha -1][ ~
>           localmake "cosalpha 1]
>       ]
> 
>       localmake "alpha arccos :cosalpha
>       ifelse (dotprod :fvec :nvec) < 0 [up :alpha] [down :alpha]
>     ]
>   ]
> 
>   ifelse :InitialPenState [pd][pu]
> end
> 
> to vecadd :a :b
> ; Adds vectors :a and :b
>   output (map [?1 + ?2] :a :b)
> end
> 
> to vecdiv :v :s
> ; Divides vector :v by scalar :s
>   output map (list "? "/ :s) :v
> end
> 
> to veclen :v
> ; Returns the length of vector :v
>   localmake "a first :v
>   localmake "b first butfirst :v
>   localmake "c first butfirst butfirst :v
>   output sqrt(:a*:a + :b*:b + :c*:c)
> end
> 
> to vecscale :s :v
> ; Multiplies vector :v by scalar :s
>   output map (list "? "* :s) :v
> end
> 
> to vecsub :a :b
> ; Subtracts 3d vector :b from 3d vector :a
>   output (map [?1 - ?2] :a :b)
> end
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--
===============================================================
George Mills (mills@softronix.com)
http://www.softronix.com/
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