Assistance fixing my hypotrochoid illustration

[xrd]

I'm trying to get this code to work (basically copied from here: https://en.wikipedia.org/wiki/Hypotrochoid)

(defn hypotrochoid [fn fn2 r big-r t d time]
  ~(+ 
    (* d (,fn ( 
      (* t (/ (- big-r r) r)  
    ))))
    ( * (- big-r r) (,fn2 t)))
)

(toodle {:speed 3 :position [100 50]}
  (set self.position 
    (hypotrochoid cos sin 3 5 2.3 2 self.age))
#  (turn 0.01)
)

(this is modeled off the loop example more or less)

I'm very new to macros and have no idea if this is correct, but hey, it compiles!

But, now I get this in the error console and am not sure how to continue. I assume this means I am not returning the correct thing (and each generator has a chance to do one of four things...)?

doodle error "need numbers or vectors"

Thanks so much for your book, I'm excited to play more with toodle and janet!

[xrd]

I was trying to recall if I was using macros just be fancy, or if there was a reason, and now I remember why. I needed to use a macro, because the formula for X and Y differ by swapping cos/sin functions.

So, I just changed the code to be like this:

(toodle 
  {:speed 3 :position [100 50]}
  (set self.position 
    [ 
      (hypotrochoid cos sin 3 5 2.3 2 self.age)
      (hypotrochoid sin cos 3 5 2.3 2 self.age)
    ]    
  ))

That still results in the same thing, but I thought the shape of the value I am returning looks better (two numbers, rather than one). But, same error.

[xrd]

Except that defn isn't a macro, but a function. I need to do some reading. :)

[xrd]

Well, converting to a defmacro does not look like it works, and I have a lot of unquotes, so I am clearly doing something wrong still.

(defmacro hypotrochoid [fn fn2 r big-r t d time]
  ~(+ 
    (* ,d (,fn ( 
      (* ,t (/ (- ,big-r ,r) ,r)  
    ))))
    ( * (- ,big-r ,r) (,fn2 ,t)))
)

(toodle 
  {:speed 5 :position [50 100]}  
  (set self.position 
    [
      (
      hypotrochoid cos sin 3 5 2.3 2 self.age
    )
    (
      hypotrochoid sin cos 3 5 2.3 2 self.age
    )
  ])
  )

Not I get doodle error "1.53333 called with 0 arguments, possibly expected 1"

[ianthehenry]

Hey! Happy to help.

So there's not actually a reason to make this a macro -- you can pass functions as arguments to other functions and call them just fine. That'll simplify things a bit.

(defn hypotrochoid [f f2 r big-r t d time]
  (+ 
    (* d (f (
      (* t (/ (- big-r r) r)
    ))))
    ( * (- big-r r) (f2 t)))
)

(toodle 
  {:speed 5 :position [50 100]}  
  (set self.position 
    [
      (
      hypotrochoid cos sin 3 5 2.3 2 self.age
    )
    (
      hypotrochoid sin cos 3 5 2.3 2 self.age
    )
  ])
  )

I renamed fn and fn2 to f and f2, because fn is a special-form -- you can create a variable called fn but you won't actually be able to call it -- not sure if that's what led you to a macro in the first place.

That gives the same error as before, but I think it's easier to spot the mistake: you have extra parentheses around the expression (* t (/ (- big-r r) r). That expression returns a number, and the extra parentheses make it try to "invoke" the number.

Taking these off gives you something that runs, but probably doesn't do what you want:

(defn hypotrochoid [f f2 r big-r t d time]
  (+ 
    (* d (f (* t (/ (- big-r r) r))))
    (* (- big-r r) (f2 t))))

(toodle 
  {:speed 5 :position [50 100]}  
  (set self.position 
    [(hypotrochoid cos sin 3 5 2.3 2 self.age)
    (hypotrochoid sin cos 3 5 2.3 2 self.age)
  ]))

It just draws a line. This is because you have two arguments t and time, and your expression uses t but time is the actual age.

(defn hypotrochoid [f f2 r big-r d t]
  (+ 
    (* d (f (* t (/ (- big-r r) r))))
    (* (- big-r r) (f2 t))))

(toodle 
  {:speed 5 :position [50 100]}  
  (set self.position 
    [(hypotrochoid cos sin 3 5 2 self.age)
    (hypotrochoid sin cos 3 5 2 self.age)
  ]))

That actually draws something! But it's very small. Let's multiply everything by 10 so we can see it:

(defn hypotrochoid [f f2 r big-r d t]
  (+ 
    (* d (f (* t (/ (- big-r r) r))))
    (* (- big-r r) (f2 t))))

(toodle 
  {:speed 5 :position [50 100]}  
  (set self.position 
    [(hypotrochoid cos sin 30 50 20 self.age)
    (hypotrochoid sin cos 30 50 20 self.age)
  ]))

Okay, not exactly right yet. The line is because we start at [50 100] but then immediately move far away from that. There's actually a different way to do drawings when you have a closed-form formula for the position like this: use cloodle instead:

(defn hypotrochoid [f f2 r big-r d t]
  (+ 
    (* d (f (* t (/ (- big-r r) r))))
    (* (- big-r r) (f2 t))))

(cloodle 
  [(hypotrochoid cos sin 30 50 20 age)
   (hypotrochoid sin cos 30 50 20 age)])

Instead of setting the position, we just return the new position, and we don't have to specify an initial position -- it will use the first returned value. So that's pretty good.

This draws really fast; let's slow it down a little:

(defn hypotrochoid [f f2 r big-r d t]
  (+ 
    (* d (f (* t (/ (- big-r r) r))))
    (* (- big-r r) (f2 t))))

(cloodle 
  (def t (/ age 100))
  [(hypotrochoid cos sin 30 50 20 t)
   (hypotrochoid sin cos 30 50 20 t)])

And I think that works!

It's not a direct translation of the formula on the wikipedia page, though -- I think a more direct translation is this:

(defn hypotrochoid [f r R t d]
  (+
    (* d (f (* t (/ (- R r) r))))
    (* (- R r) (f t))))

(def d 50)
(cloodle
  (def t (/ age 100))
  [(hypotrochoid cos 30 50 t d)
   (hypotrochoid sin 30 50 t (- d))])

But it seems that swapping the trigonometric function has same effect as negating d -- I can't 100% convince myself why that works but it seems clever!