COS 441 Homework 3

Student Names: 
Student Logins:

This is a literate Haskell file. It must type check and compile when you
submit it.

Note, on windows, ghci -i./SOE/src doesn't work. 
I used ghci -iSOE/src to extend the ghci search path so it includes
the SOE libraries (where SOE is a subdirectory containing the
SOE libraries).

> import Control.Applicative
> import Animation hiding (planets, translate)
> import Picture

Part IV

This part of the homework involves creating a model solar system.

> translate :: (Float, Float) -> Picture -> Picture
> translate v p =
>     case p of
>       Region c r   -> Region c (Translate v r)
>       p1 `Over` p2 -> (translate v p1) `Over` (translate v p2)
>       EmptyPic     -> EmptyPic
>
> -- Translate a picture behavior by a given vector behavior
> translateB :: (Behavior Float, Behavior Float) -> 
>                Behavior Picture -> 
>                Behavior Picture
> translateB (x,y) p = lift2 translate (zipB (x,y)) p
>
> -- Convert a pair of behaviors into a pair behavior
> zipB :: (Behavior a, Behavior b) -> Behavior (a,b)
> zipB (Beh b1, Beh b2) = Beh (\t -> (b1 t, b2 t))
>
> -- Construct a circle behavior
> circ :: Behavior Float -> Behavior Shape
> circ r = ell r r
>
> sun :: Behavior Picture
> sun = reg (lift0 Yellow) (shape (circ 1))

The following define the main action of the solar system simulator. 
You'll want to replace the right-hand side of planets with your solar system.

> planets :: Behavior Picture
> planets = sun
>
> main :: IO()
> main = 
>   do animateB "Solar system" planets
       
It may be useful for you to use your applicative functor for Behaviors.  Feel
free to copy it in here and use it:

> -- applicative functor for Behavior a

Next, use the provided function translateB to write a function
       
> orbit :: Behavior Picture -- the satellite
>       -> Behavior Picture -- the fixed body
>       -> Float            -- the frequency of the orbit
>       -> Float            -- the x-radius of the orbit
>       -> Float            -- the y-radius of the orbit
>       -> Behavior Picture
>
> orbit = error "define me"

that takes two picture behaviors and makes the first orbit around the second at the specified 
distance and with the specified radii. That is, the two pictures will be overlayed (using over) 
and, at each time t, the position of the satellite will be translated by xradius * cos(t * frequency) 
in the x dimension and by yradius * sin(t * frequency) in the y dimension.

Test your function by creating another circle, mercury, colored red and with radius 0.1, and 
making it orbit around the sun with a frequency of 2.0, and with radii of 2.0 and 0.2 in the 
x and y axes, respectively.

> -- running this definition in ghci should create the appropriate animation
> orbitTest = error "define me"

A problem you might have noticed is the overlay behavior of planets. For this part modify 
orbit to put planets over or under each other. 

> -- running this definition in ghci should create the next animation
> orbitTest' = error "define me"

Modify your functions (and write any support functions that you find necessary) to make the orbital 
distances and planet sizes shrink and grow by some factor (you can pass this factor as parameter 
to the orbit function), according to how far the planets are from the observer. For example, the  
mercury should look a little smaller when it is going behind the sun.  If you create a moon 
that orbits mercury, then both mercury and the moon orbits it, and the orbital distance between mercury
and the moon should decrease as they go behind the sun. 

> -- running this definition in ghci should create the next animation
> orbitTest'' = error "define me"

Choose the scaling factor so that the solar system simulation looks good to you.
Optional: Add some other planets, perhaps with their own moons. If you like, feel 
free to adjust the parameters we gave above to suit your own aesthetic or astronomical 
tastes. Make sure, though, that the features requested in previous parts - growing, 
shrinking, occlusion, etc. - remain clearly visible.