> || Produce an animation of the cse logo

>%include "graphics.m"  || Definitions of graphics constructors
>%include "myenv.m"     || Stuff I think should be in the standard ev=nvironment
>%include "vector.m"    || Vector abstract data type.

A point in 3 dimensions is a triple.

> point3d == (num,num,num)

Each cube is represented by its centre

> cube == point3d

The logo is a list of cubes.

> cubelist == [cube]

The radius of each cube

> cr = 0.35

> logooops || Oops! logo except x and z are swapped
>      = [(4,0,0),(4,0,1),(4,0,2),(4,0,3),(4,0,4), ||Bottom of S
>         (4,2,0),(4,2,1),(4,2,2),(4,2,3),(4,2,4), ||Middle of S
>         (4,4,0),(4,4,1),(4,4,2),(4,4,3),(4,4,4), ||Top of S
>         (4,1,4),(4,3,0), || Rest of S
>         (3,0,4),(2,0,4),(1,0,4),(0,0,4), || Bottom of E
>         (3,2,4),(2,2,4),(1,2,4),(0,2,4), || Middle of E
>         (3,4,4),(2,4,4),(1,4,4),(0,4,4), || Top of E
>         (3,4,0),(2,4,0),(1,4,0),(0,4,0), || Top of C
>         (0,4,1),(0,4,3)] || Rest of C

We want the origin (0,0,0) to be right in the middle so rotations look better.

> logo = [(z-2,y-2,x-2) | (x,y,z) <-logooops]

ortho projects 3d points onto plane given unit normal
We project (0,1,0) parallel to y axis.

> projection == point3d -> point
> ortho :: vector -> projection
> ortho n (x,y,z)
>    = (u $dot p, v' $dot p)
>      where v' = normalize(up $subvec (scalevec (n' $dot up) n'))
>            n' = normalize n
>            u = v' $cross n'
>            up = vz, if n = vy
>               = vy, otherwise
>            p = v[x,y,z]

isodraw draws a list of cubes using an isometric projection.

> isodraw :: cubelist -> [sys_message]
> isodraw = draw . logopic (v[1,1,1])

logopic is given a 3d point that represent a normal and draws a list of
cubes with a parallel projection parallel to that normal.
Hidden surface removal courtesy of the painter's algorithm -- we sort
the cubes by distance in viewing direction (csort is the sorted cube list)

> logopic n cs
>    = (concat [[Attrib [col] [f] | (col,f) <-zip2 colours (acube c)] | c<-csort])
>      where
>      csort = map snd (sort [(n $dot v[x,y,z],(x,y,z)) | (x,y,z) <- cs])
>      proj = ortho n
>      acube (cx,cy,cz)
>       = map (Line.map proj.f)
>          [[(cx+cr,cy+cr,cz+cr),(cx-cr,cy+cr,cz+cr),
>            (cx-cr,cy-cr,cz+cr),(cx+cr,cy-cr,cz+cr)],
>           [(cx+cr,cy+cr,cz+cr),(cx+cr,cy-cr,cz+cr),
>            (cx+cr,cy-cr,cz-cr),(cx+cr,cy+cr,cz-cr)],
>           [(cx+cr,cy+cr,cz+cr),(cx+cr,cy+cr,cz-cr),
>            (cx-cr,cy+cr,cz-cr),(cx-cr,cy+cr,cz+cr)]]
>      f xs = xs ++ [hd xs]

> colours = [Colour 1 0 0, Colour 0 0 1, Colour 1 1 0]


logopics is given a number of steps and two view directions and rotates
between them.  We use a light grey background 'cos that's the default
for most www browsers.

> logopics n v1 v2
>    = [background:(logopic (fromspherical (s1 $addvec (i $scalevec sd))) logo) | i<-[0..n]]
>      where
>      s1 = tospherical v1
>      sd = (1/n) $scalevec ((tospherical v2) $subvec s1)
>      background = fill_polygon 0.75 [(-4.1,-4.1),(4.1,-4.1),(4.1,4.1),(-4.1,4.1)]
> logoanimation 
>  = (logopics 7 (v[1,1,1]) vy) ++ tl (logopics 7 vy (v[1,1,1])) ++
>    tl (logopics 7 (v[1,1,1]) vz) ++
>    tl (logopics 12 vz vx) ++ tl (logopics 7 vx (v[1,1,1]))