LOGO-L> Notes on MSWLogo 3D

[George Mills <mills@softronix.com>]

to aaa
   ; This example truely covers the surface of a sphere with each
   ; vertex of each polygon exactly on the surface with no overlaping
   ; polygons and letting logo do all the trig involved.
   ;
   ; Place yourself in the center of a sphere and imagine you have
   ; a laser gun that can cut or mark the surface. Now you basically
   ; Shoot a dot on the surface (call that point A), then move your
   ; aim 5 degrees (:step) down, shoot another dot (call that point B).
   ; Now aim 5 degrees to the right, Shoot another dot (call that point
C).
   ; Now aim 5 degrees up, shoot another dot. Now connect the 4 dots
   ; with a string and you have your polygon. Get the idea.
   ; 
   ; This example did not run quite right on the beta (you'll see a few
   ; errors). The reason is the top and bottom of each slices' polygon
   ; is a triangle but we still shot 4 dots to produce it. That means
   ; 2 dots hit the same target (this is when we are shooting at the
poles
   ; of the sphere). I added smarts to the mswlogo to eliminate
sequential
   ; duplicate vertices (with in the first 3 vertices).
   ;
   ; The first 3 vertices are critical to MSWLogo because they are used
   ; to calculate the orientation of the polygon.
   ;
   ; Polygon restrictions:
   ;
   ; 1: A polygons first 3 vertices must form a triangle.
   ; 2: A polygon must be convex.
   ; 3: A polygon must be planar (no up,down,rr,lr between)
   ;    polystart/polyend.
   ;
   ; All these properties occur very naturally in Logo.
   ;
   ; Notes on 1: the triangle can be extremely shallow
   ;
   ; This is legal
   ;
   ; polystart
   ; make "savepos posxyz
   ; fd 100
   ; rt 0.00000001
   ; fd 100
   ; setpos :saveposxyz
   ; polyend
   ; This is legal
   ;
   ; This is NOT legal (even though it produces a convex polygon)
   ;
   ; polystart
   ; make "savepos posxyz
   ; fd 50
   ; fd 50
   ; rt 90
   ; fd 100
   ; setpos :saveposxyz
   ; polyend
   ;
   ; I could make MSWLogo smart enough to hangle that last case
   ; but in general it occurs very infrequently and you'll pay
   ; a performance price for it.
   ;
   ; This is legal
   ;
   ; polystart
   ; make "savepos posxyz
   ; fd 100
   ; rt 90
   ; fd 100
   ; rt 90
   ; fd 50
   ; fd 50
   ; setpos :saveposxyz
   ; polyend
   ;
   ; It's only the first 3 vertices that are critical
   ;
   ; Notes on 2: What does convex mean
   ;
   ; Pick any 2 coordinate within the poly and connect
   ; them with a line. If that line can go outside the
   ; polygon then it's not convex.
   ;
   ; Triangles, Squares, Circles etc. are convex.
   ; The letter "E" as a polygon is not convex.
   ;
   ; This is legal
   ;
   ; repeat 4 [fd 100 rt 90]
   ;
   ; This is NOT legal
   ;
   ; repeat 4 [fd 50 rt 90 repeat 3 [fd 25 lt 90] rt 180 fd 50 rt 90]
   ;
   ; Notes on 3: What does planar mean
   ;
   ; The polygon must be flat
   ;
   ; This is legal
   ;
   ; repeat 4 [fd 100 rt 90]
   ;
   ; This is NOT legal
   ;
   ; repeat 4 [fd 50 rr 90 rt 90 repeat 3 [fd 25 lt 90] rt 180 lr 90 fd
50 rt 90]
   ;
   ; Notes on 2 and 3:
   ;
   ; You can fix all the illegal cases I mentioned by breaking
   ; the object up into simpler polygons that meet the rules.
   ;
   perspective
   cs
   setsc [0 0 0]
   clearpalette
   ask -3 [setxyz 207 243 97]

   ht
   pu

   ; Time drawing
   localmake "start timemilli

   ; This is the color of the OBJECT not the color you'll see

   ; This example had too many colors for gif to give it justice
   ; Remember 1 blue ([0 0 128]) object may generate 100's of shades
   ; of blue. This example looks fine 16bit or 24bit color.
   ; repeat 6 [fd 100 Sphere 50 10 item repcount [[128 0 0] [0 128 0] [0
0 128] [128 128 0] [0 128 128] [128 0 128]] bk 100 rt 360/6]

   ; This example looks fine in 8bit color (which gifs inherintly are)
   ; because they are all blue spheres
   repeat 6 [fd 100 Sphere 50 10 [0 0 128] bk 100 rt 360/6]

   ; Display elapsed drawing
   (print "Define (timemilli - :start) / 1000)

   ; Time shading
   make "start timemilli

   polyview

   ; Display elapsed shading
   (print "Render (timemilli - :start) / 1000)

   stop
   repeat 100 [ask -3 [setxyz random 300 random 300 random 300 show
posxyz]]
   pd
end

to GetPoint :rad
   fd :rad
   localmake "pos posxyz
   bk :rad
   output :pos
end

to Slice :rad :step
   ; Draw an "orange" slice (just the outside surface)
   up 90
   localmake "i 0
   repeat 360/:step ~
     [
     down :i
     localmake "PointA GetPoint :rad
     down :step
     localmake "PointB GetPoint :rad
     up :step
     up :i
     rt :step
     down :i
     localmake "PointD GetPoint :rad
     down :step
     localmake "PointC GetPoint :rad
     up :step
     up :i
     lt :step
     localmake "PointE posxyz
     setposxyz :PointA
     pd
     polystart
     setposxyz :PointB
     setposxyz :PointC
     setposxyz :PointD
     setposxyz :PointA
     polyend
     pu
     setposxyz :PointE
     make "i :i + :step
     ]
   down 90
end

to Sphere :rad :step :color
   setpc :color
   ; Cover the surface of the sphere with polygons
   repeat 180/:step [Slice :rad :step rr :step]
   rr 180
end


-- 
===============================================================
George Mills (mills@softronix.com)
http://www.softronix.com/
The www page contains some very powerful educational software.
Our single most important investment is our kids.