; xModels Tutorial 6:  Polygons, Lathing and Extrusion

; xModels has a "polygon" for creating polygon objects.
; The polygon command takes a list of (x,y) points and
; connects them with line segments.  An example is given below.
; Modeling real objects (like cars or faces) in 3D requires
; that they be approximated with large numbers of polygons,
; perhaps thousands of polygons per object.  You won't want
; to do anything so complicated with xModels-3D.  But it
; does have two ways of producing fairly complicated, but also
; fairly regular, objects.  The methods are called lathing
; and extrusion.  The idea is to take a figure consisting
; of a connected sequence of line segments in the xy-plane.
; Some specified number of copies of this figure are made and
; then more line segments are added to join the copies.


animate 30


; In lathing, the copies are made by rotating the original
; figure about the y-axis.  The command for doing lathing
; is "lathe":

lathe 8  0,5 1,1 3,0 1,-1 0,-5  ; The first parameter is the number of
                                ; copies; then comes the list of points.
     yrotate 0:45  ; You can apply transformations
                   ; to lathed objects.

; Compare the figure produced by the above to the polygon
; made with the same points:

polygon 0,5 1,1 3,0 1,-1 0,-5
      xtranslate 6  ; Move it over so you can see it.

; The extra vertical line from (0,-5) back to (0,5), which
; is added to close the polygon, is not used in the lathing
; operation.  The remaining sides form the figure that is
; rotated about the y-axis by the lathe command.

; Here are more examples:

red

lathe 12 1,2 2,-2  ; Lathing a single line, to make a "lamp shade".
    xrotate 0:360  ; Tumble it about the x-axis
    xtranslate -7

blue

lathe 4  2 1:-1  3 0  4 0 ; You can use number ranges 
     translate -4 7       ;        in the point list!

; Extrusion is not quite so interesting as lathing.  In
; extrusion, the copies of the original figure are made
; by translating the original in the z-direction, instead
; of by rotating it.  The copies are spaced one unit apart, 
; although you can change that, of course, by scaling
; in the z direction.  The extruded figure extends
; equally far behind the xy-plane as it does in front
; of it.  The command for doing extrusion is "extrude".
; Here, for example, is a 3D "E":

cyan

extrude 2                          ; The number of copies.
        0,0 0,5 3,5 3,4 1,4 1,3    ; The list of points.
        2,3 2,2 1,2 1,1 3,1 3,0 0,0
   translate -7.5,-9.5,0

; And here is an example that rotates so you can see
; it better:

magenta

extrude 5 -2,-2 0,2 2,-2 ; Extrude 5 copies of an inverted "V"
    yrotate -30:30
    translate 3 -6.5