### escherflower2 -- work in progress ...
### A basic generator of icosidodecahedral symmetry by C.H. Sequin
### Enhanced by Harlan Hile and Balaji Kannan.
### Modified further by CHS -- remove veins, inside, 
### later make curve leaves as self-contained warped tetrahedra.
############################################################################


tclinit{
  set winName .slfWINDOW

  source SLFCONSTS.tcl
  source SLIDEUI.tcl

###### Geometric Parameters #################
  proc CreateZoneUI { parent name } {
    set subname "slf_[subst $name]"

    if { $parent == {} } {
	set root .$subname
    } elseif { $parent == "." } {
	set root .$subname
    } else {
	set root $parent.$subname
    }

    toplevel $root
    wm geometry $root +10+50

    set a5r [CreateScale $name $root a5r  "radius at Axis-5"    1.0 0.0 3.0 0.01   1 horizontal ]
    set a3r [CreateScale $name $root a3r  "radius at Axis-3"    1.49 0.0 3.0 0.01   1 horizontal ]
    set a2r [CreateScale $name $root a2r  "radius at Axis-2"    1.0 0.0 3.0 0.01   1 horizontal ]

    set e35i [CreateScale $name $root e35i  "edge interpolation 3-5"    0.5 -1.0  2.0 0.01   1 horizontal ]
    set e35n [CreateScale $name $root e35n  "edge 3-5 normal offset"    0.0 -1.0  1.0 0.01   1 horizontal ]
    set e35r [CreateScale $name $root e35r  "radius at edge-point 3-5"  1.0  0.0  3.0 0.01   1 horizontal ]
    
    pack $a5r $a3r $a2r $e35i $e35n $e35r -side top -fill x
  }

  proc CreateFlowerUI { parent name } {
    set subname "slf_[subst $name]"

    if { $parent == {} } {
	set root .$subname
    } elseif { $parent == "." } {
	set root .$subname
    } else {
	set root $parent.$subname
    }

    toplevel $root
    wm geometry $root +130+50

    set leafx1 [CreateScale $name $root leafx1  "leafcenter x1 disp"  0.26  -1.0  1.0 0.01   1 horizontal ]
    set leafy1 [CreateScale $name $root leafy1  "leafcenter y1 disp"  0.05  -1.0  1.0 0.01   1 horizontal ]
    set leafz1 [CreateScale $name $root leafz1  "leafcenter z1 disp"  -0.098  -1.0  1.0 0.001   1 horizontal ]
    set flowerz [CreateScale $name $root flowerz  "flower height"  0.98  0.2 1.0 0.01   1 horizontal ]
    set flowerx [CreateScale $name $root flowerx  "flower spread"  0.20  0.1  1.0 0.01   1 horizontal ]
    set a23 [CreateScale $name $root a23  "a2-3 interp"  -0.120  -2.0  3.0 .001    1 horizontal ]
    set a23b [CreateScale $name $root a23b  "a2-3 interp 2"  -0.472  -2.0  3.0 .001   1 horizontal ]
    set a23m [CreateScale $name $root a23m  "a2-3 ra2-3 interp"  0.250  -2.0  3.0 .001   1 horizontal ]
    set leafrot [CreateScale $name $root leafrot  "leaf rot"  93  0.0  360 1   1 horizontal ]
    set veinrot [CreateScale $name $root veinrot  "vein rot"  -55  -120  360 1   1 horizontal ]
    
    pack $leafx1 $leafy1 $leafz1 $flowerz $flowerx $a23 $a23b $a23m $leafrot $veinrot -side top -fill x
  }

###### Root Window with Shading Options #################
  proc CreateShadingUI { parent name } {
    set subname "slf_[subst $name]"

    if { $parent == {} } {
	set root .$subname
    } elseif { $parent == "." } {
	set root .$subname
    } else {
	set root $parent.$subname
    }

    toplevel $root
    wm geometry $root +200+230

    set shadingFrame [CreateShadingFrame $name $root]

    pack $shadingFrame -side left -fill y
  }

  proc interp {x y t} {
    return [expr $x * (1 - $t) + $t * $y];
  }

###### START EXECUTION  ##############

#### Initialize Variables -- all angles in radians, unless otherwise noted

  puts ___________________________________

  set to_deg [expr 180.0/$SLF_PI ]
  set to_rad [expr $SLF_PI/180.0 ]
  set cos_60 [expr 0.5*sqrt(3.0) ]
  set cos_36 0.809016994
  set sin_36 0.587785252
  set sin3_5 0.607061998
  set sin2_5 0.525731112
  set cos3_5 0.794654472
  set cos2_5 0.850650808

  CreateZoneUI $winName zone
  CreateFlowerUI $winName flow
  CreateShadingUI $winName gRoot

} ### end_tclinit


############################################################################
# Surfaces
############################################################################
surface sPetalRing
  color ( 1 0 1 )
endsurface

surface sHilite
  color ( 1 1 1 )
endsurface

surface sFlowerCore
  color ( 0.9 0.8 0.1 )
endsurface

surface sPink
  color ( 1.0 0.4 0.6 )
endsurface

surface sLeafA
  color ( 0.4 1.0 0.3 )
endsurface

surface sLeafB
  color ( 0.2 0.7 0.2 )
endsurface

surface sPetals
  color ( 1 0.5 0.6 )
endsurface

############################################################################
# Geometry
############################################################################

point A5 (  0 0 {expr $zone_a5r} ) endpoint
point A3 (  0 {expr $sin3_5 * $zone_a3r} {expr $cos3_5 * $zone_a3r} ) endpoint
point A2 (  {expr $sin_36 * $sin2_5 * $zone_a2r} {expr $cos_36 * $sin2_5 * $zone_a2r} {expr $cos2_5 * $zone_a2r} ) endpoint
point RA2 (  {expr -$sin_36 * $sin2_5 * $zone_a2r} {expr $cos_36 * $sin2_5 * $zone_a2r} {expr $cos2_5 * $zone_a2r} ) endpoint

### This is a pretty arbitrary way to move this vertex in all 3 dimensions,
### should be more logically tied to neighboring points.
point E35 (  {expr $zone_e35n * $zone_e35r}
             {expr ( $zone_e35i*$cos3_5*$zone_a3r + (1-$zone_e35i)*$cos_36*$sin2_5*$zone_a2r ) * $zone_e35r}
	     {expr  $zone_e35r} ) endpoint

### Introduce additional points on the inside or on the edge of the fundamental zone.
### Make sure that points on the edge are repeated with the proper offset on the other side !


#interpolate A2 and A3
point A23 ( {interp [expr $sin_36 * $sin2_5 * $zone_a2r] 0 $flow_a23}
    {interp [expr $cos_36 * $sin2_5 * $zone_a2r] [expr $sin3_5 * $zone_a3r] $flow_a23}
    {interp [expr $cos2_5 * $zone_a2r] [expr $cos3_5 * $zone_a3r] $flow_a23} )
endpoint
point RA23 ( {interp [expr -$sin_36 * $sin2_5 * $zone_a2r] 0 $flow_a23b}
    {interp [expr $cos_36 * $sin2_5 * $zone_a2r] [expr $sin3_5 * $zone_a3r] $flow_a23b}
    {interp [expr $cos2_5 * $zone_a2r] [expr $cos3_5 * $zone_a3r] $flow_a23b} )
endpoint

point A23N ( {interp [expr $sin_36 * $sin2_5 * $zone_a2r] 0 $flow_a23b}
    {interp [expr $cos_36 * $sin2_5 * $zone_a2r] [expr $sin3_5 * $zone_a3r] $flow_a23b}
    {interp [expr $cos2_5 * $zone_a2r] [expr $cos3_5 * $zone_a3r] $flow_a23b} )
endpoint
point RA23N ( {interp [expr -$sin_36 * $sin2_5 * $zone_a2r] 0 $flow_a23}
    {interp [expr $cos_36 * $sin2_5 * $zone_a2r] [expr $sin3_5 * $zone_a3r] $flow_a23}
    {interp [expr $cos2_5 * $zone_a2r] [expr $cos3_5 * $zone_a3r] $flow_a23} )
endpoint

#a point A5 that's somewhere around A5 rotated about A3
point A5R (  {expr $flow_leafx1} {expr $flow_leafy1} {expr $zone_a5r + $flow_leafz1} ) endpoint

#interpolate A23 and RA23
point AM23 ( {interp [interp [expr $sin_36 * $sin2_5 * $zone_a2r] [expr 0] $flow_a23] [interp [expr -$sin_36 * $sin2_5 * $zone_a2r] [expr 0] $flow_a23b] $flow_a23m}
	     {interp [interp [expr $cos_36 * $sin2_5 * $zone_a2r] [expr $sin3_5 * $zone_a3r] $flow_a23] [interp [expr $cos_36 * $sin2_5 * $zone_a2r] [expr $sin3_5 * $zone_a3r] $flow_a23b] $flow_a23m}
	     {interp [interp [expr $cos2_5 * $zone_a2r] [expr $cos3_5 * $zone_a3r] $flow_a23] [interp [expr $cos2_5 * $zone_a2r] [expr $cos3_5 * $zone_a3r] $flow_a23b]  $flow_a23m}
            )
endpoint

face lF1 (A23 A3 RA23) surface sLeafA endface
face lF2 (A23 A5R A23N) surface sHilite endface
face lF3 (A23 AM23 A5R) surface sLeafB endface
object oLeaf (lF1 lF2 lF3)
endobject

group gLeaf  # Main Leaf
  instance oLeaf
  endinstance
endgroup


sphere petal  
  surface sPetals
  zslices 12
  thetaslices 12
endsphere

group gZone 
  instance gLeaf
    rotate (  0 {expr $sin3_5} {expr $cos3_5} ) ( {expr $flow_leafrot} )
  endinstance
  instance petal
    scale (0.07 0.07 0.15)
    rotate (0 1 0) (15)
    translate ({expr $flow_flowerx} 0 {expr $flow_flowerz})
    rotate ( 0 0 1) (36)
  endinstance
  instance petal
    scale (0.07 0.07 0.15)
    rotate (0 1 0) (15)
    translate ({expr $flow_flowerx} 0 {expr $flow_flowerz})
  endinstance
endgroup

sphere flowercore
  surface sFlowerCore
  zslices 24
  thetaslices 24
endsphere

torus petalring
  surface sPetalRing
  thetaslices 16
  phislices 12
  minorradius 0.4
endtorus

group gPenta # 5 copies of gZone
  instance gZone
  endinstance
  instance gZone
    rotate (0 0 1)(72)
  endinstance
  instance gZone
    rotate (0 0 1)(-72)
  endinstance
  instance gZone
    rotate (0 0 1)(144)
  endinstance
  instance gZone
    rotate (0 0 1)(-144)
  endinstance
  instance flowercore
    scale ( {expr $flow_flowerx * .7} {expr $flow_flowerx * .7} {expr $flow_flowerx * .85})
    translate (0 0 {expr $flow_flowerz + 0.03})
  endinstance
  instance petalring
    scale ( {expr $flow_flowerx * .7} {expr $flow_flowerx * .7} {expr $flow_flowerx * .85})
    translate (0 0 {expr $flow_flowerz -0.01})
  endinstance
endgroup

## Now we have one 5-sided blossom; repeat this 12 times !

group gDodeca # 12 copies of gPenta
  instance gPenta
  endinstance
  instance gPenta
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(36) 
  endinstance
  instance gPenta
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(108) 
  endinstance
  instance gPenta
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(180) 
  endinstance
  instance gPenta
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(-108) 
  endinstance
  instance gPenta
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(-36) 
  endinstance
  instance gPenta
    rotate (1 0 0)(180)
  endinstance
  instance gPenta
    rotate (1 0 0)(180)
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(36) 
  endinstance
  instance gPenta
    rotate (1 0 0)(180)
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(108) 
  endinstance
  instance gPenta
    rotate (1 0 0)(180)
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(180) 
  endinstance
  instance gPenta
    rotate (1 0 0)(180)
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(-108) 
  endinstance
  instance gPenta
    rotate (1 0 0)(180)
    rotate (1 0 0)(-63.43494882) 
    rotate (0 0 1)(-36) 
  endinstance
endgroup


group gAssembly
  shading {expr $gRoot_shading}
  instance gDodeca
  endinstance
endgroup

############## LIGHTS #######################################

light lite
  type SLF_DIRECTIONAL
endlight

group gLight
  instance lite
    id instLite
    lookat
      eye ( 0.5 1.0 1.0 )
      target ( 0.0 0.0 0.0 )
      up ( 0.0 1.0 0.0 )
    endlookat
  endinstance
endgroup

light lite2
  type SLF_AMBIENT
  color (0.4 0.4 0.4)
endlight

group gLight2
  instance lite2
    id instLite2
  endinstance
endgroup


############# RENDERING ####################################

camera cam
  projection SLF_PARALLEL
  frustum ( -2 -2 -10 ) ( 2 2 5 )
endcamera

group gCam
  instance cam
    id iCam
    translate ( 0 0 1 )
  endinstance
endgroup


window WINDOW
  background (0.3 0.6 0.9)
endwindow

viewport vp WINDOW
endviewport

render vp gCam.iCam.cam gAssembly
  light gLight.instLite.lite
  light gLight2.instLite2.lite2
endrender

##############################################################