## PA2
## Joining Cubic Bezier Curves -- in 3D -- with G1 Continuity
## Sample Tcl Program prepared by Jane Yen (modified by Carlo Sequin)
################################################################################
tclinit {
set winName .slfWINDOW
source SLIDEUI.tcl
source MATH.tcl
###############################################################################
### Create Sliders for composite Bezier curve
###############################################################################
proc CreateBezierUI { 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 +50+150
### These sliders change the geometry of the Bezier curve and thus will call the _update_ function
set dist [CreateScaleCmd $name $root dist "distance" 0.08 -0.4 0.9 0.02 1 horizontal update]
set angl [CreateScaleCmd $name $root angl "direction" 0.5 -1 2 0.02 1 horizontal update]
set p3x [CreateScaleCmd $name $root p3x "point3_X" 0.0 -5 5 0.1 1 horizontal update]
set p3y [CreateScaleCmd $name $root p3y "point3_Y" 0.0 -5 5 0.1 1 horizontal update]
set zscale [CreateScaleCmd $name $root zscale "Z-scale" 0.0 0 1 0.02 1 horizontal update]
set slices [CreateScale $name $root slices "slices" 10 3 30 1 1 horizontal]
set drawSweep [CreateScale $name $root drawSweep "drawSweep" 0 0 1 1 1 horizontal]
set drawCurve [CreateScale $name $root drawCurve "drawCurve" 1 0 1 1 1 horizontal]
set drawControls [CreateScale $name $root drawControls "drawControls" 1 0 1 1 1 horizontal]
set debug [CreateScale $name $root debug "debug" 0 0 1 1 1 horizontal]
pack $dist $angl $p3x $p3y $zscale $slices $drawSweep $drawCurve $drawControls -side top -fill x
}
CreateBezierUI $winName bez
}
tclinit {
###############################################################################
### Initialize Points (do not modify)
###############################################################################
# 15 points to be interpolated
global p1x p1y p2x p2y p3x p3y p4x p4y p5x p5y p6x p6y p7x p7y p8x p8y p9x p9y
global p10x p10y p11x p11y p12x p12y p13x p13y p14x p14y p15x p15y
global p0x p0y p16x p16y p17x p17y
global p0z p1z p2z p3z p4z p5z p6z p7z p8z p9z p10z p11z p12z p13z p14z p15z p16z p17z
set p1x 7.3
set p1y -2.2
set p1z -3.0
set p2x 4.8
set p2y -0.7
set p2z -1.0
set p3x 0.0
set p3y 0.0
set p3z 0.0
set p4x 0.1
set p4y 0.5
set p4z 1.0
set p5x -0.5
set p5y 5.0
set p5z 4.0
set p6x -0.5
set p6y 4.5
set p6z 4.0
set p7x -3.0
set p7y 2.3
set p7z 3.0
set p8x -1.0
set p8y -0.3
set p8z 1.0
set p9x -5.4
set p9y -1.1
set p9z -3.0
set p10x -8.4
set p10y -3.2
set p10z 4.0
set p11x -6.0
set p11y -4.4
set p11z -4.0
set p12x -5.9
set p12y -4.8
set p12z -4.0
set p13x -0.6
set p13y -2.2
set p13z -1.0
set p14x 2.8
set p14y -3.7
set p14z 3.0
set p15x 5.5
set p15y -3.8
set p15z -1.0
# end-around reptetition for closed B-spline
set p0x [expr $p15x]
set p0y [expr $p15y]
set p0z [expr $p15z]
set p16x [expr $p1x]
set p16y [expr $p1y]
set p16z [expr $p1z]
set p17x [expr $p2x]
set p17y [expr $p2y]
set p17z [expr $p2z]
# intermediate bezier control points
set ptlist {b1_2x b1_2y b1_2z \
b2_2x b2_2y b2_2z \
b3_2x b3_2y b3_2z \
b4_2x b4_2y b4_2z \
b5_2x b5_2y b5_2z \
b6_2x b6_2y b6_2z \
b7_2x b7_2y b7_2z \
b8_2x b8_2y b8_2z \
b9_2x b9_2y b9_2z \
b10_2x b10_2y b10_2z \
b11_2x b11_2y b11_2z \
b12_2x b12_2y b12_2z \
b13_2x b13_2y b13_2z \
b14_2x b14_2y b14_2z \
b15_2x b15_2y b15_2z \
b1_3x b1_3y b1_3z \
b2_3x b2_3y b2_3z \
b3_3x b3_3y b3_3z \
b4_3x b4_3y b4_3z \
b5_3x b5_3y b5_3z \
b6_3x b6_3y b6_3z \
b7_3x b7_3y b7_3z \
b8_3x b8_3y b8_3z \
b9_3x b9_3y b9_3z \
b10_3x b10_3y b10_3z \
b11_3x b11_3y b11_3z \
b12_3x b12_3y b12_3z \
b13_3x b13_3y b13_3z \
b14_3x b14_3y b14_3z \
b15_3x b15_3y b15_3z }
foreach pt $ptlist {
global $pt
set $pt 0
}
}
tclinit {
###############################################################################
### Calculate the 2nd intermediate bezier control points
###############################################################################
proc calculate_pt2 { } {
global p0x p0y p1x p1y p2x p2y p3x p3y p4x p4y p5x p5y p6x p6y p7x p7y p8x p8y p9x p9y
global p10x p10y p11x p11y p12x p12y p13x p13y p14x p14y p15x p15y p16x p16y p17x p17y
global p0z p1z p2z p3z p4z p5z p6z p7z p8z p9z p10z p11z p12z p13z p14z p15z p16z p17z
global b1_2x b1_2y b2_2x b2_2y b3_2x b3_2y b4_2x b4_2y b5_2x b5_2y b6_2x b6_2y
global b7_2x b7_2y b8_2x b8_2y b9_2x b9_2y b10_2x b10_2y b11_2x b11_2y b12_2x b12_2y
global b13_2x b13_2y b14_2x b14_2y b15_2x b15_2y
global b1_2z b2_2z b3_2z b4_2z b5_2z b6_2z b7_2z b8_2z b9_2z b10_2z b11_2z b12_2z b13_2z b14_2z b15_2z
global b1_3z b2_3z b3_3z b4_3z b5_3z b6_3z b7_3z b8_3z b9_3z b10_3z b11_3z b12_3z b13_3z b14_3z b15_3z
global bez_dist bez_angl bez_debug bez_p3x bez_p3y bez_zscale
set p3x [expr $bez_p3x]
set p3y [expr $bez_p3y]
# for each bezier curve
for {set i 1} {$i <= 15} {incr i} {
if { $bez_debug } { puts "" }
################################################
# get points i-1, i, i+1
# point i-1
set name p[subst [expr $i - 1]]x
eval "set pt0x $$name"
set name p[subst [expr $i - 1]]y
eval "set pt0y $$name"
set name p[subst [expr $i - 1]]z
eval "set pt0z $$name"
if { $bez_debug } { puts "pt0 = ($pt0x $pt0y)" }
# point i
set name p[subst [expr $i - 0]]x
eval "set pt1x $$name"
set name p[subst [expr $i - 0]]y
eval "set pt1y $$name"
set name p[subst [expr $i - 0]]z
eval "set pt1z $$name"
if { $bez_debug } { puts "pt1 = ($pt1x $pt1y)" }
# point i + 1
set name p[subst [expr $i + 1]]x
eval "set pt2x $$name"
set name p[subst [expr $i + 1]]y
eval "set pt2y $$name"
set name p[subst [expr $i + 1]]z
eval "set pt2z $$name"
if { $bez_debug } { puts "pt2 = ($pt2x $pt2y)" }
################################################
# calculate point pi_2
## THIS IS THE SECTION YOU SHOULD MODIFY !
# Most of the elements that you need are already given
# Combine and use them in a suitable way.
# (The current formulation is just an arbitrary place holder to give you some ideas).
################################################
### midpoint of pt0 and pt2
set pt02x [expr ($pt0x + $pt2x) *0.5]
set pt02y [expr ($pt0y + $pt2y) *0.5]
set pt02z [expr ($pt0z + $pt2z)*$bez_zscale*0.5]
### vector pt1 - pt0 along incoming control segment
set v01x [expr $pt1x - $pt0x]
set v01y [expr $pt1y - $pt0y]
set v01z [expr ($pt1z - $pt0z)*$bez_zscale]
### normalize
set len01 [expr sqrt($v01x*$v01x + $v01y*$v01y + $v01z*$v01z)]
set nv01x [expr $v01x/$len01]
set nv01y [expr $v01y/$len01]
set nv01z [expr $v01z/$len01]
### vector pt2 - pt1 along outgoing control segment
set v12x [expr $pt2x - $pt1x]
set v12y [expr $pt2y - $pt1y]
set v12z [expr ($pt2z - $pt1z)*$bez_zscale]
### normalize
set len12 [expr sqrt($v12x*$v12x + $v12y*$v12y + $v12z*$v12z)]
set nv12x [expr $v12x/$len12]
set nv12y [expr $v12y/$len12]
set nv12z [expr $v12z/$len12]
### an averaged vector between the above two directions
set vavx [expr (1-$bez_angl)*$nv01x + $bez_angl*$nv12x]
set vavy [expr (1-$bez_angl)*$nv01y + $bez_angl*$nv12y]
set vavz [expr (1-$bez_angl)*$nv01z + $bez_angl*$nv12z]
### normalize
set lenav [expr sqrt($vavx*$vavx + $vavy*$vavy + $vavz*$vavz)]
set nvavx [expr $vavx/$lenav]
set nvavy [expr $vavy/$lenav]
set nvavz [expr $vavz/$lenav]
### vector pt2 - pt0 ## inspired by Catmull-Rom-splines
set v02x [expr $pt2x - $pt0x]
set v02y [expr $pt2y - $pt0y]
set v02z [expr ($pt2z - $pt0z)*$bez_zscale]
### normalize
set len02 [expr sqrt($v02x*$v02x + $v02y*$v02y + $v02z*$v02z)]
set nv02x [expr $v02x/$len02]
set nv02y [expr $v02y/$len02]
set nv02z [expr $v02z/$len02]
## Now put it all together -- somehow: ## find your own appropriate way!
### calculate pt2 of the Bezier Curve (pt1 pt2 pt3 pt4)
set x [expr $pt1x + $bez_dist*$nvavx*$len02]
set y [expr $pt1y + $bez_dist*$nvavy*$len02]
# set z [expr $pt1z + $bez_dist*$nvavz*$len02]
## perhaps?
set b[subst $i]_2x [expr $x]
set b[subst $i]_2y [expr $y]
set b[subst $i]_2z [expr 0.0]
## NEED TO FIX THIS BOGUS EXPRESSION FOR THE Z-COMPONENT
if { $bez_debug } { puts "b[expr $i]_2 ($x $y)" }
}
}
###############################################################################
### Calculate the 3rd intermediate bezier control points
###############################################################################
proc calculate_pt3 { } {
global p0x p0y p1x p1y p2x p2y p3x p3y p4x p4y p5x p5y p6x p6y p7x p7y p8x p8y p9x p9y
global p10x p10y p11x p11y p12x p12y p13x p13y p14x p14y p15x p15y p16x p16y p17x p17y
global p0z p1z p2z p3z p4z p5z p6z p7z p8z p9z p10z p11z p12z p13z p14z p15z p16z p17z
global b1_3x b1_3y b2_3x b2_3y b3_3x b3_3y b4_3x b4_3y b5_3x b5_3y b6_3x b6_3y
global b7_3x b7_3y b8_3x b8_3y b9_3x b9_3y b10_3x b10_3y b11_3x b11_3y b12_3x b12_3y
global b13_3x b13_3y b14_3x b14_3y b15_3x b15_3y
global b1_2z b2_2z b3_2z b4_2z b5_2z b6_2z b7_2z b8_2z b9_2z b10_2z b11_2z b12_2z b13_2z b14_2z b15_2z
global b1_3z b2_3z b3_3z b4_3z b5_3z b6_3z b7_3z b8_3z b9_3z b10_3z b11_3z b12_3z b13_3z b14_3z b15_3z
global bez_dist bez_angl bez_debug bez_zscale
# for each bezier curve
for {set i 1} {$i <= 15} {incr i} {
if { $bez_debug } { puts "" }
################################################
# get points i, i+1, i+2
# point i
set name p[subst [expr $i - 0]]x
eval "set pt0x $$name"
set name p[subst [expr $i - 0]]y
eval "set pt0y $$name"
set name p[subst [expr $i - 0]]z
eval "set pt0z $$name"
if { $bez_debug } { puts "pt0 = ($pt0x $pt0y)" }
# point i + 1
set name p[subst [expr $i + 1]]x
eval "set pt1x $$name"
set name p[subst [expr $i + 1]]y
eval "set pt1y $$name"
set name p[subst [expr $i + 1]]z
eval "set pt1z $$name"
if { $bez_debug } { puts "pt1 = ($pt1x $pt1y)" }
# point i + 2
set name p[subst [expr $i + 2]]x
eval "set pt2x $$name"
set name p[subst [expr $i + 2]]y
eval "set pt2y $$name"
set name p[subst [expr $i + 2]]z
eval "set pt2z $$name"
if { $bez_debug } { puts "pt2 = ($pt2x $pt2y)" }
################################################
# calculate point pi_3
## THIS IS THE SECTION YOU MAY MODIFY !
# The same basic pieces as above are given
# But a different formulation from pi_2 is used, giving not even G1 continuity.
# It is probably a good idea to use the SAME basic formulation for both points.
################################################
### midpoint of pt0 and pt2
set pt02x [expr ($pt0x + $pt2x) *0.5]
set pt02y [expr ($pt0y + $pt2y) *0.5]
set pt02z [expr ($pt0z + $pt2z)*$bez_zscale*0.5]
### vector pt1 - pt0 along incoming control segment
set v01x [expr $pt1x - $pt0x]
set v01y [expr $pt1y - $pt0y]
set v01z [expr ($pt1z - $pt0z)*$bez_zscale]
### normalize
set len01 [expr sqrt($v01x*$v01x + $v01y*$v01y + $v01z*$v01z)]
set nv01x [expr $v01x/$len01]
set nv01y [expr $v01y/$len01]
set nv01z [expr $v01z/$len01]
### vector pt2 - pt1 along outgoing control segment
set v12x [expr $pt2x - $pt1x]
set v12y [expr $pt2y - $pt1y]
set v12z [expr ($pt2z - $pt1z)*$bez_zscale]
### normalize
set len12 [expr sqrt($v12x*$v12x + $v12y*$v12y + $v12z*$v12z)]
set nv12x [expr $v12x/$len12]
set nv12y [expr $v12y/$len12]
set nv12z [expr $v12z/$len12]
### an averaged vector between the above two directions
set vavx [expr (1-$bez_angl)*$nv01x + $bez_angl*$nv12x]
set vavy [expr (1-$bez_angl)*$nv01y + $bez_angl*$nv12y]
set vavz [expr (1-$bez_angl)*$nv01z + $bez_angl*$nv12z]
### normalize
set lenav [expr sqrt($vavx*$vavx + $vavy*$vavy + $vavz*$vavz)]
set nvavx [expr $vavx/$lenav]
set nvavy [expr $vavy/$lenav]
set nvavz [expr $vavz/$lenav]
### vector pt2 - pt0
set v02x [expr $pt2x - $pt0x]
set v02y [expr $pt2y - $pt0y]
set v02z [expr ($pt2z - $pt0z)*$bez_zscale]
### normalize
set len02 [expr sqrt($v02x*$v02x + $v02y*$v02y + $v02z*$v02z)]
set nv02x [expr $v02x/$len02]
set nv02y [expr $v02y/$len02]
set nv02z [expr $v02z/$len02]
## Now put it all together -- somehow: ## find your own appropriate way!
### calculate pt2 of the Bezier Curve (pt1 pt2 pt3 pt4) ## or should you use the normalized values?
set x [expr $pt1x - $bez_dist* ((1-$bez_angl)*$v01x + $bez_angl*$v12x) ]
set y [expr $pt1y - $bez_dist* ((1-$bez_angl)*$v01y + $bez_angl*$v12y) ]
# set z [expr $pt1z - $bez_dist* ((1-$bez_angl)*$v01z + $bez_angl*$v12z) ]
## put in a working expression
## NOTE: Do NOT put any "# COMMENT" on any active Tcl line! The parser will mess it up ... :-( ###
set b[subst $i]_3x [expr $x]
set b[subst $i]_3y [expr $y]
set b[subst $i]_3z [expr 0.0]
## NEED TO FIX THIS BOGUS EXPRESSION FOR THE Z-COMPONENT
if { $bez_debug } { puts "b[expr $i]_3 ($x $y)" }
}
}
###############################################################################
### Update gets called when the "distance" slider variable changes.
### This will recompute the intermediate control points
###############################################################################
proc update { foo } {
global bez_debug
if { $bez_debug } { puts " Changed Parameters" }
if { $bez_debug } { puts "================= Calculate Point 2 =================" }
calculate_pt2
if { $bez_debug } { puts "================= Calculate Point 3 =================" }
calculate_pt3
}
}
########################################################################################
### Sweep controls and basic set-up for the new sweep -- an approximating B-spline.
########################################################################################
tclinit {
proc CreateSweepUI { parent name } {
set subname "slf_[subst $name]"
if { $parent == {} } {
set root .$subname
} elseif { $parent == "." } {
set root .$subname
} else {
set root $parent.$subname
}
toplevel $root
set spokes [CreateScale $name $root spokes "star Spokes" 2 2 7 1 1 horizontal]
set wormrad [CreateScale $name $root wormrad "star Radius" 0.4 0.1 1.0 0.05 1 horizontal]
set drawSweep [CreateScale $name $root drawSweep "drawSweep" 0 0 1 1 1 horizontal]
set drawCurve [CreateScale $name $root drawCurve "drawCurve" 0 0 1 1 1 horizontal]
set drawControls [CreateScale $name $root drawControls "drawControls" 0 0 1 1 1 horizontal]
set ptradi [CreateScale $name $root ptradi "point radius" 0.02 0.01 0.1 0.01 1 horizontal]
set minTorsion [CreateScale $name $root minTorsion "minTorsion" 0 0 1 1 1 horizontal]
set azimuth [CreateScale $name $root azimuth "azimuth" 0 -180 180 1 1 horizontal]
set twist [CreateScale $name $root twist "twist" 0 -360 360 1 1 horizontal]
set closed [CreateScale $name $root closed "closed" 0 0 1 1 1 horizontal]
pack $spokes $wormrad $drawSweep $drawCurve $drawControls $ptradi $minTorsion $azimuth $twist $closed -side top -fill x
}
CreateSweepUI $winName swp
}
(* ### An alternative cross section in the form of a triangle
point r1 ( 0 {expr $swp_wormrad} 0 ) endpoint
point r2 ( 1 {expr -$swp_wormrad} 0 ) endpoint
point r3 ( 1 2 0 ) endpoint
polyline tria
pointlist (r1 r2 r3)
endpolyline
crosssection ribbon
type polyline tria
endcrosssection
*)
crosssection csStar
type star ## a pre-defined SLIDE primitive
outerradius {expr $swp_wormrad}
innerradius 0.05
slices {expr $swp_spokes}
endcrosssection
(* ## Activate this when doing the piece-wise linear, mitered sweep!
polyline backbone
### Just using the original 15 points:
#pointlist ( b1_1 b2_1 b3_1 b4_1 b5_1 b6_1 b7_1 b8_1 b9_1 b10_1 b11_1 b12_1 b13_1 b14_1 b15_1 b1_1 )
### Using all the control and data points:
pointlist (b1_1 b1_2 b1_3 b2_1 b2_2 b2_3 b3_1 b3_2 b3_3 b4_1 b4_2 b4_3 b5_1 b5_2 b5_3
b6_1 b6_2 b6_3 b7_1 b7_2 b7_3 b8_1 b8_2 b8_3 b9_1 b9_2 b9_3 b10_1 b10_2 b10_3
b11_1 b11_2 b11_3 b12_1 b12_2 b12_3 b13_1 b13_2 b13_3 b14_1 b14_2 b14_3 b15_1 b15_2 b15_3 b1_1 )
endpolyline
*)
### ... and disable this B-spline definition when using the poly-line!
bsplinecurve backbone ## A closed cubic B-spline; endpoints have the necessary overlap.
order 4
controlpointlist (b15_1 b1_1 b2_1 b3_1 b4_1 b5_1 b6_1 b7_1 b8_1 b9_1 b10_1 b11_1 b12_1 b13_1 b14_1 b15_1 b1_1 b2_1 )
drawcontrols {expr $swp_drawControls}
slices {expr 15*$bez_slices}
endbsplinecurve
sweep ringworm ## The B-spline sweep.
path backbone
closed {expr $swp_closed}
minimizetorsion {expr $swp_minTorsion}
symmetry 5 #{expr $swp_spokes}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar endcrosssection
drawsweep {expr $swp_drawSweep}
drawpath {expr $swp_drawCurve}
endsweep
##############################
# SURFACE PROPERTY DEFINITIONS
##############################
surface sGrey
color (0.25 0.25 0.25)
endsurface
surface sBlue
color (0.25 0.25 0.9)
endsurface
surface sRed
color (0.9 0.25 0.25)
endsurface
surface sYellow
color (0.8 0.8 0.25)
endsurface
surface sGreen
color (0.25 0.9 0.25)
endsurface
####################################
# SPHERES TO MARK THE CONTROL POINTS
####################################
sphere sph
radius {expr $swp_ptradi}
endsphere
group points_to_interpolate
instance sph
surface sRed
endinstance
instance sph #1
translate ({expr $p1x} {expr $p1y} {expr $p1z*$bez_zscale})
endinstance
instance sph #2
translate ({expr $p2x} {expr $p2y} {expr $p2z*$bez_zscale})
endinstance
instance sph #3
translate ({expr $p3x} {expr $p3y} {expr $p3z*$bez_zscale})
endinstance
instance sph #4
translate ({expr $p4x} {expr $p4y} {expr $p4z*$bez_zscale})
endinstance
instance sph #5
translate ({expr $p5x} {expr $p5y} {expr $p5z*$bez_zscale})
endinstance
instance sph #6
translate ({expr $p6x} {expr $p6y} {expr $p6z*$bez_zscale})
endinstance
instance sph #7
translate ({expr $p7x} {expr $p7y} {expr $p7z*$bez_zscale})
endinstance
instance sph #8
translate ({expr $p8x} {expr $p8y} {expr $p8z*$bez_zscale})
endinstance
instance sph #9
translate ({expr $p9x} {expr $p9y} {expr $p9z*$bez_zscale})
endinstance
instance sph #10
translate ({expr $p10x} {expr $p10y} {expr $p10z*$bez_zscale})
endinstance
instance sph #11
translate ({expr $p11x} {expr $p11y} {expr $p11z*$bez_zscale})
endinstance
instance sph #12
translate ({expr $p12x} {expr $p12y} {expr $p12z*$bez_zscale})
endinstance
instance sph #13
translate ({expr $p13x} {expr $p13y} {expr $p13z*$bez_zscale})
endinstance
instance sph #14
translate ({expr $p14x} {expr $p14y} {expr $p14z*$bez_zscale})
endinstance
instance sph #15
translate ({expr $p15x} {expr $p15y} {expr $p15z*$bez_zscale})
endinstance
endgroup
#############################
# Cubic Bezier Curve Segments
#############################
point b1_1 ( {expr $p1x} {expr $p1y} {expr $p1z*$bez_zscale} ) endpoint
point b1_2 ( {expr $b1_2x} {expr $b1_2y} {expr $b1_2z} ) endpoint
point b1_3 ( {expr $b1_3x} {expr $b1_3y} {expr $b1_3z} ) endpoint
point b1_4 ( {expr $p2x} {expr $p2y} {expr $p2z*$bez_zscale} ) endpoint
beziercurve bz1
controlpointlist (b1_1 b1_2 b1_3 b1_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg1
path bz1
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b2_1 ( {expr $p2x} {expr $p2y} {expr $p2z*$bez_zscale} ) endpoint
point b2_2 ( {expr $b2_2x} {expr $b2_2y} {expr $b2_2z} ) endpoint
point b2_3 ( {expr $b2_3x} {expr $b2_3y} {expr $b2_3z} ) endpoint
point b2_4 ( {expr $p3x} {expr $p3y} {expr $p3z*$bez_zscale} ) endpoint
beziercurve bz2
controlpointlist (b2_1 b2_2 b2_3 b2_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg2
path bz2
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b3_1 ( {expr $p3x} {expr $p3y} {expr $p3z*$bez_zscale} ) endpoint
point b3_2 ( {expr $b3_2x} {expr $b3_2y} {expr $b3_2z} ) endpoint
point b3_3 ( {expr $b3_3x} {expr $b3_3y} {expr $b3_3z} ) endpoint
point b3_4 ( {expr $p4x} {expr $p4y} {expr $p4z*$bez_zscale} ) endpoint
beziercurve bz3
controlpointlist (b3_1 b3_2 b3_3 b3_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg3
path bz3
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b4_1 ( {expr $p4x} {expr $p4y} {expr $p4z*$bez_zscale} ) endpoint
point b4_2 ( {expr $b4_2x} {expr $b4_2y} {expr $b4_2z} ) endpoint
point b4_3 ( {expr $b4_3x} {expr $b4_3y} {expr $b4_3z} ) endpoint
point b4_4 ( {expr $p5x} {expr $p5y} {expr $p5z*$bez_zscale} ) endpoint
beziercurve bz4
controlpointlist (b4_1 b4_2 b4_3 b4_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg4
path bz4
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b5_1 ( {expr $p5x} {expr $p5y} {expr $p5z*$bez_zscale} ) endpoint
point b5_2 ( {expr $b5_2x} {expr $b5_2y} {expr $b5_2z} ) endpoint
point b5_3 ( {expr $b5_3x} {expr $b5_3y} {expr $b5_3z} ) endpoint
point b5_4 ( {expr $p6x} {expr $p6y} {expr $p6z*$bez_zscale} ) endpoint
beziercurve bz5
controlpointlist (b5_1 b5_2 b5_3 b5_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg5
path bz5
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b6_1 ( {expr $p6x} {expr $p6y} {expr $p6z*$bez_zscale} ) endpoint
point b6_2 ( {expr $b6_2x} {expr $b6_2y} {expr $b6_2z} ) endpoint
point b6_3 ( {expr $b6_3x} {expr $b6_3y} {expr $b6_3z} ) endpoint
point b6_4 ( {expr $p7x} {expr $p7y} {expr $p7z*$bez_zscale} ) endpoint
beziercurve bz6
controlpointlist (b6_1 b6_2 b6_3 b6_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg6
path bz6
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b7_1 ( {expr $p7x} {expr $p7y} {expr $p7z*$bez_zscale} ) endpoint
point b7_2 ( {expr $b7_2x} {expr $b7_2y} {expr $b7_2z} ) endpoint
point b7_3 ( {expr $b7_3x} {expr $b7_3y} {expr $b7_3z} ) endpoint
point b7_4 ( {expr $p8x} {expr $p8y} {expr $p8z*$bez_zscale} ) endpoint
beziercurve bz7
controlpointlist (b7_1 b7_2 b7_3 b7_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg7
path bz7
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b8_1 ( {expr $p8x} {expr $p8y} {expr $p8z*$bez_zscale} ) endpoint
point b8_2 ( {expr $b8_2x} {expr $b8_2y} {expr $b8_2z} ) endpoint
point b8_3 ( {expr $b8_3x} {expr $b8_3y} {expr $b8_3z} ) endpoint
point b8_4 ( {expr $p9x} {expr $p9y} {expr $p9z*$bez_zscale} ) endpoint
beziercurve bz8
controlpointlist (b8_1 b8_2 b8_3 b8_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg8
path bz8
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b9_1 ( {expr $p9x} {expr $p9y} {expr $p9z*$bez_zscale} ) endpoint
point b9_2 ( {expr $b9_2x} {expr $b9_2y} {expr $b9_2z} ) endpoint
point b9_3 ( {expr $b9_3x} {expr $b9_3y} {expr $b9_3z} ) endpoint
point b9_4 ( {expr $p10x} {expr $p10y} {expr $p10z*$bez_zscale} ) endpoint
beziercurve bz9
controlpointlist (b9_1 b9_2 b9_3 b9_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg9
path bz9
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b10_1 ( {expr $p10x} {expr $p10y} {expr $p10z*$bez_zscale} ) endpoint
point b10_2 ( {expr $b10_2x} {expr $b10_2y} {expr $b10_2z} ) endpoint
point b10_3 ( {expr $b10_3x} {expr $b10_3y} {expr $b10_3z} ) endpoint
point b10_4 ( {expr $p11x} {expr $p11y} {expr $p11z*$bez_zscale} ) endpoint
beziercurve bz10
controlpointlist (b10_1 b10_2 b10_3 b10_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg10
path bz10
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b11_1 ( {expr $p11x} {expr $p11y} {expr $p11z*$bez_zscale} ) endpoint
point b11_2 ( {expr $b11_2x} {expr $b11_2y} {expr $b11_2z} ) endpoint
point b11_3 ( {expr $b11_3x} {expr $b11_3y} {expr $b11_3z} ) endpoint
point b11_4 ( {expr $p12x} {expr $p12y} {expr $p12z*$bez_zscale} ) endpoint
beziercurve bz11
controlpointlist (b11_1 b11_2 b11_3 b11_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg11
path bz11
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b12_1 ( {expr $p12x} {expr $p12y} {expr $p12z*$bez_zscale} ) endpoint
point b12_2 ( {expr $b12_2x} {expr $b12_2y} {expr $b12_2z} ) endpoint
point b12_3 ( {expr $b12_3x} {expr $b12_3y} {expr $b12_3z} ) endpoint
point b12_4 ( {expr $p13x} {expr $p13y} {expr $p13z*$bez_zscale} ) endpoint
beziercurve bz12
controlpointlist (b12_1 b12_2 b12_3 b12_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg12
path bz12
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b13_1 ( {expr $p13x} {expr $p13y} {expr $p13z*$bez_zscale} ) endpoint
point b13_2 ( {expr $b13_2x} {expr $b13_2y} {expr $b13_2z} ) endpoint
point b13_3 ( {expr $b13_3x} {expr $b13_3y} {expr $b13_3z} ) endpoint
point b13_4 ( {expr $p14x} {expr $p14y} {expr $p14z*$bez_zscale} ) endpoint
beziercurve bz13
controlpointlist (b13_1 b13_2 b13_3 b13_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg13
path bz13
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b14_1 ( {expr $p14x} {expr $p14y} {expr $p14z*$bez_zscale} ) endpoint
point b14_2 ( {expr $b14_2x} {expr $b14_2y} {expr $b14_2z} ) endpoint
point b14_3 ( {expr $b14_3x} {expr $b14_3y} {expr $b14_3z} ) endpoint
point b14_4 ( {expr $p15x} {expr $p15y} {expr $p15z*$bez_zscale} ) endpoint
beziercurve bz14
controlpointlist (b14_1 b14_2 b14_3 b14_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg14
path bz14
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
point b15_1 ( {expr $p15x} {expr $p15y} {expr $p15z*$bez_zscale} ) endpoint
point b15_2 ( {expr $b15_2x} {expr $b15_2y} {expr $b15_2z} ) endpoint
point b15_3 ( {expr $b15_3x} {expr $b15_3y} {expr $b15_3z} ) endpoint
point b15_4 ( {expr $p1x} {expr $p1y} {expr $p1z*$bez_zscale} ) endpoint ## closing back to the first point
beziercurve bz15
controlpointlist (b15_1 b15_2 b15_3 b15_4)
slices {expr $bez_slices}
drawcontrols {expr $bez_drawControls}
endbeziercurve
sweep bezSeg15
path bz15
minimizetorsion {expr $swp_minTorsion}
azimuth {expr $swp_azimuth}
twist {expr $swp_twist}
endpath
crosssection csStar
endcrosssection
drawsweep {expr $bez_drawSweep}
drawpath {expr $bez_drawCurve}
endsweep
####################
# World
####################
group gWorld
instance points_to_interpolate
endinstance
### THIS IS THE APPROXIMATING B-SPLINE ###
instance
ringworm
surface sRed
endinstance
### These are the Bezier segments and sweeps ###
instance bezSeg1
surface sGreen
endinstance
instance bezSeg2
surface sGreen
endinstance
instance bezSeg3
surface sGreen
endinstance
instance bezSeg4
surface sGreen
endinstance
instance bezSeg5
surface sGreen
endinstance
instance bezSeg6
surface sGreen
endinstance
instance bezSeg7
surface sGreen
endinstance
instance bezSeg8
surface sGreen
endinstance
instance bezSeg9
surface sGreen
endinstance
instance bezSeg10
surface sGreen
endinstance
instance bezSeg11
surface sGreen
endinstance
instance bezSeg12
surface sGreen
endinstance
instance bezSeg13
surface sGreen
endinstance
instance bezSeg14
surface sGreen
endinstance
instance bezSeg15
surface sGreen
endinstance
endgroup #gWorld
group gScene
instance gWorld
endinstance
endgroup
####################
# CAMERA
####################
camera cam
projection SLF_PARALLEL
frustum ( -9 -6 -100) (9 6 100)
endcamera
group gCamera
instance cam
id instCam
translate ( 0.0 0.0 1.0 )
(*
lookat
eye ( 0.0 0.0 1.0 )
target ( 0.0 0.0 0.0 )
up ( 0.0 1.0 0.0 )
endlookat
*)
endinstance
endgroup
####################
# LIGHT
####################
light lite
type SLF_DIRECTIONAL
# type SLF_POINT
endlight
group gLight
instance lite
id instLite
# translate ( 0.0 1.0 1.0 )
lookat
eye ( 1.0 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 (0.5 0.5 0.5)
endlight
group gLight2
instance lite2
id instLite2
endinstance
endgroup
####################
# RENDER
####################
window WINDOW
origin (0.15 0.1)
size (0.75 0.5)
endwindow
viewport VIEWPORT WINDOW
origin ( 0.0 0.0 )
size ( 1.0 1.0 )
endviewport
render VIEWPORT gCamera.instCam.cam gScene
light gLight.instLite.lite
light gLight2.instLite2.lite2
endrender
######################