SPHΘRIPHΦR - Study 03Omni Symmetrical Spherical SpiralThis study examines a method for dividing the surface of a sphere with spirals. This is one of a series of studies for the creation of a visual metaphor for representing complex data clusters in spherical space.
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Spheripor Spiral
Total Render Time: 4 hours 16 minutes on Pentium 4 M 2.4 GHz, 512 MB of RAM
>Back to topSpheriphor SpiralThe following POV-Ray scene description language source code generates a spherical spiral. The intent is to enable a spiral form as a spherical metaphor or Spheriphor. In this way, the spiral form may be used as a visual metaphor for representing complex data clusters in spherical space. The methodology generates a spiral partition of a spherical volume based on conical surfaces created from a sequence of progressively smaller cones all sharing the same apex situated at the sphere's center. Polyhedral geometry is used to divide the spherical volume omni-symmetrically. In this case, the geometry used is Buckminster Fuller's Vector Equilibrium Matrix or Jitterbug. The geometry is based on the cuboctahedron which is dual of a cube and an octahedron. Buckminster Fuller's Vector Equilibrium Matrix or JitterbugThe are many articles on the web regarding Buckminster Fuller's Vector Equilibrium Matrix or Jitterbug. The reader is encouraged to search the web and discover the amazing properties of this dynamic form. For example, the following is taken from http://members.cruzio.com/~devarco/energy.htm -
POV-Ray Source CodePersistence of Vision Raytracer (POV-Ray) is used to parametrically generate images of a spherical metaphor for multi-dimensional data visualization on a digital dome projection system. This spherical metaphor, or to coin a term “Spheriphor,” takes advantage of the opportunity to visualize high-density, multi-dimensional data using spherical coordinate systems. Virtual Globes may also use the Spheriphor to display non-GIS data. This particular Spheriphor study shows how the sphere may be divided using adjoining, inter-locked spirals. UsageThe POV-Ray Spheriphor generator for this study uses one file, that is the Spheriphor_Study03.pov scene description file.
Spheriphor_Study03.pov |
/*
Copyright (c) 2006 by Thomas J. Greenbaum. Some Rights Reserved.
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
http://creativecommons.org/licenses/by-nc-sa/3.0/
Persistence Of Vision raytracer version 3.6
Spheriphor Spiral Generator, version 05 - January 5, 2007
For creation of a spherical spiral, that is a spiral partition of a spherical volume
based on conical surfaces created from a sequence of progressively smaller cones
all sharing the same apex situated at the sphere's center.
Command line options to redirect file output
Test resolution setting:
+FS24, +Lc:\Spheriphor\, +OSpheriphor001 Width=320, Height=240, +A
High resolution setting:
+FS24, +Lc:\Spheriphor\, +OSpheriphor001 Width=3072, Height=2304, +A
NOTES: +FS24 = System File (Windows BMP) 24bit color depth
*/
#include "stdinc.inc"
#include "math.inc"
// Increase max_trace_level to calculate multiple layers of transparent objects
global_settings { max_trace_level 20 }
/*
// Transparent colors - takes a long time to render with trans_no set close to 1.0
#declare trans_no = 0.7 ;
#declare Color01 = color rgbf <0.196078, 0.600000, 0.800000, trans_no> ;
#declare Color02 = color rgbf <0.950000, 0.950000, 0.050000, trans_no> ;
#declare Color03 = color rgbf <0.000000, 1.000000, 0.498039, trans_no> ;
#declare Color04 = color rgbf <1.000000, 0.000000, 0.000000, trans_no> ;
#declare Color05 = color rgbf <0.137255, 0.137255, 0.556863, trans_no> ;
*/
// Solid color for quick render
#declare Color01 = color rgb <0.196078, 0.600000, 0.800000> ;
#declare Color02 = color rgb <0.950000, 0.950000, 0.050000> ;
#declare Color03 = color rgb <0.000000, 1.000000, 0.498039> ;
#declare Color04 = color rgb <1.000000, 0.000000, 0.000000> ;
#declare Color05 = color rgb <0.137255, 0.137255, 0.556863> ;
#declare Cone_finish =
finish {
ambient 0.500
diffuse 0.400
specular 1.000
roughness 0.001
reflection {.3}
}
// *** Define the Parameters
#declare Cone_AngDe = 5 ; // Delta between consecutive cone angles
#declare Cone_AngTh = 1 ; // Angular thickness between outer and inner cone walls
#declare Cone_Ht01 = 100 ; // Initial height of cone from base to cap
#declare Cone_Ang01 = 45.5 ; // Initial cone angle (at apex)
#declare Pt_Center = <0,0,0> ; // Point - Center of sphere and apex (base point) of cones
#declare Pt_Cap01 = <0,Cone_Ht01,0> ; // Point - Cap point of cone 01
#declare Cap_Rad01 = tand(Cone_Ang01)*Cone_Ht01 ; // Radius of initial cone cap
#declare Sphr_Rado = Cap_Rad01/sind(Cone_Ang01) ; // Radius of outer sphere
#declare Sphr_Radi = Sphr_Rado*.9 ; // Radius of inner sphere (difference object)
// *** Outer cone dimensions
#declare Cone_Ang02 = Cone_Ang01-Cone_AngDe*1 ; // Cone angle 02
#declare Cone_Ang03 = Cone_Ang01-Cone_AngDe*2 ; // Cone angle 03
#declare Cone_Ang04 = Cone_Ang01-Cone_AngDe*3 ; // Cone angle 04
#declare Cone_Ang05 = Cone_Ang01-Cone_AngDe*4 ; // Cone angle 05
#declare Cone_Ang06 = Cone_Ang01-Cone_AngDe*5 ; // Cone angle 06
#declare Cone_Ang07 = Cone_Ang01-Cone_AngDe*6 ; // Cone angle 07
#declare Cone_Ang08 = Cone_Ang01-Cone_AngDe*7 ; // Cone angle 08
#declare Cone_Ang09 = Cone_Ang01-Cone_AngDe*8 ; // Cone angle 09
#declare Cone_Ht02 = cosd(Cone_Ang02)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 02 from base to cap
#declare Cap_Rad02 = tand(Cone_Ang02)*Cone_Ht02 ; // Radius of cone 02 cap
#declare Pt_Cap02 = <0,Cone_Ht02,0> ; // Point - Cap point of cone 02
#declare Cone_Ht03 = cosd(Cone_Ang03)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 03 from base to cap
#declare Cap_Rad03 = tand(Cone_Ang03)*Cone_Ht03 ; // Radius of cone 03 cap
#declare Pt_Cap03 = <0,Cone_Ht03,0> ; // Point - Cap point of cone 03
#declare Cone_Ht04 = cosd(Cone_Ang04)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 04 from base to cap
#declare Cap_Rad04 = tand(Cone_Ang04)*Cone_Ht04 ; // Radius of cone 04 cap
#declare Pt_Cap04 = <0,Cone_Ht04,0> ; // Point - Cap point of cone 04
#declare Cone_Ht05 = cosd(Cone_Ang05)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 05 from base to cap
#declare Cap_Rad05 = tand(Cone_Ang05)*Cone_Ht05 ; // Radius of cone 05 cap
#declare Pt_Cap05 = <0,Cone_Ht05,0> ; // Point - Cap point of cone 05
#declare Cone_Ht06 = cosd(Cone_Ang06)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 06 from base to cap
#declare Cap_Rad06 = tand(Cone_Ang06)*Cone_Ht06 ; // Radius of cone 06 cap
#declare Pt_Cap06 = <0,Cone_Ht06,0> ; // Point - Cap point of cone 06
#declare Cone_Ht07 = cosd(Cone_Ang07)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 07 from base to cap
#declare Cap_Rad07 = tand(Cone_Ang07)*Cone_Ht07 ; // Radius of cone 07 cap
#declare Pt_Cap07 = <0,Cone_Ht07,0> ; // Point - Cap point of cone 07
#declare Cone_Ht08 = cosd(Cone_Ang08)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 08 from base to cap
#declare Cap_Rad08 = tand(Cone_Ang08)*Cone_Ht08 ; // Radius of cone 08 cap
#declare Pt_Cap08 = <0,Cone_Ht08,0> ; // Point - Cap point of cone 08
#declare Cone_Ht09 = cosd(Cone_Ang09)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 09 from base to cap
#declare Cap_Rad09 = tand(Cone_Ang09)*Cone_Ht09 ; // Radius of cone 09 cap
#declare Pt_Cap09 = <0,Cone_Ht09,0> ; // Point - Cap point of cone 09
// *** Inner cones dimensions (difference objects)
#declare Cone_Ang01i = Cone_Ang01-Cone_AngTh ; // Inner Cone angle 01
#declare Cone_Ang02i = Cone_Ang02-Cone_AngTh ; // Inner Cone angle 02
#declare Cone_Ang03i = Cone_Ang03-Cone_AngTh ; // Inner Cone angle 03
#declare Cone_Ang04i = Cone_Ang04-Cone_AngTh ; // Inner Cone angle 04
#declare Cone_Ang05i = Cone_Ang05-Cone_AngTh ; // Inner Cone angle 05
#declare Cone_Ang06i = Cone_Ang06-Cone_AngTh ; // Inner Cone angle 06
#declare Cone_Ang07i = Cone_Ang07-Cone_AngTh ; // Inner Cone angle 07
#declare Cone_Ang08i = Cone_Ang08-Cone_AngTh ; // Inner Cone angle 08
#declare Cone_Ang09i = Cone_Ang09-Cone_AngTh ; // Inner Cone angle 09
#declare Cone_Ht01i = cosd(Cone_Ang01i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 02 from base to cap
#declare Cap_Rad01i = tand(Cone_Ang01i)*Cone_Ht01i ; // Radius of cone 02 cap
#declare Pt_Cap01i = <0,Cone_Ht01i,0> ; // Point - Cap point of cone 02
#declare Cone_Ht02i = cosd(Cone_Ang02i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 02 from base to cap
#declare Cap_Rad02i = tand(Cone_Ang02i)*Cone_Ht02i ; // Radius of cone 02 cap
#declare Pt_Cap02i = <0,Cone_Ht02i,0> ; // Point - Cap point of cone 02
#declare Cone_Ht03i = cosd(Cone_Ang03i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 03 from base to cap
#declare Cap_Rad03i = tand(Cone_Ang03i)*Cone_Ht03i ; // Radius of cone 03 cap
#declare Pt_Cap03i = <0,Cone_Ht03i,0> ; // Point - Cap point of cone 03
#declare Cone_Ht04i = cosd(Cone_Ang04i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 04 from base to cap
#declare Cap_Rad04i = tand(Cone_Ang04i)*Cone_Ht04i ; // Radius of cone 04 cap
#declare Pt_Cap04i = <0,Cone_Ht04i,0> ; // Point - Cap point of cone 04
#declare Cone_Ht05i = cosd(Cone_Ang05i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 05 from base to cap
#declare Cap_Rad05i = tand(Cone_Ang05i)*Cone_Ht05i ; // Radius of cone 05 cap
#declare Pt_Cap05i = <0,Cone_Ht05i,0> ; // Point - Cap point of cone 05
#declare Cone_Ht06i = cosd(Cone_Ang06i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 06 from base to cap
#declare Cap_Rad06i = tand(Cone_Ang06i)*Cone_Ht06i ; // Radius of cone 06 cap
#declare Pt_Cap06i = <0,Cone_Ht06i,0> ; // Point - Cap point of cone 06
#declare Cone_Ht07i = cosd(Cone_Ang07i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 07 from base to cap
#declare Cap_Rad07i = tand(Cone_Ang07i)*Cone_Ht07i ; // Radius of cone 07 cap
#declare Pt_Cap07i = <0,Cone_Ht07i,0> ; // Point - Cap point of cone 07
#declare Cone_Ht08i = cosd(Cone_Ang08i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 08 from base to cap
#declare Cap_Rad08i = tand(Cone_Ang08i)*Cone_Ht08i ; // Radius of cone 08 cap
#declare Pt_Cap08i = <0,Cone_Ht08i,0> ; // Point - Cap point of cone 08
#declare Cone_Ht09i = cosd(Cone_Ang09i)*Cap_Rad01/sind(Cone_Ang01) ; // Height of cone 09 from base to cap
#declare Cap_Rad09i = tand(Cone_Ang09i)*Cone_Ht09i ; // Radius of cone 09 cap
#declare Pt_Cap09i = <0,Cone_Ht09i,0> ; // Point - Cap point of cone 09
// *** Difference objects
#declare Diff_Base =
box {<-200,-200,0>,<200,200,200>
no_shadow
}
#declare Diff_45 =
union {
object { Diff_Base
}
object { Diff_Base
rotate <0,135,0>
}
}
// *** Cone objects // Inner-most spiral with smallest radius
#declare Cone_09 =
difference {
difference {
cone {Pt_Center,0,Pt_Cap09,Cap_Rad09 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap09i,Cap_Rad09i }
}
#declare Cone_08 = // Next larger spiral
union {
difference {
difference {
cone {Pt_Center,0,Pt_Cap08,Cap_Rad08 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap08i,Cap_Rad08i }
}
object { Cone_09 // Includes inner spiral
rotate <0,45,0>
rotate <0,0,Cone_AngDe>
}
}
#declare Cone_07 =
union {
difference {
difference {
cone {Pt_Center,0,Pt_Cap07,Cap_Rad07 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap07i,Cap_Rad07i }
}
object { Cone_08
rotate <0,45,0>
rotate <0,0,Cone_AngDe>
}
}
#declare Cone_06 =
union {
difference {
difference {
cone {Pt_Center,0,Pt_Cap06,Cap_Rad06 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap06i,Cap_Rad06i }
}
object { Cone_07
rotate <0,45,0>
rotate <0,0,Cone_AngDe>
}
}
#declare Cone_05 =
union {
difference {
difference {
cone {Pt_Center,0,Pt_Cap05,Cap_Rad05 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap05i,Cap_Rad05i }
}
object { Cone_06
rotate <0,45,0>
rotate <0,0,Cone_AngDe>
}
}
#declare Cone_04 =
union {
difference {
difference {
cone {Pt_Center,0,Pt_Cap04,Cap_Rad04 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap04i,Cap_Rad04i }
}
object { Cone_05
rotate <0,45,0>
rotate <0,0,Cone_AngDe>
}
}
#declare Cone_03 =
union {
difference {
difference {
cone {Pt_Center,0,Pt_Cap03,Cap_Rad03 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap03i,Cap_Rad03i }
}
object { Cone_04
rotate <0,45,0>
rotate <0,0,Cone_AngDe>
}
}
#declare Cone_02 =
union {
difference {
difference {
cone {Pt_Center,0,Pt_Cap02,Cap_Rad02 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap02i,Cap_Rad02i }
}
object { Cone_03
rotate <0,45,0>
rotate <0,0,Cone_AngDe>
}
}
#declare Spiral =
union {
difference {
difference {
cone {Pt_Center,0,Pt_Cap01,Cap_Rad01 }
object { Diff_45 }
}
cone {Pt_Center,0,Pt_Cap01i,Cap_Rad01i }
}
object { Cone_02
rotate <0,45,0>
rotate <0,0,Cone_AngDe>
}
}
// Two spirals joined at the outer cone edges to create a double ended spiral
#declare Two_Spirals =
union {
object { Spiral
rotate <0,45,0> // Rotate 45 degrees about y-axis to align outer cone edge to x-axis
}
object { Spiral
rotate <0,225,0> // Rotate 225 degrees (45+180) about y-axis
rotate <0,0,90> // Rotate 90 degrees about z-axis to align two spiral edges
}
}
// Give the Two Spirals color and finish
#declare Two_Spirals_Red =
object { Two_Spirals
pigment { Color04 }
finish { Cone_finish }
}
#declare Two_Spirals_Blu =
object { Two_Spirals
pigment { Color01 }
finish { Cone_finish }
}
#declare Two_Spirals_Yel =
object { Two_Spirals
pigment { Color02 }
finish { Cone_finish }
}
#declare Two_Spirals_Gre =
object { Two_Spirals
pigment { Color03 }
finish { Cone_finish }
}
// Three double spirals - Red
#declare Spheri_Spiral_Red =
difference {
union {
object { Two_Spirals_Red
}
object { Two_Spirals_Red
rotate <90,0,0>
rotate <0,180,0>
}
object { Two_Spirals_Red
rotate <0,0,90>
rotate <0,90,0>
}
}
difference {
sphere { Pt_Center,Sphr_Rado
pigment { Color04 } // Outer sphere
finish { Cone_finish }
}
sphere { Pt_Center,Sphr_Radi // Inner sphere (difference object)
pigment { Color04 }
finish { Cone_finish }
}
}
}
// Three double spirals - Blue
#declare Spheri_Spiral_Blu =
difference {
union {
object { Two_Spirals_Blu
rotate <0,90,0>
}
object { Two_Spirals_Blu
rotate <-90,0,0>
}
object { Two_Spirals_Blu
rotate <0,0,180>
}
}
difference {
sphere { Pt_Center,Sphr_Rado
pigment { Color01 } // Outer sphere
finish { Cone_finish }
}
sphere { Pt_Center,Sphr_Radi // Inner sphere (difference object)
pigment { Color01 }
finish { Cone_finish }
}
}
}
// Three double spirals - Yellow
#declare Spheri_Spiral_Yel =
difference {
union {
object { Two_Spirals_Yel
rotate <0,180,0>
}
object { Two_Spirals_Yel
rotate <90,0,0>
}
object { Two_Spirals_Yel
rotate <0,0,90>
rotate <0,270,0>
}
}
difference {
sphere { Pt_Center,Sphr_Rado
pigment { Color02 } // Outer sphere
finish { Cone_finish }
}
sphere { Pt_Center,Sphr_Radi // Inner sphere (difference object)
pigment { Color02 }
finish { Cone_finish }
}
}
}
// Three double spirals - Green
#declare Spheri_Spiral_Gre =
difference {
union {
object { Two_Spirals_Gre
rotate <0,270,0>
}
object { Two_Spirals_Gre
rotate <90,0,0>
rotate <0,90,0>
}
object { Two_Spirals_Gre
rotate <0,0,90>
}
}
difference {
sphere { Pt_Center,Sphr_Rado
pigment { Color03 } // Outer sphere
finish { Cone_finish }
}
sphere { Pt_Center,Sphr_Radi // Inner sphere (difference object)
pigment { Color03 }
finish { Cone_finish }
}
}
}
#declare Spheri_Spiral =
union {
object { Spheri_Spiral_Red }
object { Spheri_Spiral_Blu }
object { Spheri_Spiral_Yel }
object { Spheri_Spiral_Gre }
}
object { Spheri_Spiral
//rotate <0,45,0>
//rotate <45,0,0>
}
/* Show the difference object - test only
object { Diff_45
pigment { Color01 }
finish { Cone_finish }
}
*/
// B A C K G R O U N D
background { color White }
// L I G H T S
#declare L_dst1 = 160 ;
#declare L_dst2 = 200 ;
#declare L_clr1 = Gray60 ;
#declare L_clr2 = Gray30 ;
#declare F_dst = L_dst1*.75 ;
// Four lights opposite top cubic corners
light_source {
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