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It seems to me that the engine used to throw an error when this happened...
Render attached. The last orange point is out of position. Why this happens at
-60 or 300 degrees and not on the other side, I don't know.
I found a possible workaround, but it's not pretty.
Watch the value of m1:
m1 = 0.500000 / -0.866025 = -0.577350
m2 = 0.327327 / -0.944911 = -0.346410
PC: <1.500000,0.866025,0.000000>
PD: <0.000000,1.732051,0.000000>
PE: <2.000000,1.732051,0.000000>
PF: <-0.500000,2.598076,0.000000>
m1 = -0.500000 / -0.866025 = 0.577350
m2 = -0.654654 / -0.755929 = 0.866025
PC: <0.000000,1.732051,0.000000>
PD: <-1.500000,0.866025,0.000000>
PE: <-0.500000,2.598076,0.000000>
PF: <-2.500000,0.866025,0.000000>
m1 = -1.000000 / -0.000000 = 3900231685776980.500000
m2 = -0.981981 / 0.188982 = -5.196152
PC: <-1.500000,0.866025,0.000000>
PD: <-1.500000,-0.866025,0.000000>
PE: <-2.500000,0.866025,0.000000>
PF: <-2.000000,-1.732051,0.000000>
m1 = -0.500000 / 0.866025 = -0.577350
m2 = -0.327327 / 0.944911 = -0.346410
PC: <-1.500000,-0.866025,0.000000>
PD: <-0.000000,-1.732051,0.000000>
PE: <-2.000000,-1.732051,0.000000>
PF: <0.500000,-2.598076,0.000000>
m1 = 0.500000 / 0.866025 = 0.577350
m2 = 0.654654 / 0.755929 = 0.866025
PC: <-0.000000,-1.732051,0.000000>
PD: <1.500000,-0.866025,0.000000>
PE: <0.500000,-2.598076,0.000000>
PF: <2.500000,-0.866025,0.000000>
m1 = 1.000000 / -0.000000 = -7800463371553961.000000
m2 = 0.981981 / -0.188982 = -5.196152
PC: <1.500000,-0.866025,0.000000>
PD: <1.500000,0.866025,0.000000>
PE: <2.500000,-0.866025,0.000000>
PF: <2.000000,1.732051,0.000000>
m1 = 1.000000 / -0.000000 = -7800463371553961.000000
m2 = 0.981981 / -0.188982 = -5.196152
Regards,
A.D.B.
Original Scene: Version 3.8.0-alpha.9606898.unofficial
/*
Persistence of Vision Ray-Tracer Scene Description File
Name: shm_2018-4.pov
Vers: 3.6
Desc: Spiral Honeycomb Mosaic
Date: 10 - 24 - 18
Auth: Anthony D. Baye
*/
#include "kolors.inc"
#include "math.inc"
#default { pigment { White }
finish { diffuse 0.6 specular 0.3 roughness 0.01 fresnel on } }
light_source { <2.0, 3.0, -5.0> color rgb 1 }
camera {
perspective
location <0.0, 0.0, -15.0>
up y
right (image_width/image_height)*x
look_at 0.0
}
#macro Arrow(S, D, L, C)
union {
cylinder { S, S+D*L 0.015625 }
cone { S+D*L, 0.01325, S+D*L+0.125*D, 0.0 }
pigment { C }
finish { diffuse 0.6 specular 0.3 roughness 0.05 fresnel on }
}
#end
#macro det2d(U,V)
#local retval = U.x*V.y - U.y*V.x;
retval
#end
#macro IPoint(UI1, UI2, VI1, VI2)
#local Ud = vnormalize(UI2 - UI1);
#local Vd = vnormalize(VI2 - VI1);
// !! The problem is here !!
#local m1 = Ud.y / Ud.x;
#local m2 = Vd.y / Vd.x;
// Workaround: ensure that x-coord is always slightly non-zero.
// Problem: This introduces a slight error which grows larger with distance.
// #local m1 = Ud.y / (Ud.x != 0 & Ud.x != -0 ? Ud.x : 0.00000000001 );
// #local m2 = Vd.y / (Vd.x != 0 & Vd.x != -0 ? Vd.x : 0.00000000001 );
#debug concat("m1 = " str(Ud.y,0,6) " / " str(Ud.x,0,6) " = " str(m1,0,6)
"\n")
#debug concat("m2 = " str(Vd.y,0,6) " / " str(Vd.x,0,6) " = " str(m2,0,6)
"\n")
#local rX = (m1*UI1.x - m2*VI1.x + VI1.y - UI1.y)/(m1 - m2);
#local rY = m1*(rX - UI1.x) + UI1.y;
#local retval = <rX,rY, 0.0>;
retval
#end
#macro ShowPoints(RAD, ORDER, ADV)
#local THETA = atand(sqrt(3)/2)*(ORDER - 1);
#local BP = vrotate((RAD*<cosd(60), sind(60), 0.0> - <R, 0.0,
0.0>)*pow(sqrt(7),(ORDER - 1)),THETA*z);
#local A = vrotate(RAD*<cosd(60), sind(60), 0.0>*pow(sqrt(7),(ORDER -
1)),THETA*z);
#local B = vrotate((2*RAD*cosd(30))*<cosd(30), sind(30),
0.0>*pow(sqrt(7),(ORDER - 1)),THETA*z);
#local G = vrotate((2*RAD*cosd(30))*<cosd(90), sind(90),
0.0>*pow(sqrt(7),(ORDER - 1)),THETA*z);
#local D = B + RAD*sqrt(3)*<cosd(60), sind(60), 0.0>;
#local E = G + RAD*sqrt(3)*<cosd(120), sind(120), 0.0>;
union {
sphere { A 0.09375 pigment { Red } }
sphere { B 0.09375 pigment { Yellow } }
sphere { G 0.09375 pigment { Yellow } }
sphere { D 0.09375 pigment { Green } }
sphere { E 0.09375 pigment { Green } }
sphere { IPoint(B,G,D,E) 0.125
pigment { Orange } finish { diffuse 0.6 specular 0.3 roughness 0.05
fresnel on } }
}
#end
#declare R = 1.0;
#macro Hex(MajR)
union {
#for(I,0,300,60)
cylinder { MajR*<cosd(I), sind(I), 0.0> MajR*<cosd(I+60), sind(I+60), 0.0>
0.015625 }
#end
}
#end
#macro cMod(A, B)
#local retval = A - floor(A/B)*B;
retval
#end
#local LV0 =
Hex(R)
#macro Flag(PIG, S)
union {
cylinder { <0.0,0.0,0.0> R*S*<cosd(0), sind(0), 0.0> 0.015625 }
cylinder { <0.0,0.0,0.0> R*S*<cosd(60), sind(60), 0.0> 0.015625 }
Arrow(R*S*<1.0, 0.0, 0.0>, <cosd(60),sind(60), 0.0> - <1, 0, 0.0>,
3*R*sqrt(7), PIG)
pigment { PIG }
}
#end
#macro Point(LOC, COL)
sphere { LOC 0.0625 pigment {COL} }
#end
#declare LV1 =
union {
object { LV0 }
#for(A,0,5,1)
object { LV0 translate R*sqrt(3)*<cosd(30 + 60*A), sind(30 + 60*A), 0.0> }
#end
}
LV1
// Point(<R, 0, 0>, Yellow)
// #for(A,0,5,1)
// Point(R*sqrt(3)*<cosd(30 + 60*A), sind(30 + 60*A), 0.0>, Yellow)
//
// #end
// object { Point(R*sqrt(7)*<1.0, 0.0, 0.0>, Yellow) rotate atand(sqrt(3)/2)*z }
// object { Point(R*sqrt(7)*<1.0, 0.0, 0.0>, Yellow) rotate (atand(sqrt(3)/2) +
60)*z }
#declare PA = <R,0,0>;
#declare PB = R*<cosd(60), sind(60), 0.0>;
#declare PC = R*sqrt(3)*<cosd(30), sind(30), 0.0>;
#declare PD = R*sqrt(3)*<cosd(90), sind(90), 0.0>;
#declare PE = vrotate(PA*sqrt(7),atand(sqrt(3)/2)*z);
#declare PF = vrotate(PA*sqrt(7),(atand(sqrt(3)/2) + 60)*z);
Point(PA,Yellow)
Point(PB,Yellow)
Flag(Blue, R)
#for(A,0,5,1)
union {
object { Flag(Red, R*sqrt(3)) rotate (30.0 + 60*A)*z }
object { Flag(Green, R*sqrt(7)) rotate (atand(sqrt(3)/2) + 60*A)*z }
}
#local ORIG = IPoint(
vrotate(PC,60*A*z),
vrotate(PD,60*A*z),
vrotate(PE,60*A*z),
vrotate(PF,60*A*z)
);
#debug concat("PC: <" vstr(3,vrotate(PC,60*A*z),",",0,6) ">\n")
#debug concat("PD: <" vstr(3,vrotate(PD,60*A*z),",",0,6) ">\n")
#debug concat("PE: <" vstr(3,vrotate(PE,60*A*z),",",0,6) ">\n")
#debug concat("PF: <" vstr(3,vrotate(PF,60*A*z),",",0,6) ">\n")
Point(vrotate(PC,60*A*z),Green)
Point(vrotate(PD,60*A*z),Green)
Point(vrotate(PE,60*A*z),Yellow)
Point(vrotate(PF,60*A*z),Yellow)
Point(ORIG, Orange)
object { LV1 translate ORIG }
#end
Point(IPoint(vrotate(PC,300*z), vrotate(PD,300*z), vrotate(PE,300*z),
vrotate(PF,300*z)),Red)
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Download 'shm_2018-4.png' (126 KB)
Preview of image 'shm_2018-4.png'
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