common:Generic
reb:InvertSphere
reb:InvertMobius
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Object
class
Derived from the public C code of Curtis McMullen and
material from Indra's Pearls by Mumford, Series and Wright
A new method for InitSpheres is needed, as both spheres
and Kleinian Group matricies must be initalized.
class InvertMobius(InvertSphere) {
; <p>
; Derived from the public C code of Curtis McMullen and
; material from Indra's Pearls by Mumford, Series and Wright
; A new method for InitSpheres is needed, as both spheres
; and Kleinian Group matricies must be initalized.
;
public:
import "common.ulb"
; constructor for Mobius (Kleinian) sphere inversions
func InvertMobius(Generic pparent)
invertSphere.Invertsphere(0)
PARAFUZZ = 1e-3, LINEFUZZ = 1e-5, im = (0,1),gi = 0
fii = 4, fks = 1, fk = fks, scale = 0.7, sscale = 1, iend = 4
ss = new SphereArray(50000000)
InitSpheresK()
endfunc
; Initialize spheres, inversion matricies and trace values
func InitSpheresK()
; This function initializes the base sphere(s), the Kleinian group
; inversion matrices and the trace values
complex Fc[4]
float Fz[4]
float Fr[4]
int i = 0
complex ta = @ta
complex tb = @tb
float cir = @cir
complex cira = @cira
Complex cirs = @cirs
float rada = @rada
float rads = @rads
float radam = @radam
complex m = @m
complex tab = 0
complex gz0 = 0
complex gz = 0
complex gQ = 0
complex gR = 0
complex tabAB = @tabAB
Fz[0] = 0
Fz[1] = 0
Fz[2] = 0
Fz[3] = 0
if @cusptype == "Nearby group"
ta = (1.91,-0.05)
tb = (2,0)
cir = 0.297
elseif @cusptype == "Accident"
ta = (1.9021130325903071442328786667588,0)
tb = (1.9021130325903071442328786667588,0)
elseif @cusptype == "Troel's Point"
ta = (1.6168866453,-0.7056734968)
tb = (2,0)
cir = 0.13091
elseif @cusptype == "Degenerate Spiral"
ta = (1.9264340533,-0.0273817919)
tb = (2,0)
cir = 0.2419
elseif @cusptype == "Double Cusp"
tb = (2,0)
if @cusp == "0/1"
ta = (2,0)
cir = 0.5
elseif @cusp == "1/100"
ta = (1.99599050389291,-0.000302826761310194)
cir = 0.3091
elseif @cusp == "2/99"
ta = (1.99599050389291,-0.000302826761310194)
cir = 0.2676
elseif @cusp == "3/100"
ta = (1.99118310579765,-0.000982081178197968)
cir = 0.2427
elseif @cusp == "4/99"
ta = (1.98427416931522,-0.00237401043014847)
cir = 0.2351
elseif @cusp == "1/15"
ta = (1.95859103011179,-0.0112785606117653)
cir = 0.32870768
elseif @cusp == "1/10"
ta = (1.91342329586682,-0.0362880775225429)
cir = 0.32365169
elseif @cusp == "2/19"
ta = (1.90377999779718,-0.0395799512688805)
cir = 0.2604321
elseif @cusp == "1/9"
ta = (1.89640725094921,-0.0487530128986506)
cir = 0.32176507
elseif @cusp == "7/43"
ta = (1.80785523999043,-0.136998687907137)
cir = 0.229796
elseif @cusp == "3/10"
ta = (1.65831239517773,-0.5)
cir = 0.2316625
elseif @cusp == "2/5"
ta = (1.64213876865348,-0.766588417465459)
cir = 0.2665884
elseif @cusp == "1/2"
ta = (1.73205080756888,-1)
cir = 0.36602539
elseif @cusp == "21/34"
ta = (1.6179907967521,-1.29170028664218)
cir = 0.166461
endif
endif
; Grandma's Special algorithm
if !(@cusptype == "Grandma's Special #2" || @cusptype == "Maskit")
if @showcusp == "Both"
Fc[0] = 1-cir
Fr[0] = cir
Fc[1] = -(1-cir)
Fr[1] = cir
Fc[2] = (0,0)
Fr[2] = 1
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
s.sph[2] = new Sphere(Fc[2],Fz[2],Fr[2],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
ss.sph[2] = s.sph[2]
elseif @showcusp == "Alternate"
Fc[0] = (1-cir)
Fr[0] = cir
Fc[1] = -(1-cir)
Fr[1] = cir
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
elseif @showcusp == "Standard"
Fc[0] = (0,0)
Fr[0] = 1
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
ss.sph[0] = s.sph[0]
endif
complex tab = (ta*tb+sqrt(ta*ta*tb*tb-4*(ta*ta+tb*tb)))/2
if @alttab
tab = (ta*tb-sqrt(ta*ta*tb*tb-4*(ta*ta+tb*tb)))/2
endif
complex gz0 = (tab-2)*tb/(tb*tab-2*ta+2*(0,1)*tab)
mob[0] = new Mobius((tb-(0,2))/2, tb/2, tb/2, conj((tb-(0,2))/2))
mob[1] = new Mobius(mob[0].m_d, -mob[0].m_b, -mob[0].m_c, mob[0].m_a)
mob[2] = new Mobius(ta/2, (ta*tab-2*tb-(0,4))*gz0/(2*tab-4), \
(ta*tab-2*tb+(0,4))/((2*tab+4)*gz0), ta/2)
if @trans
temp1 = mob[2].m_b
mob[2].m_b = mob[2].m_c
mob[2].m_c = temp1
endif
mob[3] = new Mobius(mob[2].m_d, -mob[2].m_b, -mob[2].m_c, mob[2].m_a)
endif
; Figure 11.1 from the Indra's Pearls book
if @cusptype == "Indra 11.1"
tabAB = (0,0)
tb = (2,0)
sscale = 2.4
ta = (1.924781, 0.047529)
cirs = (0, 0.272591599)
rads = 0.41421381
cira = (0.168208, 0)
rada = 0.2211131
endif
; Grandma's Special #2 algorithm
if !(@cusptype == "Grandma's Special" || @cusptype == "Maskit" ||\
@cusptype == "Double Cusp" || @cusptype == "Nearby Group" ||\
@cusptype == "Troel's Point"|| @cusptype == "Degenerate Spiral")
if @showcusp == "Both"
Fc[0] = cirs
Fr[0] = rads-cabs(cirs)
if @lines
Fr[0] = -Fr[0]
endif
Fc[1] = -cirs
Fr[1] = Fr[0]
Fc[2] = cira
Fr[2] = rada-cabs(cira)
if @linea
Fr[2] = -Fr[2]
endif
Fc[3] = -cira
Fr[3] = Fr[2]
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
s.sph[2] = new Sphere(Fc[2],Fz[2],Fr[2],0,0)
s.sph[3] = new Sphere(Fc[3],Fz[3],Fr[3],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
ss.sph[2] = s.sph[2]
ss.sph[3] = s.sph[3]
elseif @showcusp == "Alternate"
Fc[0] = cira
Fr[0] = rada-cabs(cira)
if @linea
Fr[0] = -Fr[0]
endif
Fc[1] = -cira
Fr[1] = Fr[0]
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
else
Fc[0] = cirs
Fr[0] = rads-cabs(cirs)
if @lines
Fr[0] = -Fr[0]
endif
Fc[1] = -cirs
Fr[1] = Fr[0]
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
endif
gz = 0.5*sqrt(ta^2*tb^2-4*ta^2-4*tb^2+4*tabAB+8)
tab = 0.5*ta*tb-gz
if @alttab
tab = 0.5*ta*tb+gz
endif
gQ = sqrt(2-tabAB)
gR = sqrt(2+tabAB)
if cabs(tabAB+im*gQ*gR)<2
gR = -gR
endif
gz0 = (tab-2)*(tb+gR)/(tb*tab-2*ta+im*gQ*tab)
mob[0] = new Mobius((tb-im*gQ)/2, (tb*tab-2*ta-im*gQ*tab)/((2*tab+4)*gz0),\
(tb*tab-2*ta+im*gQ*tab)*gz0/(2*tab-4), (tb+im*gQ)/2)
mob[1] = new Mobius(mob[0].m_d, -mob[0].m_b, -mob[0].m_c, mob[0].m_a)
mob[2] = new Mobius(ta/2, (ta*tab-2*tb+2*im*gQ)/((2*tab+4)*gz0), \
(ta*tab-2*tb-2*im*gQ)*gz0/(2*tab-4), ta/2)
if @trans
temp1 = mob[2].m_b
mob[2].m_b = mob[2].m_c
mob[2].m_c = temp1
endif
mob[3] = new Mobius(mob[2].m_d, -mob[2].m_b, -mob[2].m_c, mob[2].m_a)
endif
if @cusptype == "Maskit"
if @showcuspm == "Predefined"
if @cuspm == "0/1"
m = (0,2)
radam = 0.5
elseif @cuspm == "1/15"
m = (-0.0112785606117653, 1.95859103011179)
radam = 0.489661311
elseif @cuspm == "1/10"
m = (-0.0362880775225429,1.91342329586682)
radam = 0.47852888
elseif @cuspm == "2/19"
m = (-0.0395799512688805,1.90377999779718)
radam = 0.35214005
elseif @cuspm == "1/9"
m = (-0.0487530128986506,1.89640725094921)
radam = 0.4744165
elseif @cuspm == "7/43"
m = (-0.136998687907137,1.80785523999043)
radam = 0.2983515
elseif @cuspm == "3/10"
m = (-0.5,1.65831239517773)
radam = 0.3015111
elseif @cuspm == "2/5"
m = (-0.766588417465459,1.64213876865348)
radam = 0.363491
elseif @cuspm == "1/2"
m = (-1,1.73205080756888)
radam = 0.57735015
elseif @cuspm == "21/34"
m = (1.29170028664218,1.6179907967521)
radam = 0.1997052
endif
endif
if @showcuspm == "Both" || (@showcuspm == "Predefined" \
&& @showcuspm2 == "Both")
Fc[0] = 1 + flip(radam)
Fr[0] = radam
Fc[1] = (1,0)
Fr[1] = 0
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
elseif @showcuspm == "Alternate" || (@showcuspm == "Predefined" \
&& @showcuspm2 == "Alternate")
Fc[0] = 1 + flip(radam)
Fr[0] = radam
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
ss.sph[0] = s.sph[0]
else
Fc[0] = (1,0)
Fr[0] = 0
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
ss.sph[0] = s.sph[0]
endif
mob[0] = new Mobius(m, 1, 1, 0)
mob[1] = new Mobius(mob[0].m_d, -mob[0].m_b, -mob[0].m_c, mob[0].m_a)
mob[2] = new Mobius(1, 0, 2, 1)
mob[3] = new Mobius(mob[2].m_d, -mob[2].m_b, -mob[2].m_c, mob[2].m_a)
endif
; normalize the matrices
i = 0
while i < 4
mob[i].Normalize(mob[i])
i = i + 1
endwhile
endfunc
; Inverts a sphere - Mobius inversion The return value may be a sphere or a plane. <br>
; @param target = sphere to be inverted
; @param inverter = not used.
; @param level = recursion level
; @param gen = index of generator matrix
;------------------------------------------------
Sphere func Inverse(Sphere target, Sphere inverter, int level, int gen)
mob[5] = new Mobius(0,0,0,0)
mob[5].CircToMob(mob[5],target)
mob[gen].MConj(mob[5],mob[5])
Sphere ns = new Sphere(0,0,0,0,0)
mob[5].MobToCirc(level,gen,ns)
return ns
endfunc
; Top level recursion function
func Recurse()
int l = 0
int ir = 0
int si = 0
int sj = 0
int j = 0
bool done = false
int c = 0
float ddx = 0
float ddy = 0
float ddr = 0
sphere rra
bool continue = false
int ifinal = 0
int istack = 0
int nold = 0
int nfinal = 1
int iii = 0
int k = 0
int lev = 0
if @showcusp == "Both"
j = 3
iii = 2
elseif @showcusp == "Standard"
j = 1
iii = 0
else
j = 2
iii = 1
endif
if @cusptype == "Grandma's Special #2"
if @showcusp == "Both"
j = 4
iii = 3
else
j = 2
iii = 1
endif
endif
if @cusptype == "Maskit"
if @showcuspm == "Both" || (@showcuspm == "Predefined" && \
@showcuspm2 == "Both")
j = 2
iii = 1
else
j = 1
iii = 0
endif
endif
iii = iii + 1
lev = 1
while lev <= mlevel && j < flength
gi = 0
while gi < iend && j < flength
k = 0
while k <= iii && j < flength
ss.sph[j] = Inverse(ss.sph[k],ss.sph[0],lev,gi)
if ss.sph[j].frad >= 0 && abs(ss.sph[j].frad) < fminsphere
j = j - 1
endif
if j > flength
lev = mlevel + 1
k = iii + 1
endif
j = j+1
k = k + 1
endwhile
if j > flength
gi = 5
endif
gi = gi + 1
endwhile
; sort array by circle identity
l = round(j/2)+1
ir = j
continue = true
repeat
if l > 1
l = l-1
rra = ss.sph[l-1]
else
rra = ss.sph[ir-1]
ss.sph[ir-1] = ss.sph[0]
ir = ir-1
if ir == 0
ss.sph[0] = rra
continue = false
endif
endif
if continue == true
si = l
sj = 2*l
endif
while (sj <= ir) && (continue == true)
if sj < ir
ddx = real(ss.sph[sj-1].fcen)-real(ss.sph[sj].fcen)
ddy = imag(ss.sph[sj-1].fcen)-imag(ss.sph[sj].fcen)
ddr = ss.sph[sj-1].frad-ss.sph[sj].frad
c = 0
done = false
; Lines precede circles
if ss.sph[sj-1].frad <= 0 && ss.sph[sj].frad > 0
c = -1
done = true
elseif ss.sph[sj].frad <= 0 && ss.sph[sj-1].frad > 0
c = 1
done = true
elseif ddx < -thresh
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif ss.sph[sj-1].frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c < 0
sj = sj + 1
endif
endif
ddx = real(rra.fcen)-real(ss.sph[sj-1].fcen)
ddy = imag(rra.fcen)-imag(ss.sph[sj-1].fcen)
ddr = rra.frad-ss.sph[sj-1].frad
c = 0
done = false
; ; Lines precede circles
if rra.frad <= 0 && ss.sph[sj-1].frad > 0
c = -1
done = true
elseif ss.sph[sj-1].frad <= 0 && rra.frad > 0
c = 1
done = true
elseif ddx < -thresh
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif rra.frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c < 0
ss.sph[si-1] = ss.sph[sj-1]
si = sj
sj = sj + sj
else
sj = ir + 1
endif
endwhile
if (continue == true)
ss.sph[si-1] = rra
endif
until continue == false
; eliminate duplicates in place
; ir = oldj-iii+1
; l = oldj-iii
ir = j+1
l = j
while ir < j
ddx = real(ss.sph[ir].fcen)-real(ss.sph[ir-1].fcen)
ddy = imag(ss.sph[ir].fcen)-imag(ss.sph[ir-1].fcen)
ddr = ss.sph[ir].frad-ss.sph[ir-1].frad
c = 0
done = false
; Lines precede circles
if ss.sph[ir].frad <= 0 && ss.sph[ir-1].frad > 0
c = -1
done = true
elseif ss.sph[ir-1].frad <= 0 && ss.sph[ir].frad > 0
c = 1
done = true
elseif ddx < -thresh && !done
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif ss.sph[ir].frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c == 0
ir = ir + 1
else
ss.sph[l] = ss.sph[ir]
ir = ir +1
l = l + 1
endif
endwhile
j = j-(ir-l)+1
; move to final array, skipping dups
ifinal = 0
istack = 0
nold = nfinal
while ifinal < nold && istack < j && nfinal < flength
ddx = real(s.sph[ifinal].fcen)-real(ss.sph[istack].fcen)
ddy = imag(s.sph[ifinal].fcen)-imag(ss.sph[istack].fcen)
ddr = s.sph[ifinal].frad-ss.sph[istack].frad
c = 0
done = false
; Lines precede circles
if s.sph[ifinal].frad <= 0 && ss.sph[istack].frad > 0
c = -1
done = true
elseif ss.sph[istack].frad <= 0 && s.sph[ifinal].frad > 0
c = 1
done = true
elseif ddx < -thresh
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif s.sph[ifinal].frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c < 0
ifinal = ifinal + 1
endif
if c == 0
istack = istack + 1
endif
if c > 0
s.sph[nfinal] = ss.sph[istack]
nfinal = nfinal + 1
istack = istack + 1
endif
endwhile
while istack < j && nfinal < flength
s.sph[nfinal] = ss.sph[istack]
nfinal = nfinal + 1
istack = istack + 1
endwhile
ir = nold
while ir <nfinal
ss.sph[ir-nold] = s.sph[ir]
ir = ir+1
endwhile
j = nfinal-nold
; sort final array by circle identity
l = round((nfinal)/2)+1
ir = nfinal
continue = true
repeat
if l > 1
l = l-1
rra = s.sph[l-1]
else
rra = s.sph[ir-1]
s.sph[ir-1] = s.sph[0]
ir = ir-1
if ir == 0
s.sph[0] = rra
continue = false
endif
endif
if continue == true
si = l
sj = 2*l
endif
while (sj <= ir) && (continue == true)
if sj < ir
ddx = real(s.sph[sj-1].fcen)-real(s.sph[sj].fcen)
ddy = imag(s.sph[sj-1].fcen)-imag(s.sph[sj].fcen)
ddr = s.sph[sj-1].frad-s.sph[sj].frad
c = 0
done = false
; Lines precede circles
if s.sph[sj-1].frad <= 0 && s.sph[sj].frad > 0
c = -1
done = true
elseif s.sph[sj].frad <= 0 && s.sph[sj-1].frad > 0
c = 1
done = true
elseif ddx < -thresh
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif s.sph[sj-1].frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c < 0
sj = sj + 1
endif
endif
ddx = real(rra.fcen)-real(s.sph[sj-1].fcen)
ddy = imag(rra.fcen)-imag(s.sph[sj-1].fcen)
ddr = rra.frad-s.sph[sj-1].frad
c = 0
done = false
; Lines precede circles
if rra.frad <= 0 && s.sph[sj-1].frad > 0
c = -1
done = true
elseif s.sph[sj-1].frad <= 0 && rra.frad > 0
c = 1
done = true
elseif ddx < -thresh
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif rra.frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c < 0
s.sph[si-1] = s.sph[sj-1]
si = sj
sj = sj + sj
else
sj = ir + 1
endif
endwhile
if (continue == true)
s.sph[si-1] = rra
endif
until continue == false
iii = j-1
if j == 0
lev = mlevel+1
else
lev = lev+1
endif
endwhile
fk = nfinal-1
ss = 0
heapsort(s,fk)
vanquish(s,fk)
SizeAndRot()
if @zsort
heapsortz(s, fk)
endif
endfunc
; Size and rotate spheres
func SizeAndRot()
if @cusptype == "Nearby group" && @trans
sscale = 0.05
elseif @cusptype == "Double Cusp" && @trans
if @cusp == "1/15"
sscale = 0.015
elseif @cusp == "0/1"
sscale = 0.5
elseif @cusp == "2/19"
sscale = 0.025
elseif @cusp == "1/9"
sscale = 0.04
elseif @cusp == "7/43"
sscale = 0.035
elseif @cusp == "2/5"
sscale = 0.2
endif
endif
int i = 0
while i < fk
if s.sph[i].frad > 0
; size routines
if s.sph[i].frad > @maxsphere
s.sph[i].frad = 0
endif
if @cusptype == "Maskit"
s.sph[i].fcen = (s.sph[i].fcen+(0,-1))*#magn*scale*sscale
else
s.sph[i].fcen = s.sph[i].fcen*#magn*scale*sscale
endif
s.sph[i].fz = s.sph[i].fz*#magn*scale*sscale
s.sph[i].frad = s.sph[i].frad*#magn*scale*sscale
; rotation around the z axis
;
float fx = real(s.sph[i].fcen)
float fy = imag(s.sph[i].fcen)
float fz = s.sph[i].fz
float xx = real(s.sph[i].fcen)
fx = fx*cos(#angle) - fy*sin(#angle)
fy = fy*cos(#angle) + xx*sin(#angle)
s.sph[i].fcen = fx + flip(fy)
; rotation around the y axis
;
xx = fx
fx = fz*sin(@yang*#pi/180) + fx*cos(@yang*#pi/180)
fz = fz*cos(@yang*#pi/180) - xx*sin(@yang*#pi/180)
s.sph[i].fcen = fx + flip(fy)
s.sph[i].fz = fz
; rotation around the x axis
;
float yy = fy
fy = fy*cos(@xang*#pi/180) - fz*sin(@xang*#pi/180)
fz = yy*sin(@xang*#pi/180) + fz*cos(@xang*#pi/180)
s.sph[i].fcen = fx + flip(fy)
s.sph[i].fz = fz
endif
i = i + 1
endwhile
endfunc
float PARAFUZZ
float LINEFUZZ
complex im
Mobius mob[6]
int gi
int iend
float sscale
spherearray ss
default:
title = "Mobius Inversions"
int param v_mobinvert
caption = "Version (Mobius Inversions)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_mobinvert < 101
endparam
float param minsphere
caption = "Min sphere size"
default = 0.001
min = 0.000001
endparam
float param maxsphere
caption = "Max sphere size"
default = 0.7
endparam
int param maxLevel
caption = "Recursion level"
default = 100
min = 0
max = 200
endparam
float param radadj
caption = "Gen Rad adj"
default = 1.0
visible = false
endparam
float param bradadj
caption = "Base Rad adj"
default = 1.0
visible = false
endparam
bool param reflect
caption = "Reflect Object"
default = false
endparam
float param xang
caption = "X Axis Rotation"
default = 0.0
endparam
float param yang
caption = "Y Axis Rotation"
default = 0.0
endparam
heading
text = "For rotation around the Z Axis use the rotation angle on the Location Tab."
endheading
heading
text = "Use these methods with care, as only certain combinations of \
parameters will give satisfactory results. Use of the help file \
is essential. Use of the 'Explore' feature is not recommended."
visible = @cusptype == "Grandma's Special" || @cusptype == "Grandma's Special #2" \
|| @cusptype == "Maskit"
endheading
heading
text = "The Grandma algorithms come from 'Indra's Pearls' by Mumford, \
Series and Wright. Consult the book for use of the trace parameters."
visible = @cusptype == "Grandma's Special" || @cusptype == "Grandma's Special #2"
endheading
heading
text = "The Maskit algorithm comes from 'Indra's Pearls' by Mumford, \
Series and Wright. Consult the book for use of the Maskit parameters."
visible = @cusptype == "Maskit"
endheading
param cusptype
caption = "Group"
default = 7
enum = "Accident" "Indra 11.1" "Degenerate Spiral" "Double Cusp" \
"Grandma's Special" "Grandma's Special #2" "Maskit" "Nearby Group" \
"Troel's Point"
endparam
param cusp
caption = "Cusp"
default = 5
enum = "0/1" "1/100" "2/99" "3/100" "4/99" "1/15" "1/10" "2/19" "1/9" \
"7/43" "3/10" "2/5" "1/2" "21/34"
visible = @cusptype == "Double Cusp"
endparam
param showcusp
caption = "Cusp view"
default = 1
enum = "Both" "Standard" "Alternate"
visible = !(@cusptype == "Maskit" || @cusptype == "Accident")
endparam
param showcuspm
caption = "Cusp view"
default = 1
enum = "Both" "Standard" "Alternate" "Predefined"
visible = @cusptype == "Maskit"
endparam
param showcuspm2
caption = "Cusp view"
default = 1
enum = "Both" "Standard" "Alternate"
visible = @cusptype == "Maskit" && @showcuspm == "Predefined"
endparam
heading
text = "Slowly increase 'gen circle' until good circle packing is observed."
visible = @cusptype == "Grandma's special"&& @showcusp != "Standard"
endheading
param @cir
caption ="Gen circle"
default = 0.01
hint = "Slowly increase until good circle packing is observed."
visible = @cusptype == "Grandma's special"&& @showcusp != "Standard"
endparam
heading
text = "These parameters set the size and position of the 'Standard' \
generator circles."
visible = @cusptype == "Grandma's special #2"&& @showcusp != "Alternate"
endheading
param @cirs
caption ="Gen circle std"
default = (0,0)
visible = (@cusptype == "Grandma's special #2"&& @showcusp != "Alternate")
endparam
param @rads
caption ="Rad ref std"
default = 1.0
visible = (@cusptype == "Grandma's special #2"&& @showcusp != "Alternate")
endparam
bool param @lines
caption ="Generate as line"
default = false
visible = (@cusptype == "Grandma's special #2"&& @showcusp != "Alternate")
endparam
heading
text = "These parameters set the size and position of the 'Alternate' \
generator circles."
visible = @cusptype == "Grandma's special #2"&& @showcusp != "Standard"
endheading
param @cira
caption ="Gen circle alt"
default = (0,0)
visible = (@cusptype == "Grandma's special #2"&& @showcusp != "Standard")
endparam
param @rada
caption ="Rad ref alt"
default = 1.0
visible = (@cusptype == "Grandma's special #2"&& @showcusp != "Standard")
endparam
heading
text = "This parameter set the size and position of the 'Alternate' \
generator circle."
visible = @cusptype == "Maskit"&& @showcusp != "Standard"
endheading
param @radam
caption ="Rad ref"
default = 0.5
visible = @cusptype == "Maskit"&& @showcuspm != "Standard" && \
@showcuspm != "Predefined"
endparam
bool param @linea
caption ="Generate as line"
default = false
visible = (@cusptype == "Grandma's special #2"&& @showcusp != "Standard")
endparam
complex param m
caption = "Maskit param"
default = (0.0112785606117653,1.95859103011179)
visible = @cusptype == "Maskit" && @showcuspm != "Predefined"
endparam
param cuspm
caption = "Cusp"
default = 1
enum = "0/1" "1/15" "1/10" "2/19" "1/9" "7/43" "3/10" "2/5" "1/2" "21/34"
visible = @cusptype == "Maskit" && @showcuspm == "Predefined"
endparam
complex param ta
caption = "Trace a"
default = (1.95,0.02)
visible = @cusptype == "Grandma's Special" || @cusptype == "Grandma's Special #2"
endparam
complex param tb
caption = "Trace b"
default = 3
visible = @cusptype == "Grandma's Special" || @cusptype == "Grandma's Special #2"
endparam
bool param alttab
caption ="Alternate trace ab"
default = false
visible = @cusptype == "Grandma's Special" || @cusptype == "Grandma's Special #2"
endparam
complex param tabAB
caption = "Trace abAB"
default = -2
visible = @cusptype == "Grandma's Special #2"
endparam
bool param trans
caption = "Transpose transform"
default = false
visible = @cusptype != "Maskit"
endparam
}
| Constructor Summary | |
|---|---|
InvertMobius()
|
|
InvertMobius(Generic pparent)
constructor for Mobius (Kleinian) sphere inversions |
|
| Method Summary | |
|---|---|
void |
InitSpheresK()
Initialize spheres, inversion matricies and trace values |
Sphere |
Inverse(Sphere target,
Sphere inverter,
int level,
int gen)
Inverts a sphere - Mobius inversion The return value may be a sphere or a plane. |
void |
Recurse()
Top level recursion function |
void |
SizeAndRot()
Size and rotate spheres |
| Methods inherited from class reb:InvertSphere |
|---|
findbound, heapify, heapifyz, heapsort, heapsortz, InitSpheres, recurse2, siftdown, siftdownz, swap, vanquish |
| Methods inherited from class common:Generic |
|---|
GetParent |
| Methods inherited from class Object |
|---|
|
| Constructor Detail |
|---|
public InvertMobius(Generic pparent)
public InvertMobius()
| Method Detail |
|---|
public void InitSpheresK()
public Sphere Inverse(Sphere target,
Sphere inverter,
int level,
int gen)
Inverse in class InvertSpheretarget - = sphere to be invertedinverter - = not used.level - = recursion levelgen - = index of generator matrixpublic void Recurse()
Recurse in class InvertSpherepublic void SizeAndRot()
|
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