How to use this complex parametric equation to draw curve in iOS

Question

just found this demo code to using parametric equation draw in iOS

you can see that key code is to generate this array of points

let points: [CGPoint] = 0.stride(to: M_PI * 2, by: 0.01).map
{
    let x = pow(sin($0), 3)
    var y = 13 * cos($0)
    y -= 5 * cos(2 * $0)
    y -= 2 * cos(3 * $0)
    y -= cos(4 * $0)
    y /= 16

    return CGPoint(x: 320 + (x * 300), y: 280 + (y * -300))
}

which is just using this equation

now what I want to draw is more complex one mao curve

but the problem I encounter is there is a mathematic sign in the parametric equation provided by the site that I don't know how to convert to iOS code, this one

UPDATE: now I encounter a new problem: "Expression was too complex to be solved in reasonable time", any idea besides break it down into small expression like the heart curve did in its y above, because manually break it down it's too overwhelming

and the whole code is list below

func sgn(t: Double) -> Double{
    switch t {
    case _ where t < 0:
        return -1.0
    case _ where t > 0:
        return 1.0
    default:
        return 0.0
    }
}
func theta(t: Double) -> Double {
    switch t {
    case _ where t < 0:
        return 0.0
    case _ where t > 0:
        return 1.0
    default:
        return 0.5
    }
}
let pi = M_PI

let layer = CAShapeLayer()
layer.lineCap = kCALineCapRound
layer.lineJoin = kCALineCapRound

self.view.layer.addSublayer(layer)


let points: [CGPoint] = 0.stride(to: M_PI * 2, by: 0.01).map
    { t in
         var x = ((-10/47*sin(30/41-17*t)-11/4*sin(83/58-15*t)-47/17*sin(79/53-13*t)+21080/33*sin(t+63/40)+179/32*sin(2*t+28/17)+263/25*sin(3*t+85/54)+1552/47*sin(4*t+146/31)+2015/77*sin(5*t+30/19)+286/31*sin(6*t+117/25)+1308/17*sin(7*t+67/42)+158/37*sin(8*t+77/17)+1017/26*sin(9*t+61/38)+107/18*sin(10*t+79/46)+863/39*sin(11*t+29/18)+74/23*sin(12*t+12/7)+110/63*sin(14*t+163/35)+29/31*sin(16*t+75/41)+2/7*sin(18*t+64/25)+305/37*sin(19*t+18/11)+9/34*sin(20*t+91/32)+316/45*sin(21*t+64/39)+16/15*sin(22*t+119/27)+179/35*sin(23*t+23/14)+38/51*sin(24*t+131/65)+1969/19)*theta(103*pi-t)*theta(t-99*pi)+(-44/31*sin(81/52-6*t)-47/19*sin(14/9-5*t)-206/75*sin(39/25-4*t)-77/16*sin(69/44-3*t)-416/25*sin(25/16-2*t)-1496/19*sin(47/30-t)-3315/19)*theta(99*pi-t)*theta(t-95*pi)+(732/7*sin(t+41/26)+111/17*sin(2*t+18/11)+187/20*sin(3*t+43/27)+37/24*sin(4*t+44/27)+157/45*sin(5*t+59/37)+5507/30)*theta(95*pi-t)*theta(t-91*pi)+(-19/42*sin(37/24-2*t)+3067/18*sin(t+11/7)+281/16*sin(3*t+96/61)+13/27*sin(4*t+159/34)+215/38*sin(5*t+30/19)+1121/34)*theta(91*pi-t)*theta(t-87*pi)+(-1/20*sin(17/14-16*t)+3995/36*sin(t+11/7)+353/25*sin(2*t+69/44)+209/18*sin(3*t+11/7)+349/66*sin(4*t+49/31)+67/17*sin(5*t+43/27)+84/43*sin(6*t+60/37)+79/30*sin(7*t+149/93)+93/38*sin(8*t+30/19)+37/22*sin(9*t+74/47)+91/57*sin(10*t+68/43)+43/29*sin(11*t+43/27)+42/23*sin(12*t+45/28)+28/31*sin(13*t+77/47)+17/36*sin(14*t+41/25)+17/86*sin(15*t+8/5)+12/29*sin(17*t+65/42)+11/31*sin(18*t+49/31)+31/47*sin(19*t+45/28)+13/31*sin(20*t+33/20)+5/43*sin(21*t+168/37)+9/46*sin(22*t+109/68)+26/29*sin(23*t+41/26)+31/47*sin(24*t+43/27)+5/21*sin(25*t+50/31)+2855/14)*theta(87*pi-t)*theta(t-83*pi)+(-5/33*sin(32/21-24*t)-16/17*sin(20/13-23*t)-64/39*sin(80/51-17*t)-1/28*sin(14/9-15*t)+3240/31*sin(t+11/7)+341/25*sin(2*t+52/33)+888/71*sin(3*t+63/40)+286/191*sin(4*t+31/19)+170/29*sin(5*t+68/43)+18/29*sin(6*t+80/17)+67/23*sin(7*t+91/58)+2/33*sin(8*t+36/31)+19/36*sin(9*t+51/32)+23/28*sin(10*t+21/13)+39/34*sin(11*t+65/41)+3/26*sin(12*t+39/20)+47/43*sin(13*t+37/23)+1/117*sin(14*t+825/206)+58/35*sin(16*t+47/30)+34/19*sin(18*t+62/39)+27/29*sin(19*t+127/27)+3/28*sin(20*t+245/52)+54/37*sin(21*t+53/33)+23/31*sin(22*t+21/13)-6998/27)*theta(83*pi-t)*theta(t-79*pi)+(2069/16*sin(t+11/7)+82/21*sin(2*t+14/3)+443/29*sin(3*t+19/12)+79/30*sin(4*t+30/19)+148/29*sin(5*t+19/12)+27/25*sin(6*t+33/20)+73/31*sin(7*t+27/17)+8893/37)*theta(79*pi-t)*theta(t-75*pi)+(-11/32*sin(31/22-2*t)+4451/49*sin(t+11/7)+515/68*sin(3*t+102/65)+1/20*sin(4*t+9/13)+79/30*sin(5*t+47/30)+17/37*sin(6*t+11/7)+47/30*sin(7*t+107/68)-10305/46)*theta(75*pi-t)*theta(t-71*pi)+(-5/24*sin(74/59-26*t)-22/25*sin(16/11-23*t)-5/29*sin(29/25-20*t)-62/41*sin(46/31-17*t)-48/25*sin(20/13-15*t)-113/24*sin(38/25-12*t)-231/40*sin(39/25-9*t)-89/39*sin(47/32-7*t)-104/19*sin(48/31-5*t)-182/15*sin(37/24-4*t)-140/19*sin(31/20-2*t)+3287/23*sin(t+107/68)+564/23*sin(3*t+113/24)+8/3*sin(6*t+13/8)+241/30*sin(8*t+37/23)+71/30*sin(10*t+14/9)+17/12*sin(11*t+44/27)+16/25*sin(13*t+67/39)+10/11*sin(14*t+81/52)+3*sin(16*t+21/13)+17/14*sin(18*t+127/27)+56/39*sin(19*t+117/73)+41/44*sin(21*t+159/34)+54/65*sin(22*t+27/17)+17/35*sin(24*t+159/34)+5/27*sin(25*t+44/29)-17/10)*theta(71*pi-t)*theta(t-67*pi)+(1987/31*sin(t+11/7)+305/28*sin(2*t+80/17)+751/28*sin(3*t+11/7)+191/30*sin(4*t+30/19)+313/33*sin(5*t+63/40)+122/73*sin(6*t+127/27)+113/34*sin(7*t+41/26)+23/30*sin(8*t+11/7)+73/27*sin(9*t+68/43)+3943/17)*theta(67*pi-t)*theta(t-63*pi)+(1593/29*sin(t+179/38)+191/29*sin(2*t+127/27)+678/97*sin(3*t+113/24)+44/19*sin(4*t+169/36)+63/34*sin(5*t+108/23)+17/16*sin(6*t+75/16)-6319/33)*theta(63*pi-t)*theta(t-59*pi)+(-9/29*sin(32/51-88*t)-39/29*sin(64/41-85*t)-19/27*sin(114/115-26*t)-30/43*sin(45/31-21*t)-14/11*sin(42/29-15*t)-13/38*sin(20/33-9*t)+15919/28*sin(t+39/25)+5859/34*sin(2*t+61/13)+1289/20*sin(3*t+229/49)+899/26*sin(4*t+26/17)+315/16*sin(5*t+145/31)+707/104*sin(6*t+26/17)+71/20*sin(7*t+3/2)+142/17*sin(8*t+188/41)+182/31*sin(10*t+28/19)+69/43*sin(11*t+356/79)+84/19*sin(12*t+55/39)+376/51*sin(13*t+87/62)+89/13*sin(14*t+67/46)+152/27*sin(16*t+69/47)+73/20*sin(17*t+57/43)+13/9*sin(18*t+3/2)+5/34*sin(19*t+70/41)+19/9*sin(20*t+47/36)+143/43*sin(22*t+43/33)+191/30*sin(23*t+31/24)+107/23*sin(24*t+35/27)+78/25*sin(25*t+32/25)+139/33*sin(27*t+43/33)+155/37*sin(28*t+43/33)+375/47*sin(29*t+141/106)+16/25*sin(30*t+145/38)+265/18*sin(31*t+232/53)+849/29*sin(32*t+61/14)+451/18*sin(33*t+204/47)+18/13*sin(34*t+327/77)+453/19*sin(35*t+6/5)+821/39*sin(36*t+43/37)+371/48*sin(37*t+37/32)+139/29*sin(38*t+107/25)+67/12*sin(39*t+343/78)+1033/100*sin(40*t+38/33)+435/59*sin(41*t+46/45)+327/43*sin(42*t+37/32)+264/53*sin(43*t+55/13)+19/35*sin(44*t+51/77)+771/71*sin(45*t+35/32)+85/24*sin(46*t+11/12)+30/23*sin(47*t+67/40)+139/22*sin(48*t+109/26)+170/41*sin(49*t+46/41)+195/32*sin(50*t+46/51)+154/71*sin(51*t+41/34)+63/17*sin(52*t+54/13)+42/25*sin(53*t+91/24)+185/77*sin(54*t+17/30)+773/103*sin(55*t+16/15)+68/11*sin(56*t+73/17)+113/24*sin(57*t+48/35)+351/53*sin(58*t+92/21)+643/60*sin(59*t+65/59)+153/23*sin(60*t+193/45)+62/25*sin(61*t+66/47)+37/33*sin(62*t+31/8)+79/20*sin(63*t+153/35)+213/25*sin(64*t+25/23)+721/68*sin(65*t+59/14)+237/28*sin(66*t+33/29)+20/7*sin(67*t+131/28)+242/41*sin(68*t+31/32)+57/86*sin(69*t+1/21)+86/21*sin(70*t+147/38)+203/102*sin(71*t+12/17)+159/47*sin(72*t+29/35)+23/16*sin(73*t+400/87)+28/25*sin(74*t+87/34)+377/113*sin(75*t+177/43)+173/61*sin(76*t+29/31)+25/21*sin(77*t+7/17)+69/19*sin(78*t+94/25)+34/33*sin(79*t+19/5)+9/28*sin(80*t+199/83)+140/93*sin(81*t+178/39)+339/127*sin(82*t+61/48)+107/20*sin(83*t+125/31)+81/20*sin(84*t+29/32)+27/26*sin(86*t+47/14)+9/25*sin(87*t+15/19)+149/75*sin(89*t+45/89)+29/21*sin(90*t+151/44)+75/26*sin(91*t+251/66)+50/21*sin(92*t+23/32)+62/55*sin(93*t+8/63)+23/11*sin(94*t+55/16)+51/26*sin(95*t+257/72)+38/25*sin(96*t+227/57)+314/209*sin(97*t+15/37)+11/9*sin(98*t+416/119)+11584/59)*theta(59*pi-t)*theta(t-55*pi)+(-43/31*sin(53/34-18*t)-58/35*sin(61/39-17*t)-55/19*sin(36/23-16*t)-155/59*sin(61/39-15*t)-45/19*sin(41/27-9*t)-46/13*sin(95/61-8*t)-360/23*sin(58/37-7*t)-77/15*sin(53/34-4*t)+27845/41*sin(t+91/58)+259/26*sin(2*t+212/45)+7843/86*sin(3*t+146/31)+2557/50*sin(5*t+146/31)+3931/786*sin(6*t+271/58)+31/23*sin(10*t+174/37)+79/24*sin(11*t+75/16)+86/47*sin(12*t+135/29)+97/24*sin(13*t+174/37)+76/29*sin(14*t+136/29)+30867/253)*theta(55*pi-t)*theta(t-51*pi)+(-5/31*sin(1/3-12*t)-23/52*sin(119/99-11*t)-166/33*sin(17/12-4*t)-196/41*sin(123/88-3*t)+327/34*sin(t+155/58)+297/40*sin(2*t+35/17)+35/44*sin(5*t+142/61)+3/5*sin(6*t+5/19)+11/19*sin(7*t+19/25)+23/58*sin(8*t+67/31)+12/31*sin(9*t+62/45)+5/12*sin(10*t+57/32)+27/13)*theta(51*pi-t)*theta(t-47*pi)+(2957/51*sin(t+7/22)+296/41)*theta(47*pi-t)*theta(t-43*pi)+(-1/2*sin(46/37-12*t)-233/35*sin(58/41-6*t)-491/47*sin(12/13-4*t)-227/12*sin(26/29-2*t)+7589/21*sin(t+23/18)+825/43*sin(3*t+19/24)+103/39*sin(5*t+7/12)+29/37*sin(7*t+43/14)+69/20*sin(8*t+130/31)+17/14*sin(9*t+137/56)+16/25*sin(10*t+129/37)+28/41*sin(11*t+71/29)+18979/130)*theta(43*pi-t)*theta(t-39*pi)+(-13/48*sin(31/24-7*t)-7/24*sin(29/25-6*t)-35/18*sin(59/69-2*t)+127/34*sin(t+7/55)+107/42*sin(3*t+94/21)+319/62*sin(4*t+569/122)+59/28*sin(5*t+22/13)+1/16*sin(8*t+139/37)+6/23*sin(9*t+4/27)+5/19*sin(10*t+119/41)+3/25*sin(11*t+44/19)+3/17*sin(12*t+338/89)-1419/7)*theta(39*pi-t)*theta(t-35*pi)+(-15/104*sin(31/38-10*t)-8/27*sin(26/29-8*t)-66/35*sin(4/23-4*t)-102/47*sin(41/36-t)+133/46*sin(2*t+31/13)+219/28*sin(3*t+93/35)+31/28*sin(5*t+182/67)+20/23*sin(6*t+5/38)+39/77*sin(7*t+119/53)+6/17*sin(9*t+95/28)+3/11*sin(11*t+73/24)+1/15*sin(12*t+26/29)+9908/49)*theta(35*pi-t)*theta(t-31*pi)+(-17/36*sin(29/32-3*t)-73/122*sin(53/38-2*t)+537/20*sin(t+5/4)+7/32*sin(4*t+184/41)+13/31*sin(5*t+21/5)+3/43*sin(6*t+9/22)+4507/22)*theta(31*pi-t)*theta(t-27*pi)+(-15/32*sin(40/31-6*t)-2/9*sin(2/7-5*t)-14/17*sin(73/55-4*t)-43/28*sin(50/37-2*t)+727/27*sin(t+20/17)+17/15*sin(3*t+4/35)-1416/7)*theta(27*pi-t)*theta(t-23*pi)+(-17/39*sin(35/33-16*t)-15/13*sin(5/8-14*t)-115/67*sin(52/35-10*t)-115/37*sin(11/45-7*t)-136/43*sin(26/25-6*t)-703/43*sin(41/28-4*t)-506/35*sin(1/114-3*t)-1405/34*sin(34/29-2*t)+413/48*sin(t+149/39)+241/32*sin(5*t+55/46)+195/44*sin(8*t+298/85)+73/27*sin(9*t+79/33)+59/28*sin(11*t+132/35)+13/22*sin(12*t+202/47)+11/20*sin(13*t+55/21)+99/74*sin(15*t+125/28)+5740/9)*theta(23*pi-t)*theta(t-19*pi)+(-23/26*sin(11/54-8*t)-112/29*sin(9/23-5*t)+137/33*sin(t+68/45)+33/19*sin(2*t+234/55)+604/57*sin(3*t+325/324)+541/47*sin(4*t+47/27)+36/19*sin(6*t+143/35)+37/28*sin(7*t+7/4)+26/33*sin(9*t+57/20)+24/49*sin(10*t+15/32)+1/8*sin(11*t+69/16)+17/42*sin(12*t+21/22)+901/40)*theta(19*pi-t)*theta(t-15*pi)+(4831/29*sin(t+46/29)+100/53*sin(2*t+38/29)+471/28*sin(3*t+49/29)+71/31*sin(4*t+95/31)+212/33*sin(5*t+38/25)+35/39*sin(6*t+164/55)+1163/291*sin(7*t+65/38)+14/23*sin(8*t+73/18)+467/36)*theta(15*pi-t)*theta(t-11*pi)+(-1/2*sin(4/25-8*t)-17/23*sin(1/20-6*t)-46/29*sin(1/12-4*t)-29/15*sin(36/37-2*t)+3308/37*sin(t+28/19)+576/67*sin(3*t+46/37)+87/25*sin(5*t+23/21)+78/47*sin(7*t+22/21)+3643/17)*theta(11*pi-t)*theta(t-7*pi)+(-41/20*sin(12/11-5*t)+9878/119*sin(t+76/33)+71/22*sin(2*t+133/29)+267/31*sin(3*t+76/21)+55/32*sin(4*t+3/31)+89/88*sin(6*t+23/24)+40/53*sin(7*t+3/25)+44/87*sin(8*t+34/11)+6/13*sin(9*t+40/27)-7131/31)*theta(7*pi-t)*theta(t-3*pi)+(-24/31*sin(16/17-16*t)-149/41*sin(50/37-9*t)-133/52*sin(23/32-8*t)-303/32*sin(1/734-7*t)+10523/20*sin(t+32/23)+431/20*sin(2*t+31/10)+1144/27*sin(3*t+139/36)+456/47*sin(4*t+81/34)+390/47*sin(5*t+146/81)+158/33*sin(6*t+14/27)+41/35*sin(10*t+43/20)+29/19*sin(11*t+82/33)+64/41*sin(12*t+42/31)+67/43*sin(13*t+47/43)+16/35*sin(14*t+41/20)+49/73*sin(15*t+59/88)+2388/37)*theta(3*pi-t)*theta(t+pi))*theta(sqrt(sgn(sin(t/2))))
            var y = ((-407/57*sin(35/24-24*t)-42/31*sin(41/28-23*t)-49/16*sin(67/46-22*t)-26/37*sin(38/31-21*t)-76/35*sin(59/39-20*t)-310/73*sin(43/28-18*t)-11*sin(44/29-13*t)-580/41*sin(32/21-10*t)-3258/65*sin(63/41-9*t)-252/17*sin(56/37-8*t)-6254/51*sin(17/11-6*t)-1481/27*sin(71/46-5*t)-465/32*sin(73/47-3*t)+3651/50*sin(t+30/19)+8318/27*sin(2*t+30/19)+134/21*sin(4*t+127/27)+807/19*sin(7*t+19/12)+252/11*sin(11*t+155/97)+139/32*sin(12*t+49/30)+417/38*sin(14*t+51/31)+149/38*sin(15*t+117/70)+173/24*sin(16*t+13/8)+16/7*sin(17*t+12/7)+62/43*sin(19*t+87/56)-18494/25)*theta(103*pi-t)*theta(t-99*pi)+(-80/29*sin(47/30-5*t)-177/25*sin(113/72-3*t)-1901/33*sin(47/30-t)+599/31*sin(2*t+52/33)+77/41*sin(4*t+14/9)+11/9*sin(6*t+61/39)+2609/12)*theta(99*pi-t)*theta(t-95*pi)+(-1566/241*sin(58/37-3*t)-1857/50*sin(47/30-t)+464/31*sin(2*t+11/7)+59/24*sin(4*t+11/7)+20/17*sin(5*t+136/29)+7997/31)*theta(95*pi-t)*theta(t-91*pi)+(-15/29*sin(67/43-5*t)-129/25*sin(36/23-4*t)-148/61*sin(36/23-3*t)-103/33*sin(69/44-2*t)-29/17*sin(80/51-t)-4753/32)*theta(91*pi-t)*theta(t-87*pi)+(-24/19*sin(32/21-25*t)-229/98*sin(48/31-22*t)-83/31*sin(54/35-19*t)-37/9*sin(31/20-17*t)-46/19*sin(36/23-14*t)-71/23*sin(25/16-12*t)-29/19*sin(57/37-10*t)-49/15*sin(25/16-7*t)-396/113*sin(14/9-5*t)-181/36*sin(36/23-4*t)-176/25*sin(47/30-3*t)-1055/57*sin(80/51-2*t)-353/21*sin(113/72-t)+17/43*sin(6*t+63/40)+1/36*sin(8*t+1/22)+9/34*sin(9*t+50/33)+113/38*sin(11*t+47/30)+5/8*sin(13*t+27/17)+45/38*sin(15*t+174/37)+11/8*sin(16*t+61/39)+188/31*sin(18*t+19/12)+16/27*sin(20*t+61/13)+5/17*sin(21*t+23/13)+39/22*sin(23*t+68/43)+12/13*sin(24*t+25/16)+12966/29)*theta(87*pi-t)*theta(t-83*pi)+(-101/25*sin(23/15-23*t)-223/46*sin(25/16-19*t)-603/116*sin(80/51-17*t)-45/58*sin(14/9-15*t)-77/41*sin(65/42-11*t)-1/36*sin(59/98-10*t)-108/25*sin(47/30-9*t)-110/41*sin(39/25-7*t)-2479/826*sin(14/9-6*t)-166/33*sin(69/44-4*t)-266/23*sin(69/44-t)+62/33*sin(2*t+146/31)+1/7*sin(3*t+38/27)+1/64*sin(5*t+6/35)+27/23*sin(8*t+37/24)+49/40*sin(12*t+179/38)+39/11*sin(13*t+65/41)+53/71*sin(14*t+80/17)+255/98*sin(16*t+36/23)+110/17*sin(18*t+49/31)+8/33*sin(20*t+31/22)+38/11*sin(21*t+50/31)+35/32*sin(22*t+47/29)+11/23*sin(24*t+69/44)+52347/113)*theta(83*pi-t)*theta(t-79*pi)+(-128/59*sin(36/23-6*t)-75/29*sin(36/23-4*t)-853/40*sin(47/30-2*t)-1601/43*sin(102/65-t)+139/25*sin(3*t+39/25)+99/38*sin(5*t+19/12)+32/19*sin(7*t+81/52)+10547/30)*theta(79*pi-t)*theta(t-75*pi)+(-1/19*sin(57/37-7*t)+129/38*sin(t+41/26)+952/47*sin(2*t+212/45)+23/12*sin(3*t+169/36)+77/19*sin(4*t+146/31)+27/40*sin(5*t+35/22)+61/36*sin(6*t+146/31)+23311/66)*theta(75*pi-t)*theta(t-71*pi)+(-217/87*sin(49/32-8*t)+4673/114*sin(t+52/33)+1582/25*sin(2*t+30/19)+271/26*sin(3*t+65/41)+1036/29*sin(4*t+65/41)+151/43*sin(5*t+221/47)+240/19*sin(6*t+30/19)+277/31*sin(7*t+179/38)+346/35*sin(9*t+77/48)+136/23*sin(10*t+52/33)+41/13*sin(11*t+75/16)+29/23*sin(12*t+64/39)+23/35*sin(13*t+29/21)+5/27*sin(14*t+79/23)+12/31*sin(15*t+59/38)+41/16*sin(16*t+50/31)+17/30*sin(17*t+52/29)+5/17*sin(18*t+67/43)+23/25*sin(19*t+127/27)+43/38*sin(20*t+29/18)+11/17*sin(21*t+96/59)+23/45*sin(22*t+50/31)+13/44*sin(23*t+49/11)+20/33*sin(24*t+56/37)+1/12*sin(25*t+127/33)+4/27*sin(26*t+34/19)+3826/57)*theta(71*pi-t)*theta(t-67*pi)+(-67/36*sin(47/30-9*t)-629/118*sin(53/34-5*t)-49/30*sin(58/39-2*t)+7133/32*sin(t+245/52)+397/23*sin(3*t+146/31)+43/31*sin(4*t+48/31)+7/16*sin(6*t+50/33)+190/73*sin(7*t+245/52)+9/26*sin(8*t+18/11)-1822/15)*theta(67*pi-t)*theta(t-63*pi)+(4511/50*sin(t+179/38)+503/126*sin(2*t+65/41)+53/6*sin(3*t+179/38)+78/47*sin(4*t+51/32)+282/83*sin(5*t+80/17)+27/47*sin(6*t+51/32)+613/27)*theta(63*pi-t)*theta(t-59*pi)+(-8/9*sin(7/17-85*t)-12/17*sin(13/9-81*t)-22/31*sin(49/39-75*t)-29/41*sin(3/8-73*t)-22/19*sin(29/43-69*t)-31/47*sin(39/32-12*t)+353/3*sin(t+202/43)+4111/19*sin(2*t+61/13)+956/25*sin(3*t+14/9)+533/20*sin(4*t+89/19)+167/21*sin(5*t+183/40)+116/25*sin(6*t+131/28)+139/22*sin(7*t+55/36)+231/25*sin(8*t+149/32)+199/23*sin(9*t+70/47)+121/39*sin(10*t+649/139)+12/35*sin(11*t+66/35)+43/25*sin(13*t+17/11)+25/12*sin(14*t+79/17)+91/27*sin(15*t+41/29)+23/32*sin(16*t+205/44)+17/31*sin(17*t+121/27)+99/28*sin(18*t+114/25)+73/47*sin(19*t+19/13)+27/32*sin(20*t+193/43)+9/14*sin(21*t+64/33)+12/37*sin(22*t+197/46)+32/51*sin(23*t+119/29)+179/36*sin(24*t+190/43)+143/46*sin(25*t+131/30)+85/43*sin(26*t+146/33)+42/31*sin(27*t+536/119)+99/100*sin(28*t+108/23)+158/53*sin(29*t+76/65)+227/27*sin(30*t+27/23)+421/23*sin(31*t+17/14)+499/29*sin(32*t+65/54)+281/26*sin(33*t+73/61)+17/36*sin(34*t+78/17)+75/7*sin(35*t+178/41)+460/27*sin(36*t+125/29)+515/34*sin(37*t+73/17)+363/43*sin(38*t+179/42)+376/51*sin(39*t+412/97)+163/23*sin(40*t+38/9)+439/53*sin(41*t+174/41)+161/24*sin(42*t+127/30)+145/22*sin(43*t+106/25)+106/19*sin(44*t+135/32)+137/33*sin(45*t+67/16)+103/20*sin(46*t+245/57)+61/29*sin(47*t+94/23)+550/97*sin(48*t+171/40)+6/17*sin(49*t+187/72)+48/25*sin(50*t+102/23)+19/40*sin(51*t+41/12)+86/23*sin(52*t+101/24)+62/35*sin(53*t+157/40)+143/71*sin(54*t+251/57)+5/3*sin(55*t+41/29)+527/111*sin(56*t+47/11)+152/39*sin(57*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        return CGPoint(x: 320 + (x * 300), y: 280 + (y * -300))
}

let path = CGPathCreateMutable()

CGPathAddLines(path, nil, points, points.count)

layer.path = path

Answer 1

There a few issues here:

1. If look at the bottom of that formula on that web site, it defines θ to be the Heaviside step function.

2. You are doing integer division. You really want to be doing floating point division. E.g. rather than 10/47, you want 10.0/47.0.

3. You are striding from 0 to 2π, but you need to go from 0 to 104π.

4. These formulae are too complicated for Swift to compile. You'll want to split them up into separate lines.

5. In that equation you found online, there's something that looked curious, namely two occurrences of θ(sqrt(sgn(sin(t/2)))). Taking the square root of the sgn function is wrong (the is no real square root of -1). So I simplified those to just θ(sin(t/2)) and the curve behaved more reasonably.

Pulling this all together, I've taken your code sample, done some macros to split up those long formulae into separate statements, you end up with something like the code snippet here: https://gist.github.com/robertmryan/427f7e9b562ae153c7c1 (Stack Overflow is not letting me paste the full code here because it exceeds the maximum allowed length of a post.)

That yields the following image:

Note, all of those annoying lines back to the origin are a result of how this Mao curve is represented. It's not a single stroke, but rather a series of separate curves misleading stored as a single set of points. You could test for 0.0, 0.0, to eliminate that, but personally I'd break it up into separate arrays of points. I'll leave that for you.