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标题: ios - 如何使用这个复杂的参数方程在 iOS 中绘制曲线 [打印本页]

作者: 菜鸟教程小白 时间: 2022-12-12 10:46
标题: ios - 如何使用这个复杂的参数方程在 iOS 中绘制曲线

刚找到这个在 iOS 中使用参数方程绘制的演示代码

可以看到关键代码就是生成这个点数组

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))
}

这只是使用 this equation

现在我想画的是更复杂的一个mao curve

但我遇到的问题是网站提供的参数方程中有一个数学符号，我不知道如何转换为iOS代码，这个

更新:现在我遇到了一个新问题:“表达式太复杂，无法在合理的时间内解决”，除了像心形曲线在上面的 y 中所做的那样将其分解成小表达式之外的任何想法，因为手动分解它太过分了

下面是完整的代码

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*t+47/39)+95/33*sin(58*t+49/11)+1381/345*sin(59*t+19/18)+167/125*sin(60*t+57/13)+19/31*sin(61*t+31/27)+37/32*sin(62*t+35/32)+63/94*sin(63*t+119/26)+16/13*sin(64*t+74/53)+29/6*sin(65*t+121/29)+57/47*sin(66*t+47/26)+61/27*sin(67*t+760/169)+241/39*sin(68*t+149/150)+31/12*sin(70*t+34/29)+49/37*sin(71*t+60/13)+73/37*sin(72*t+25/24)+25/28*sin(74*t+49/29)+42/23*sin(76*t+45/37)+69/25*sin(77*t+98/23)+41/27*sin(78*t+37/24)+29/15*sin(79*t+131/31)+16/11*sin(80*t+13/12)+29/28*sin(82*t+94/29)+11/21*sin(83*t+177/38)+32/17*sin(84*t+43/47)+31/28*sin(86*t+13/7)+145/42*sin(87*t+192/49)+49/32*sin(88*t+19/21)+67/48*sin(89*t+1/13)+33/28*sin(90*t+151/48)+40/21*sin(91*t+121/31)+33/20*sin(92*t+11/15)+106/49*sin(93*t+1/9)+17/19*sin(94*t+98/59)+7/3*sin(95*t+176/45)+97/29*sin(96*t+20/31)+50/27*sin(97*t+2/9)+17/7*sin(98*t+136/41)+16260/23)*theta(59*pi-t)*theta(t-55*pi)+(-142/41*sin(39/25-17*t)-68/33*sin(38/25-15*t)-25/12*sin(23/15-13*t)-23/12*sin(65/42-12*t)-497/33*sin(36/23-6*t)-105/19*sin(25/16-5*t)-1996/33*sin(47/30-4*t)-802/73*sin(113/72-t)+11015/34*sin(2*t+212/45)+354/35*sin(3*t+146/31)+109/14*sin(7*t+221/47)+16/15*sin(8*t+41/25)+217/69*sin(9*t+144/31)+17/13*sin(10*t+233/50)+82/29*sin(11*t+164/35)+3/7*sin(14*t+36/23)+224/79*sin(16*t+35/22)+43/14*sin(18*t+69/43)+7930/11)*theta(55*pi-t)*theta(t-51*pi)+(-13/25*sin(19/28-9*t)-16/33*sin(38/41-7*t)+181/15*sin(t+112/27)+159/32*sin(2*t+33/49)+259/38*sin(3*t+106/31)+57/13*sin(4*t+109/35)+8/27*sin(5*t+20/31)+35/22*sin(6*t+77/25)+41/32*sin(8*t+34/19)+23/42*sin(10*t+44/41)+22/35*sin(11*t+117/25)+17/32*sin(12*t+13/22)-9500/9)*theta(51*pi-t)*theta(t-47*pi)+(-2423/42*sin(36/29-t)-38027/36)*theta(47*pi-t)*theta(t-43*pi)+(-232/21*sin(59/47-5*t)-380/27*sin(2/17-4*t)-472/19*sin(19/18-3*t)+3307/21*sin(t+7/37)+1527/17*sin(2*t+76/65)+25/33*sin(6*t+23/20)+281/36*sin(7*t+134/33)+37/27*sin(8*t+57/25)+52/23*sin(9*t+54/13)+21/5*sin(10*t+19/9)+54/25*sin(11*t+172/51)+105/32*sin(12*t+53/46)-12945/26)*theta(43*pi-t)*theta(t-39*pi)+(-11/30*sin(36/43-11*t)-7/23*sin(3/11-7*t)-73/19*sin(1/49-3*t)-19/28*sin(4/31-t)+9/13*sin(2*t+21/62)+905/226*sin(4*t+4/25)+24/19*sin(5*t+111/40)+17/27*sin(6*t+41/23)+13/27*sin(8*t+57/20)+13/31*sin(9*t+5/27)+5/23*sin(10*t+59/18)+13/77*sin(12*t+123/37)+7606/23)*theta(39*pi-t)*theta(t-35*pi)+(-2/9*sin(7/25-11*t)-2/17*sin(17/32-9*t)-4/31*sin(25/17-7*t)-9/20*sin(41/39-5*t)+7/4*sin(t+53/28)+34/9*sin(2*t+109/26)+45/8*sin(3*t+217/51)+49/38*sin(4*t+37/36)+7/22*sin(6*t+90/181)+5/23*sin(8*t+11/25)+3/29*sin(10*t+169/41)+4/21*sin(12*t+305/76)+6727/20)*theta(35*pi-t)*theta(t-31*pi)+(-5/3*sin(23/34-3*t)-2989/130*sin(9/28-t)+13/30*sin(2*t+37/16)+5/6*sin(4*t+29/10)+15/41*sin(5*t+55/46)+5/23*sin(6*t+91/27)+9085/27)*theta(31*pi-t)*theta(t-27*pi)+(-56/45*sin(16/17-3*t)-2344/125*sin(19/43-t)+5/6*sin(2*t+20/19)+26/23*sin(4*t+75/31)+4/35*sin(5*t+654/187)+28/113*sin(6*t+118/37)+14511/44)*theta(27*pi-t)*theta(t-23*pi)+(-31/17*sin(29/48-14*t)-50/27*sin(33/98-13*t)-41/15*sin(11/39-10*t)-133/66*sin(5/18-8*t)-1171/19*sin(7/29-2*t)-1421/10*sin(27/22-t)+1347/59*sin(3*t+25/8)+942/43*sin(4*t+29/20)+740/49*sin(5*t+18/17)+47/8*sin(6*t+132/35)+167/13*sin(7*t+169/94)+67/19*sin(9*t+53/33)+16/81*sin(11*t+49/44)+35/18*sin(12*t+4/15)+9/23*sin(15*t+116/37)+19/11*sin(16*t+9/37)+2031/17)*theta(23*pi-t)*theta(t-19*pi)+(-23/30*sin(25/63-12*t)-163/109*sin(17/27-10*t)-sin(20/31-8*t)-104/11*sin(22/35-3*t)-98/27*sin(53/52-t)+138/55*sin(2*t+251/58)+177/17*sin(4*t+8/37)+269/84*sin(5*t+75/17)+28/29*sin(6*t+72/23)+20/19*sin(7*t+55/28)+68/45*sin(9*t+66/31)+31/37*sin(11*t+155/59)-6747/22)*theta(19*pi-t)*theta(t-15*pi)+(-103/38*sin(25/34-8*t)-439/219*sin(19/17-7*t)-159/31*sin(3/13-5*t)-35/26*sin(7/24-4*t)-387/83*sin(5/7-3*t)+944/19*sin(t+79/26)+329/31*sin(2*t+17/36)+25/12*sin(6*t+155/44)-4790/31)*theta(15*pi-t)*theta(t-11*pi)+(-84/31*sin(92/61-4*t)-3*sin(14/9-3*t)-381/31*sin(39/35-2*t)+925/46*sin(t+259/86)+48/43*sin(5*t+53/16)+27/29*sin(6*t+105/44)+11/21*sin(7*t+38/21)+7/31*sin(8*t+227/76)+11503/35)*theta(11*pi-t)*theta(t-7*pi)+(-16/21*sin(13/16-7*t)+245/12*sin(t+26/21)+199/20*sin(2*t+11/20)+47/26*sin(3*t+17/7)+70/51*sin(4*t+41/21)+22/9*sin(5*t+258/59)+29/31*sin(6*t+242/81)+7/24*sin(8*t+13/22)+26/37*sin(9*t+55/64)+8693/27)*theta(7*pi-t)*theta(t-3*pi)+(-16/9*sin(27/31-12*t)-103/38*sin(37/36-8*t)-63/25*sin(5/26-7*t)-58204/85*sin(4/21-t)+371/34*sin(2*t+109/27)+632/39*sin(3*t+71/27)+262/33*sin(4*t+13/16)+283/41*sin(5*t+43/24)+58/33*sin(6*t+79/32)+59/21*sin(9*t+77/20)+42/19*sin(10*t+81/35)+178/179*sin(11*t+17/19)+11/35*sin(13*t+67/16)+11/25*sin(14*t+14/13)+11/30*sin(15*t+135/29)+16/49*sin(16*t+70/43)+6851/32)*theta(3*pi-t)*theta(t+pi))*theta(sqrt(sgn(sin(t/2))))

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

let path = CGPathCreateMutable()

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

layer.path = path

Best Answer-推荐答案

这里有几个问题:

如果查看该网站上该公式的底部，它会将 θ 定义为 Heaviside step function .

你正在做整数除法。你真的很想做浮点除法。例如。而不是 10/47，您需要 10.0/47.0。

您正从 0 迈向 2π，但您需要从 0 迈向 104π.

这些公式太复杂，Swift 无法编译。您需要将它们分成不同的行。

在您在网上找到的那个等式中，有一些看起来很奇怪的东西，即 θ(sqrt(sgn(sin(t/2)))) 的两次出现。 sgn 函数的平方根是错误的(-1 不是真正的平方根)。所以我将它们简化为 θ(sin(t/2)) 并且曲线表现得更合理。

将所有这些放在一起，我采用了您的代码示例，执行了一些宏以将这些长公式拆分为单独的语句，您最终得到类似于此处的代码片段的内容:https://gist.github.com/robertmryan/427f7e9b562ae153c7c1 (Stack Overflow 不允许我在此处粘贴完整代码，因为它超出了帖子的最大允许长度。)

这会产生以下图像:

请注意，所有这些回到原点的恼人线条都是毛泽东曲线呈现方式的结果。它不是单个笔划，而是一系列单独的曲线，误导性地存储为一组点。您可以测试 0.0, 0.0 以消除它，但我个人会将其分解为单独的点数组。我会把它留给你。

关于ios - 如何使用这个复杂的参数方程在 iOS 中绘制曲线，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/35703391/

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