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Trifoil knot

 

  0<t<2*pi ,  t(step)=pi/40

Fx(t)=-2*cos(t)-1/2*cos(5*t)+3*sin(2*t)

Fy(t)=-3*cos(2*t)+2*sin(t)-1/2*sin(5*t)

Fz(t)=2*cos(3*t)

 

Torus Knot

 

  0<t<2*pi  ,  t(step)=pi/50

Fx(t)=sin(2*x)*(10.0 + 6*cos(3*x))

Fy(t)=cos(2*x)*(10.0 + 6*cos(3*x))

Fz(t)=6*sin(3*x)

 

  0<t<2*pi   ,  t(step)=pi/50

  0<a<2*pi  ,  a(step)=pi/10

Fx(t)=sin(2*x)*(10.0 + 6*cos(3*x))

          +cos(a)

Fy(t)=cos(2*x)*(10.0 + 6*cos(3*x))

          +sin(a)

Fz(t)=6*sin(3*x)

Five Crossing Knot 1

  0<t<2*pi ,  t(step)=pi/40

Fx(t) = -88*cos(t) + 115*sin(t) - 475*cos(2*t) - 127*sin(2*t) - 87*cos(3*t) + 36*sin(3*t) + 11*cos(4*t) - 19*sin(4*t)

Fy(t) = 89*cos(t) - 32*sin(t) - 172*cos(2*t) + 294*sin(2*t) + 76*cos(3*t) + 102*sin(3*t) - 61*cos(4*t) + 113*sin(4*t)

Fz(t) = 44*cos(t) - 69*sin(t) + 34*cos(2*t) + 223*sin(2*t) + 16*cos(3*t)+ 120*sin(3*t) + 42*cos(4*t) - 125*sin(4*t)

Five Crossing Knot 2

  0<t<2*pi  ,  t(step)=pi/40

Fx(t) = - 33*cos(t) + 43*sin(t) + 214*sin(2*t) - 101*cos(3*t) - 47*sin(3*t) + 11*sin(4*t)

Fy(t) = - 57*cos(t) + 99*sin(t) - 54*cos(2*t) - 159*sin(2*t) - 117*cos(3*t) - 5*sin(3*t) - 31*cos(4*t) - 45*sin(4*t)

Fz(t) = 34*cos(t) - 21*sin(t) - 100*cos(2*t) - 93*sin(2*t) - 27*cos(3*t) - 16*sin(3*t) + 52*cos(4*t) + 84*sin(4*t)

Six Crossing Knot 1

  0<t<2*pi ,  t(step)=pi/40

Fx(t) = 12*cos(t) + 20*sin(t) - 163*cos(2*t) + 76*sin(2*t) - 87*cos(3*t) - 15*sin(3*t) - 21*cos(4*t) + 14*sin(4*t)+ 24*cos(5*t) - 50*sin(5*t)

Fy(t) = 29*cos(t) + 78*sin(t) - 180*cos(2*t) + 58*sin(2*t) + 88*cos(3*t) + 72*sin(3*t) - 14*sin(4*t)

Fz(t) = - 30*cos(t) - 78*sin(t) - 111*cos(2*t) + 37*sin(2*t) - 67*cos(3*t) - 51*sin(3*t) + 31*cos(4*t) + 8*sin(4*t) - 11*cos(5*t) + 65*sin(5*t)

Six Crossing Knot 2

  0<t<2*pi  ,  t(step)=pi/40

Fx(t) = - 6*cos(t) - 21*sin(t) - 195*cos(2*t) + 92*sin(2*t) - 64*cos(3*t) - 23*sin(3*t) - 6*cos(4*t) + 13*sin(4*t) + 24*cos(5*t) + 15*sin(5*t) + 41*sin(6*t)

Fy(t) = 21*cos(t) - 24*sin(t) - 207*cos(2*t) - 72*sin(2*t) + 112*cos(3*t) - 7*sin(3*t) - 13*cos(4*t) - 40*sin(4*t) - 27*cos(5*t) - 3*sin(5*t) - 17*cos(6*t)

Fz(t) = -18*cos(t) - 13*sin(t) + 113*cos(2*t) - 107*sin(2*t) + 86*cos(3*t) - 9*sin(3*t) - 26*cos(4*t) - 7*sin(4*t) + 24*cos(5*t) + 33*sin(5*t) + 21*cos(6*t) + 31*sin(6*t)

Six Crossing Knot 3

  0<t<2*pi  ,  t(step)=pi/40

Fx(t) = - 40*cos(t) + 32*sin(t) + 69*cos(2*t) - 12*sin(2*t) + 120*cos(3*t) - 52*sin(3*t) - 56*cos(4*t) + 46*sin(4*t) -17*sin(5*t) + 14*cos(6*t) + 19*sin(6*t)

Fy(t) = 90*cos(t) + 89*sin(t) - 142*cos(2*t) + 147*sin(2*t) + 74*cos(3*t) + 85*sin(3*t) - 56*sin(4*t) + 23*cos(5*t) + 16*cos(6*t) + 7*sin(6*t)

Fz(t) = 52*cos(t) + 64*sin(t) + 53*cos(2*t) + 35*sin(2*t) + 77*cos(3*t) - 87*sin(3*t) + 101*cos(4*t) - 19*sin(4*t) - 5*cos(5*t) + 2*sin(5*t) + 3*cos(6*t) + 9*sin(6*t)

Figure 8 Knot

  0<t<2*pi ,  t(step)=pi/40

Fx(t) = 32*cos(t) - 51*sin(t) - 104*cos(2*t) - 34*sin(2*t) + 104*cos(3*t) - 91*sin(3*t)

Fy(t) = 94*cos(t) + 41*sin(t) + 113*cos(2*t) - 68*cos(3*t) - 124*sin(3*t)

Fz(t) = 16*cos(t) + 73*sin(t) - 211*cos(2*t) - 39*sin(2*t) - 99*cos(3*t) - 21*sin(3*t)

Funny Looking Knot 1

  0<t<2*pi  ,  t(step)=pi/40

Fx(t) = - 22*cos(t) - 128*sin(t) - 44*cos(3*t) - 78*sin(3*t)

Fy(t) = - 10*cos(2*t) - 27*sin(2*t) + 38*cos(4*t) + 46*sin(4*t)

Fz(t) = 70*cos(3*t)-40*sin(3*t)

Funny Looking Knot 2

  0<t<2*pi  ,  t(step)=pi/40

Fx(t) = - 22*cos(t) - 128*sin(t) - 44*cos(3*t) - 78*sin(3*t)

Fy(t) = 11*cos(t) - 43*cos(3*t) + 34*cos(5*t) - 39*sin(5*t)

Fz(t) = 70*cos(3*t) - 40*sin(3*t) + 8*cos(5*t)- 9*sin(5*t)

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Last modified: 15/09/2002.