SetDirectory["C:\\drorbn\\AcademicPensieve\\2015-09\\K34"]

T=π(1-Cos[t/2]);
R=-Cos[t/2];
A=3.5;
b=-2.6;
a=1.95;
r=0.2*0.4*(9*(R^4)+1)*(Sqrt[1-(R^2)]);
circ= {0,Sin[θ]*r,Cos[θ]*r};
dx=-0.5545454545*((Sin[T])^2)+6.1*(10+Cos[T])/11*Cos[T]+1.3*Sin[T/2];
dy=4.875*Cos[1.95*T+0.05*π];
n=(Sqrt[(dx^2)+(dy^2)]);
dx=dx/n;
dy=dy/n;
rotMat=(({{dx, -dy, 0}, {dy, dx, 0}, {0, 0, 0.5*(1+2*(((t/π-1))^2))}}));
result=rotMat.circ;
coords={
0.2*((A-b)*((10.0+Cos[T])/11.0)*Sin[T]+b*Cos[T/2])+result[[1]],
0.5*Sin[a*T-(a-2)*π]+result[[2]],
result[[3]],
If[t<7/8*π, (1-Cos[t*8/7])/2, 0.7*(Cos[8*t-7*π])+0.3]
};

ColorFunction->Function[{x,y,z,t,θ}, Hue[coords[[4]]]]

MakeImage["Dalvit2KnotBroken",
ParametricPlot3D[coords[[1;;3]], {t,0,2π}, {θ,0,2π},
RegionFunction->Function[{x,y,z,t,θ}, Not[
z>0.075∨3.04<t<3.09∨3.2<t<3.25∨(0.08^2)<2(((t-0.72))^2)+(((θ-π/2))^2)<(0.2^2)∨(0.08^2)<2((((2π-t)-0.72))^2)+(((θ-3π/2))^2)<(0.2^2)
]],
Boxed -> False, Axes -> None, Mesh -> None, PlotStyle -> Opacity[0.7], PlotPoints->400,
ViewPoint->{1.80444,-2.11026,1.93412},ViewVertical->{-0.0657752,0.0609542,5.23912}
], ImageSize->720]