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More Shape-Shifting in 3D based on Intersecting Cylinders

Erik Mahieu
Posted 7 years ago
POSTED BY: Erik Mahieu
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Erik Mahieu
Erik Mahieu
Posted 7 years ago

The two additional arguments t1 and t2 are the angles t in the ParametricPlot3D that will split the ring"set" into 2 separate "rings". By lack of finding a formula, I determined these two angles experimentally by means of another Mathematica notebook With a Manipulate introducing the two new variables t1 and t2 this was very easy. See the notebook attached in which the complete code for the rings is included

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POSTED BY: Erik Mahieu

roseRingsetCF might be defined something like?

roseRingsetCF=Compile[{{\[Theta], _Real},{r, _Real},{\[Theta]0, _Real},{d, _Real},{n, _Integer},{\[Alpha], _Real}},Module[{t1,t2},(*2 part composite curve*)t1=Sec[2 ArcTan[Cot[n (\[Theta]-\[Theta]0)/2]]/n];
t2=Sec[\[Alpha]] Sqrt[-d^2+r^2+2 d Cos[\[Pi]/n] t1 Sin[\[Theta]]-Cos[\[Pi]/n]^2 t1^2 Sin[\[Theta]]^2];
{(*part1*)roseRing1CF[\[Theta],r,\[Theta]0,d,n,\[Alpha],t1,t2],(*part 2*)roseRing2CF[\[Theta],r,\[Theta]0,d,n,\[Alpha],t1,t2]}]];

Michael
POSTED BY: Michael Kelly

There is no function roseRingsetCF function defined in [2]. Instead there are functions roseRing1CF and roseRing2CF. However these functions take 8 arguments whereas roseRingsetCF takes only 6 arguments. I understand that roseRingsetCF will probably be defined along the lines of 

Through[{roseRing1CF,roseRing2CF}[##]]&[t,r,\[Theta]0,d,n,\[Pi]/2+\[Alpha],t1,t2]

but this still leaves unspecified the last two arguments t1 and t2. Are they to be defined like t and s in the definition of polyRingsetCF ?

Regards

Michael Kelly
POSTED BY: Michael Kelly

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