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Let an array of curves in cartesian coordinates be given in parameter representation, with curve parameter π‘ and array variable π

π₯=π₯(π‘,π)

π¦=π¦(π‘,π)

Condition for envelope is:

π/ππ‘ π₯(π‘,π) π/ππ π¦(π‘,π)=π/ππ π₯(π‘,π) π/ππ‘ π¦(π‘,π)

Solving this equation will give a relationship how the array variable π depends on the curve parameter π‘ along the envelope:

π_πππ£ (π‘)=Ξ¨(π‘)

But now here comes the question.

What if i want not the envelope of all array variables. Instead I want for example c from 0.5...1.0. How can I consider this in the function?

The target would be to give a limit for c.

Would be great to get a hint for that.

BG

MK