[Csnd] Question re: Canonical manual description of wterrain2 curve param.

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1

These two equations appear identical to me. I'm not great at math but I assume there should be a difference between the two. Am I simply overlooking something?
kcurve=2: limacon
        fx(t) = kx + krx * sin(t) * (cos(t) + kcurveparam)
        fy(t) = ky + kry * cos(t) * (cos(t) + kcurveparam)
kcurve=3: cornoid
        fx(t) = kx + krx * sin(t) * (cos(t) + kcurveparam)
        fy(t) = ky + kry * cos(t) * (cos(t) + kcurveparam)

Can anyone suggest which one is incorrect and what the correct equation is?

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2

Looking this up, it appears the two equations, which are the same, describe a limaçon shape but someone needs to check that the code agrees to it.

The cornoid seems to have a cos^2 inside the parenthesis.

That said, I know next to nothing about the subject.

Prof. Victor Lazzarini
Maynooth University
Ireland

3

The correct formula for cornoid which is also implemented in the opcode is

fx(t) = kx + krx * cos(t) * cos(2*t);
fy(t) = ky + kry * sin(t) * (kcurveparam + cos(2*t));

it's wrong in the manual.

An visual demo of the wterrain2 opcode can be found here: