member 428835
Hi PF!
Given a 2D plane, the following is a parameterization of a circular arc with contact angle ##\alpha## to the x-axis: $$\left\langle \frac{\sin s}{\sin\alpha},\frac{\cos s - \cos\alpha}{\sin\alpha} \right\rangle : s \in [-\alpha,\alpha]$$
However, I am trying to parameterize a circle based on contact angle ##\alpha## with a wedge centered at the origin; one example of such a wedge might be ##y=|x|## (though I will change the wedge angle ##\beta##, so ideally the parameterization would be a function of both ##\alpha## and ##\beta##).
In this way, we can think of the above parameterization as a limiting value for ##\beta = \pi##.
Given a 2D plane, the following is a parameterization of a circular arc with contact angle ##\alpha## to the x-axis: $$\left\langle \frac{\sin s}{\sin\alpha},\frac{\cos s - \cos\alpha}{\sin\alpha} \right\rangle : s \in [-\alpha,\alpha]$$
However, I am trying to parameterize a circle based on contact angle ##\alpha## with a wedge centered at the origin; one example of such a wedge might be ##y=|x|## (though I will change the wedge angle ##\beta##, so ideally the parameterization would be a function of both ##\alpha## and ##\beta##).
In this way, we can think of the above parameterization as a limiting value for ##\beta = \pi##.
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