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Cissoid

The name Cissoid was first used by de Castillon in Philosophical Transactions of the Royal Society in 1741.

The Cissoid is an unbounded plane curve with a single cusp, which is symmetric about the line of tangency of the cusp, and whose pair of symmetrical branches both approach the same asymptote as a point moving along the Cissoid moves farther away from the cusp. Moreover, if a circle is drawn passing through the cusp and tangent to the asymptote, then any line joining the cusp and a point on the Cissoid can be extended so that it intersects the asymptote, and the length of such extension is equal to the length between the cusp and the intersection of the line with the circle.

Its polar equation is:

The parametric equations for the Cissoid are:

To plot function graph use the folowing script:

# Example
# 2D. Cissoid

# z must be zero
z = 0

# t-parameter
tmin = 0.2*pi
tmax = 1.8*pi
tgrid = 400

# Constant
a = 3

# Calculations
r = 2*a * (1/cos(t) - cos(t))

x = r * cos(t)
y = r * sin(t)