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Strophoid

Strophoid is a cubic curve generated by increasing or diminishing the radius vector of a variable point P on a straight line by the distance PA of the point from the foot of the perpendicular drawn from the origin to the fixed line.

The polar equation is:

To plot function graph use the folowing script:

# Example
# 2D. Strophoid

# z must be zero
z = 0

# t-parameter
tmin = -0.97*pi
tmax = 0.97*pi
tgrid = 400

# Constant
a = 2

# Calculations
r = a * (1/cos(t) + tan(t))

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