I want to Build Parameterized Spiral Geometry.
To offset a constant distant d on a Archimedean spiral.
Like the picture shows
The original parametric form of Archimedean Spiral is:
$$x(t) = a\cdot t\cdot \cos(t)$$
$$y(t) = a\cdot t\cdot \sin(t)$$
Then my target new equation which has same period sine waves on Archimedean spiral is : $$x(t) = (at + \sin(bt^2)) \cos(t)$$ $$y(t) = (at + \sin(bt^2)) \sin(t)$$
I successfully use the equation in the picture above draw a Parameterized Spiral on Desmos:
https://www.desmos.com/calculator/jerewqqzuc
My goal is to make a d offset on the spiral which has same period sine wave on it and control the amplitude of the sine wave. Please help me !Thanks! similar example: Equation of sine wave around a spiral?