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# Hypotrochoid

Hypotrochoid is a curve traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.

The parametric equations for a Hypotrochoid are:  Use the folowing script to plot function Hypotrochoid:

 # Example # 2D. Hypotrochoid scale = 8 # z must be zero z = 0 # t-parameter tmin = 0 tmax = 6*pi tgrid = 400 # Constant a = 5.0 b = 3.0 d = 5.0 k = a - b m = (a - b) / b # Calculations x = k * cos(t) + d * cos(m * t) y = k * sin(t) - d * sin(m * t)

Special case. Hypotrochoid with d = r: Hypocycloid

 # Example # 2D. Hypotrochoid scale = 8 # z must be zero z = 0 # t-parameter tmin = 0 tmax = 6*pi tgrid = 400 # Constant a = 5.0 b = 3.0 d = 3.0 k = a - b m = (a - b) / b # Calculations x = k * cos(t) + d * cos(m * t) y = k * sin(t) - d * sin(m * t)

Special case. Hypotrochoid with R = 2r: Ellipse

 # Example # 2D. Hypotrochoid scale = 8 # z must be zero z = 0 # t-parameter tmin = 0 tmax = 6*pi tgrid = 400 # Constant a = 6.0 b = 3.0 d = 5.0 k = a - b m = (a - b) / b # Calculations x = k * cos(t) + d * cos(m * t) y = k * sin(t) - d * sin(m * t)