Quick Parametric Curves
Here is the shortest possible way of generating quick parametric curves in Rhino Python. So, you may change the f, g, and h functions to test any function curve. In this Python code, the list comprehension [(f(t), g(t), h(t)) for t in [t0 + i*dt for i in range(int((t1-t0)/dt)+1)]] works by first generating a list of t values from t0 to t1 with an increment of dt using the inner comprehension. The outer comprehension then iterates over these t values, computing the x, y, and z coordinates for each point using the functions f(t), g(t), and h(t), respectively. Finally, this results in a list of 3D points I used rs.AddPolyline to create a polyline in Rhino. In Python, a lambda function is a small anonymous function with one expression. This means, it is evaluated and returned when the function is called.
Below Rhino Python script generates a 2D parametric curve in Rhino based on user-defined functions f and g. They define the x and y coordinates of points along the curve. The graph function iterates over a range of t values from t0 to t1 with a step of dt, calculates the coordinates using f and g, and adds the polyline to Rhino.
import rhinoscriptsyntax as rs, math
def graph(f, g, t0, t1, dt):
rs.AddPolyline([(f(t), g(t), 0) for t in [t0 + i*dt for i in range(int((t1-t0)/dt)+1)]])
f = lambda t: t * math.sin(t)
g = lambda t: t * math.cos(t)
graph(f, g, -1, 12, 0.01)
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