How can I generate an arc in numpy?

Question

If I know the center(x,y,z) of the arc and the diameter, and the starting and ending point, how can I generate the values between the start and the end?

Answer 1

It sounds like your "arc" is an circular approximation to a curve between two known points. I guessing this from the word "diameter" (which is twice the radius) in your post. To do this you parameterize the circle (t) -> (x,y) where t goes from 0..2pi. Given a center, two end points and a radius we can approximate a portion of the curve like this:

from numpy import cos,sin,arccos
import numpy as np

def parametric_circle(t,xc,yc,R):
    x = xc + R*cos(t)
    y = yc + R*sin(t)
    return x,y

def inv_parametric_circle(x,xc,R):
    t = arccos((x-xc)/R)
    return t

N = 30
R = 3
xc = 1.0
yc = 3.0

start_point = (xc + R*cos(.3), yc + R*sin(.3))
end_point   = (xc + R*cos(2.2), yc + R*sin(2.2))


start_t = inv_parametric_circle(start_point[0], xc, R)
end_t   = inv_parametric_circle(end_point[0], xc, R)

arc_T = np.linspace(start_t, end_t, N)

from pylab import *
X,Y = parametric_circle(arc_T, xc, yc, R)
plot(X,Y)
scatter(X,Y)
scatter([xc],[yc],color='r',s=100)
axis('equal')
show()

This example is only in 2D, but it is easily adaptable since the curve will always lie along the plane between the two points and the center.