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View Full Version : Create an arc between two points


hotshotiguana
03-22-2012, 09:11 AM
I have two x, z points - for example ([1.722, .46], [3.94, .026]) - and I am trying to draw an arc (or a great (or small) circle) between the two points. I also have calculated 50 control x, z points between the points if this is beneficial to the solution.

Currently, I am using viz.LINE_STRIP to create about 50 line segments between the two points and it doesn't look at all.

Any help would be great and please let me know if more information is needed.

Thanks,
Chris

farshizzo
03-22-2012, 10:11 AM
What exactly is wrong with your current solution? Is the arc not smooth enough? If so, you will just need to create more control points.

hotshotiguana
03-22-2012, 10:44 AM
I am not calculating the y-values correctly. When drawn, it looks like a staircase between the two points.

farshizzo
03-22-2012, 10:56 AM
Can you post some sample code?

hotshotiguana
03-22-2012, 11:28 AM
So I transferred some Matlab code into Python and then did a 3D plot, see below code.

import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

def get_sphere_line(center, pt_1, pt_2):
"""
Get the coordinates to craft an arc
"""
x0, y0, z0 = center
x1, y1, z1 = pt_1
x2, y2, z2 = pt_2
v1 = [x1 - x0, y1 - y0, z1 - z0] # Vector from center to 1st point
r = np.linalg.norm(v1) # The radius
v2 = [x2 - x0, y2 - y0, z2 - z0] # Vector from center to 2nd point
v3 = np.cross(np.cross(v1, v2), v1) # v3 lies in plane of v1 & v2 and is orthog. to v1
v3 = r*v3/np.linalg.norm(v3) # Make v3 of length r
# Let t range through the inner angle between v1 and v2
t = np.linspace(0, np.arctan2(np.linalg.norm(np.cross(v1, v2)), np.dot(v1, v2)), num=100)[:, np.newaxis].T
v = np.array(v1)[:, np.newaxis]*np.cos(t) + np.array(v3)[:, np.newaxis]*np.sin(t) # v traces great circle path, relative to center
xs, ys, zs = v[0, :] + x0, v[1, :] + y0, v[2, :] + z0
return xs, ys, zs
xs, ys, zs = get_sphere_line([2.85, 0.001, 0.238], [1.722, .001, .46], [3.94, 0.001, 0.026])
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(xs, ys, zs)
plt.show()

The below code is how I am trying to implement it in Vizard, but it isn't working properly.

vs = get_sphere_line([2.85, 0.001, 0.238], [1.722, .001, .46], [3.94, .001, 0.026])
viz.startLayer(viz.LINE_STRIP)
viz.lineWidth(5)
viz.vertexColor(viz.YELLOW)
for v in vs:
viz.vertex([v[0], v[1], v[2]])
viz.endLayer()

hotshotiguana
03-22-2012, 12:07 PM
I found the problem, here is my solution in Vizard:
xs, ys, zs = get_sphere_line([2.85, -1., 0.238], [1.722, .001, .46],
[3.94, .001, 0.026])
viz.startLayer(viz.LINE_STRIP)
viz.lineWidth(5)
viz.pointSize(5)
viz.vertexColor(viz.YELLOW)
for pos in zip(xs, ys, zs):
viz.vertex([pos[0], pos[1], pos[2]])
points = viz.endLayer()