I want to draw bead-stick model as I attached.
The position of the beads must be randomized in specific space I set.
Could you recommend any method?
I think that Monte Carlro method can be used for obtain the randomized coordinate of the sphere center in specific space.
Then, I draw the 3D sphere in CATIA SW using script and the coordinates.
However, I dont know how can I set constant distance between two coordinate of the center.
Thank you
Without delving into the equations. As I see, the problem you post has three conditions: the first is that the sum of the distance between the centers = 2 * radius. The second condition is that the distance from the center to the edge of the tube is > = radius (in this case I would tell you that in the real life of the second ball up, all would be against the edge, but the truth is that it is not what you asked). The third condition is that these values should be located sequentially since a ball position is fixed only KNOWING precedent one position (saying this in statistical terms you have n-1 degrees of freedom in that system. About the method of simulation of Monte Carlo I would develop a sequential system of location of the balls where the center of each ball is randomly selected from 2 * radius from previous ball, discarding the value if it does not meet the following conditions:
a) The center of the current ball is above the center of the previous ball
b) the center is between both edges
c) the horizontal distance from the center to both edges is> = radius
If all three conditions are not met the sample is discarded, another sample is selected.
I hope to be helpful...
Dear Dr Pablo Constantino
Thank you for your reply.
How about Self-Avoiding Walk method of Monte Carlo??
I am not sure of the approach you want to give to the problem of the self-avoiding walk. As I understand it, the Monte Carlo method does not offer the best solutions, but any solution (let's say brute force). If you consider getting the SAW with many steps, possibly the time to obtain an acceptable result can be long. Perhaps with better algorithms you can achieve better paths, and less time processing.
CASE 1. Free randomization. Assuming the most complicated case, which is that the step can be done in any direction, (without restricting to a specific x, y, or z axis) would say the following:
As you intend to work in the Euclidean space, I would recommend to choose randomly the next point in geographic coordinates and then, having the direction vector, obtaining the point at a distance = step from the previous point, checking in each case new point that the distance to the center does not is greater than the radius. After this you could obtain spheric coordinates of each point.
Problem: How to verify the condition of self-avoider. This is complicated for the random Euclidean space, an algorithm should be designed to find intersections between each generated segment instead of point coincidence as you work with grids, nothing that I could solve "bird flight".
CASE 2 Three-dimensional grid SAW. Restricting the path only to a movement in spherical coordinates (x, y and z), is easier. In this case, you randomly choose a random axis and advance a distance of 1 step on that axis. Then you compare if any of the previous points match the 3 coordinates and, if so, discard the point and sample another.
PROBLEM: how to get a SAW of length = n
1) Get each point as described above.
2) If the sequence reaches a point < n where there is no option to achieve the self-preventing condition for following, move back one position in the sequence and re-sample between the two remaining coordinates.
3) If the same happens with the three axes of this penultimate point, discard the sequences to the previous point and so on.
This brute force method should work, however it can be quite inefficient especially for very long chains.
Regards
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