Hi all,
Consider a plane with circle on it. The circle and the plane have same vector/normal (i,j,k).
The inputs i have are Radius of the circle (4mm), co-ordinate of the circle center point on plane (x,y,z) and the nornal/vector of the plane / circle center point (i,j,k).
My requirement is, to place 12 points on the circle at equal distance. The co-ordinates of those points have to be calculated using the available data.
I have tried using the mathematical equations, but i am struggling to solve this. Kindly help me on this.
Thanks,
Prabhu P
Hi, if (x0,y0,z0) are the coordinates of the center and R is the radius, any point on the circle has the following coordinates:
x= x0 + R*cos(theta)
y = y0 + R*sin(theta)
z = z0
where theta is an angle between 0 and 2Pi.
Thus, if you want to locate 12 points on the circle at equal angular distance, these points simply correspond to:
theta = k*delta_theta k = 0,1,...,11
with delta_theta = Pi/6
Dear Prabhu Prakash,
Hope you find the calculations in the attached file are helpful.
I think Richard answer is correct under the assumption that
the circle lies in the plane z = z0 .
My calculations consider the general case according to your original assumptions.
Best regards
Hi Richard, thank you for the quick turnaround. But, in my case, the vector will varry accordingly. sometimes it will be towards x, or y or z. It is not a defined one and that too we cant say that the vectot will be true (i.e., purely x or y or z).
Hi Issam, thank you.
It lloks strange for me to understand, since i am not in a pure mathematical domain. I am trying yo have a deep understanding on it.
Can you please explain what the "e" stands for.
Dear Prabhu Prakash,
e1 =(1,0,0), e2 =(0,1,0) and e3 =(0,0,1)
In fact, if you substitute for θ =0 , then the coefficients of e1 , e2 , and e3
are the required coordinates of the first point and similarly for the other values of θ.
Notice that the attached calculations required the knowledge of the spherical coordinates.
You can browse an introductory text about the calculus of several variables.
PS.
One can follow another approach, but that will cost more calculations
and radicals appeared.
Best regards
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