I want to find out points whose coordinates are within the volume formed by a cone shape.

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Tamoor Shafique
Tamoor Shafique on 27 Apr 2022
Edited: Matt J on 28 Apr 2022
I have plotted few points in a 3D volume as shown in the figure below:
I want to plot a 3D righ Cone from a few specefic points as shown:
These cones are 3D volumes and I want to find out points whose coordinates are within each cone. for example which point is within yello cone and which one in red and which one in purple cone.
Can some one help?

Accepted Answer

Bruno Luong
Bruno Luong on 28 Apr 2022
Edited: Bruno Luong on 28 Apr 2022
  • the cone center is C: (3 x 1)
  • coneangle is the cone angle (0 to pi, pi corresponds to the extreme case where the cone takes the whole space)
  • the cone axis is N: (3 x 1), oriented toward the direction you consider to be in
  • Point P: (3 x 1) the point coordinates to be check
Check inside the half of the cone is
dot(P-C, N) >= cos(coneangle/2) * norm(N) * norm(P-C)
You can compute once
cos(coneangle/2) * norm(N)
if you have many points P to check.
Tamoor Shafique
Tamoor Shafique on 28 Apr 2022
I got it. sorry for being so dumb.
Thank you very much and much appreciated.
I have resolved this problem

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More Answers (1)

Matt J
Matt J on 27 Apr 2022
Draw a vector from the cone vertex to the point and compute the angle of this vector to the cone's axis. If the angle is less than the angular width of the cone, then the point is inside the cone. This assumes that the cone is not of finite length.

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