# Computing Apex of Vertical Cone Using Data Points

1. Apr 13, 2008

### Saeid

Dear All
I have a problem that can be represented in two different forms.
Problem is related to propagation of waves in 2D space with respect of time (time is Z axis).
I have three random points in the 3D Space.
How many vertical right circular, infinite cones with specific predetermined angle between conical surface and axis we can find that passes these three points?
I need the 3D coordinates of the apex point.
Three points are in one side of cone. I.e., if we draw a plane perpendicular to axis of cone that meets the axis in apex point, all three points will fall in one side of the plane.
Another representation of the problem is, if I draw three vertical right circular, infinite cones with specific predetermined angle between conical surface and axis which their apex points are these three points in the 3D space, how many points I can find that belongs to surface of these three cones? Or, in how many points these three cones coincide with each other?
What will be the result if I use four different points in the space?
If my points (data points) have noise (inaccuracy) what methods exist or you suggest for solving it?
In all cases the axis of the cone is parallel with Z axis.
Do you know any text book or paper related to this problem?

Thank you