Bigger picture, I have a point cloud containing a Zylinder (not the whole zylinder as points, just half of the surface, data is from a 3d scan). I have one given point on this Zylinder and its radius (but no information, so the given point can be anywhere on the zylinder) to start for segmenting all points of the Zylinder. For a fast approach I do not want to check all points and also not do some region growing from neighbour to neighbour. So I thought I'll go with a possion disk sampling of the points and check with some condition if the sampled point could be part of the Zylinder.
So when a new point is sampled I want to check if it is possibly on the zylinder. Given the two points now, I know P1 is on the Zylinder. The distance from P1 to P2 is the radius r from a sphere which should intersect the Zylinder if P2 is also on the zylinder. I guess there is not a perfect fit for this condition, with just one point to check, but later on there will be more near by points which are assumed to be on the zylinder surface and then it should be a suitable condition if P2 seems to be on the surface compaired with several other points known to be on the surface.
However, I am not into 3d geometry math. So I fail on building the condition formular.
Anyone an idea how to check if a Point part of the intersection of a sphere and a zylinder?