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I have

  • a cylinder C
  • a straight line segment $L = L_0 \rightarrow L_1$ on the surface of the cylinder. A helix in 3D
  • a point P on the surface of the cylinder.
  • Note that the equation to the line, in the coordinate system of the cylinder surface is $L = L_0 + \mathbf{v}t$ where $\mathbf{v} = L_1 - L_0$

I wish to find closest point on L from P.

Note L is finite length and can have any orientation and all distances are measured along the surface of the cylinder.

bradgonesurfing
  • 257
  • As it is a striaght line with the above equation lying on the cylinder, I think this st. line should be parallel to the axis of the cylinder, and thus to find the point Q on L which satifies shortest distance between L and P, it is enough to find the intersection between the st line L and the ring of the cylinder which passes through P and has axis same as axis of cylinder. – Nizar Jan 27 '16 at 12:18
  • I think you have misunderstood. It is a straight line in the coordinate system of the surface of the cylinder. In 3D it is a helix. I updated the question to make that clear. – bradgonesurfing Jan 27 '16 at 12:19
  • How are you measuring the distance from P to L $-$ along the surface of the cylinder, or in 3-space? – TonyK Jan 27 '16 at 12:22
  • If you are measuring the distance in 3-space, see this question. It doesn't allow for L being finite, so you will have to modify the answer accordingly. – TonyK Jan 27 '16 at 12:34
  • All distances are measured along the surface of the cylinder. Updated question to make this clear sorry. – bradgonesurfing Jan 27 '16 at 12:38

0 Answers0