Results 1 to 2 of 2

Math Help - 3D Engine Geometry Shortest distance from a point to a line in 3D

  1. #1
    Newbie
    Joined
    Apr 2011
    From
    Ireland
    Posts
    8

    3D Engine Geometry Shortest distance from a point to a line in 3D

    My notes for this topic are not very clear and certain steps of how to do this type of calculation have been skipped. I was hoping someone could do this sum out for me so I could use it as an example it would really be appreciated.


    s = starting point v = any q =direction from any point

    d =
    ._____________________
    .| ........................ 2
    .| .........2 [(q -s).v]
    .| (q -s) - _________
    .|................ .....2
    V................|v|


    Find the distance between the point q = [0,2,2] and the line defined by: p(t)= [ 0,0,0,] + t[1,0,0]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by aoibha View Post
    My notes for this topic are not very clear and certain steps of how to do this type of calculation have been skipped. I was hoping someone could do this sum out for me so I could use it as an example it would really be appreciated.


    s = starting point v = any q =direction from any point

    d =
    ._____________________
    .| ........................ 2
    .| .........2 [(q -s).v]
    .| (q -s) - _________
    .|................ .....2
    V................|v|


    Find the distance between the point q = [0,2,2] and the line defined by: p(t)= [ 0,0,0,] + t[1,0,0]
    That is an ingenious (but not easy to read!) way to write the formula



    The line "s = starting point v = any q =direction from any point" seems to be completely garbled and misleading. I think that what it ought to say is this: you are given a point q, and a line whose equation is p(t) = s + tv. Here, s is a point on the line (the "starting point") and v is the direction vector of the line.

    So to find the distance from the point [0,2,2] to the line p(t)= [0,0,0,] + t[1,0,0], you should take q = [0,2,2], s = [0,0,0], v = [1,0,0], and plug those vectors into the formula.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 22nd 2013, 03:40 PM
  2. Coordinate geometry- point to line distance
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 25th 2011, 03:04 PM
  3. Replies: 2
    Last Post: January 25th 2011, 05:46 AM
  4. Shortest distance between point and line
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: June 1st 2010, 01:48 AM
  5. Replies: 1
    Last Post: April 15th 2009, 08:47 AM

Search Tags


/mathhelpforum @mathhelpforum