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

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    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]
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    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.
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