SOLVED: Find closest point on line

[Jenna Huntsman]

Hey all,

My math knowledge has failed me and I need some advice:

I need to find a point on a line, with vector A being the line's origin and vector B being it's direction (the line is of infinite length).

I need to find the closest point to vector P on the line.

How can I do this?

I've been looking at these functions (from the LSL wiki) but they're producing garbage numbers:

Pulled from :http://wiki.secondlife.com/wiki/Geometric

vector gLXdV(vector O,vector D,vector A){
    return (O-A)-((O-A)*D)*D;}

vector gLXnX(vector O,vector D,vector A){
    return gLXdV(O,D,A) + A;}

//O = Origin, D = Direction, A = abitrary point.

Thanks!

 

In the above example, I need to find C

 

EDIT:

Solved it, just needed to take a break

vector LinePoint(vector origin, vector dir, vector point)
{
    //This made Jenna sad :C
    vector dirNorm = (dir-origin)/llVecDist(dir,origin);
    vector x = point-origin;
    vector Lp = dirNorm*((x.x*dirNorm.x)+(x.y*dirNorm.y)+(x.z*dirNorm.z)); //offset relative to the origin
    return Lp+origin;
}

 

Edited February 5, 2022 by Jenna Huntsman
Solved, had a brainfart

[Quistess Alpha]

One minor improvement,

(x.x*dirNorm.x)+(x.y*dirNorm.y)+(x.z*dirNorm.z)

is actually the same as

(x*dirnorm)

And writing it myself because I find the problem interesting and (no offense yours might be more efficient) I find your version a bit hard to parse:

vector LinePoint(vector origin, vector dir, vector point)
{
    vector dirNorm = llVecNorm(dir-origin);
    float dist = llVecDist(dir,point);
    return origin + dirNorm*dist;
}

 

[Jenna Huntsman]

19 minutes ago, Quistess Alpha said:

One minor improvement,

(x.x*dirNorm.x)+(x.y*dirNorm.y)+(x.z*dirNorm.z)

is actually the same as

(x*dirnorm)

And writing it myself because I find the problem interesting and (no offense yours might be more efficient) I find your version a bit hard to parse:

vector LinePoint(vector origin, vector dir, vector point)
{
    vector dirNorm = llVecNorm(dir-origin);
    float dist = llVecDist(dir,point);
    return origin + dirNorm*dist;
}

 

No worries - the solution I came to was based on a formula I found elsewhere which (presumably) couldn't multiply vectors directly; hence writing it out long form - my brain isn't working very well today

[Quistess Alpha]

oop, and it turns out your version is more correct, geometry is hard: https://en.wikipedia.org/wiki/Dot_product

vector LinePoint(vector origin, vector dir, vector point)
{
    vector dirNorm = llVecNorm(dir-origin);
    float dist = dirnorm*(point-origin);
    return origin + dirNorm*dist;
}

Was scratching my head for a bit trying to figure out what the dot product was doing in there. turns out AC and AP have different lengths. (AP is longer)

[arton Rotaru]

23 hours ago, Jenna Huntsman said:

I've been looking at these functions (from the LSL wiki) but they're producing garbage numbers:

Pulled from :http://wiki.secondlife.com/wiki/Geometric

vector gLXdV(vector O,vector D,vector A){
    return (O-A)-((O-A)*D)*D;}

vector gLXnX(vector O,vector D,vector A){
    return gLXdV(O,D,A) + A;}

//O = Origin, D = Direction, A = abitrary point.

FWIW, these do work when you feed in D as a direction (D-O) already,  as a unit vector.