javascript - Projecting a point onto a path -

suppose have ordered array containing points (lat, lon) describing path, , have point (lat, lon) describing current location.

how can project point onto path (and place point in appropriate place in array)?

what tried searching nearest 2 points , assume it's in middle of them. it's guess, fails.

what way of doing this?

i see this:

• p0,p1 path line segment endpoints
• p position
• q' closest point on line in 3d cartessian
• q q' corrected spherical projection

so:

1. convert points 3d cartessian coordinates

2. compute perpendicular distance point , line

   • q'=p0+(dot(p-p0,p1-p0)*(p1-p0)/(|p-p0|*|p1-p0|))
   • perpendicular_distance = |p-q'|

3. find segment smallest perpendicular_distance

   and use rest of bullets

4. compute q

   if use sphere instead of ellipsoid know radius if not either compute radius algebraically or use average:

   r=0.5*(|p0-(0,0,0)|+|p1-(0,0,0)|) 

   assuming (0,0,0) earth's center. can more precise if weight position:

   w=|q'-p0|/|p1-p0| r=(1-w)*|p0-(0,0,0)|+w*|p1-(0,0,0)| 

   now correct position of q'

   q=q'*r/|q'| 

   set vector q' q size r if not obvious enough. |p0-(0,0,0)|=|p0| wanted sure how got ...

5. convert q cartesian spherical coordinates

[notes]

• |a| size of vector a done like: |a|=sqrt(ax*ax+ay*ay+az*az)

• dot(a,b) dot product of vectors a,b done like: dot(a,b)=(a.b)=ax*bx+ay*by+az*bz

  if path not complex shaped can use binary search find closest segment. distance comparison not need sqrt ...