IntersectQ: See if a line intersects with a point up to some precision

IntersectQ

(* Written for http://stackoverflow.com/q/4126473/421225 *)

(* SlowIntersectQ is too slow to use in EdgeRenderingFunction *)

SlowIntersectQ[{start_,end_},pt_,r_?Positive]/;Length[start]==Length[end]==Length[pt]:=Module[{t},
    TrueQ[NMinValue[{Norm[((1.-t)start+t end)-pt],0<t<1},t,WorkingPrecision->$MachinePrecision]<r]]

(* Since we only care about straight lines, here's a faster implementation *)
(* from: http://stackoverflow.com/q/849211/421225 *)

linDistance[{start_,end_},pt_]:=Module[{param},
  param=((pt-start).(end-start))/Norm[end-start]^2;
  Which[
    param<0,EuclideanDistance[start,pt], (*If outside bounds*)
    param>1,EuclideanDistance[end,pt],(*If outside bounds*)
    True,EuclideanDistance[pt,start+param (end-start)] (*Normal distance*)
  ]];

IntersectQ[{start_,end_},pt_,r_?Positive]/;Length[start]==Length[end]==Length[pt]:=Module[{t},
    TrueQ[linDistance[{start,end},pt]<r]]

(* Test the function *)

IntersectQ[{{-1,0},{1,0}},#,.05]&/@{{0,0},{0,0.01},{0,0.05},{0,0.1}}=={True,True,False,False}