Geo::Spline 0.16

Geo::Spline is a Perl module to calculate geographic locations between GPS fixes.

SYNOPSIS

use Geo::Spline;
my $p0={time=>1160449100.67, #seconds
lat=>39.197807, #degrees
lon=>-77.263510, #degrees
speed=>31.124, #m/s
heading=>144.8300}; #degrees clockwise from North
my $p1={time=>1160449225.66,
lat=>39.167718,
lon=>-77.242278,
speed=>30.615,
heading=>150.5300};
my $spline=Geo::Spline->new($p0, $p1);
my %point=$spline->point(1160449150);
print "Lat:", $point{"lat"}, ", Lon:", $point{"lon"}, "nn";

my @points=$spline->pointlist();
foreach (@points) {
print "Lat:", $_->{"lat"}, ", Lon:", $_->{"lon"}, "n";
}

This program was developed to be able to calculate the position between two GPS fixes using a 2-dimensional 3rd order polynomial spline.

f(t) = A + B(t-t0) + C(t-t0)^2 + D(t-t0)^3 #position in X and Y
f(t) = B + 2C(t-t0) + 3D(t-t0)^2 #velocity in X and Y

I did some simple Math (for an engineer with a math minor) to come up with these formulas to calculate the unknowns from our knowns.

A = x0 # when (t-t0)=0 in f(t)
B = v0 # when (t-t0)=0 in f(t)
C = (x1-A-B(t1-t0)-D(t1-t0)^3)/(t1-t0)^2 # solve for C from f(t)
C = (v1-B-3D(t1-t0)^2)/2(t1-t0) # solve for C from f(t)
D = (v1(t1-t0)+B(t1-t0)-2x1+2A)/(t1-t0)^3 # equate C=C then solve for D