# NAME

Geo::Spline - 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
my \$p1={time=>1160449225.66,
lat=>39.167718,
lon=>-77.242278,
speed=>30.615,
my \$spline=Geo::Spline->new(\$p0, \$p1);
my %point=\$spline->point(1160449150);
print "Lat:", \$point{"lat"}, ", Lon:", \$point{"lon"}, "\n\n";

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

# DESCRIPTION

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``````

# CONSTRUCTOR

## new

``  my \$spline=Geo::Spline->new(\$p0, \$p1);``

# METHODS

## ellipsoid

Method to set or retrieve the current ellipsoid object. The ellipsoid is a Geo::Ellipsoids object.

``````  my \$ellipsoid=\$obj->ellipsoid;  #Default is WGS84

\$obj->ellipsoid('Clarke 1866'); #Built in ellipsoids from Geo::Ellipsoids
\$obj->ellipsoid({a=>1});        #Custom Sphere 1 unit radius``````

## point

Method returns a single point from a single time.

``````  my \$point=\$spline->point(\$t1);
my %point=\$spline->point(\$t1);``````

## pointlist

Method returns a list of points from a list of times.

``````  my \$list=\$spline->pointlist(\$t1,\$t2,\$t3);
my @list=\$spline->pointlist(\$t1,\$t2,\$t3);``````

## timelist

Method returns a list of times (n+1). The default will return a list with an integer number of seconds between spline end points.

``````  my \$list=\$spline->timelist(\$samples);
my @list=\$spline->timelist(); ``````

# TODO

Integrate a better Lat, Lon to meter conversions.

# BUGS

Please send to the geo-perl email list.

# LIMITS

I use a very rough conversion from degrees to meters and then back. It is accurate for short distances.

# AUTHOR

Michael R. Davis qw/perl michaelrdavis com/