# Finding Points on Curves at Arc Length Distances

This guide demonstrates how to find points that are a specified distance from the start of curves using C/C++.

## Problem

For a given length from the beginning of a curve, you would like to get the curve’s parameter at this point.

## Solution

The two functions on ON_Curve that are useful for determining the parameter of the point on a curve that is a prescribed arc length distance from the start of a curve are:

• ON_Curve::GetNormalizedArcLengthPoint
• ON_Curve::GetNormalizedArcLengthPoints

To use these functions, calculate a normalized arc length parameter. That is, a parameter on the curve where 0.0 = the start of the curve, 0.5 = the midpoint of the curve, and 1.0 = the end of the curve.

NOTE: To determine the parameter of the point on a curve that is a prescribed arc length distance from the end of a curve, just reverse the curve before calling one of the above curve members.

## Sample

The following code sample demonstrates how to use these functions:

CRhinoCommand::result CCommandTest::RunCommand( const CRhinoCommandContext& context )
{
CRhinoGetObject go;
go.SetCommandPrompt( L"Select curve" );
go.SetGeometryFilter( CRhinoGetObject::curve_object );
go.GetObjects( 1, 1 );
if( go.CommandResult() != success )
return go.CommandResult();

const CRhinoObjRef& obj_ref = go.Object(0);
const ON_Curve* crv = obj_ref.Curve();
if( 0 == crv )
return failure;

double crv_length = 0.0;
if( !crv->GetLength(&crv_length) )
return failure;

CRhinoGetNumber gn;
gn.SetCommandPrompt( L"Length from start" );
gn.SetLowerLimit( 0.0, TRUE );
gn.SetUpperLimit( crv_length, TRUE );
gn.GetNumber();
if( gn.CommandResult() != success )
return gn.CommandResult();

// Cook up a normalized arc length parameter,
// where 0.0 <= s <= 1.0.
double length = fabs( gn.Number() );
double s = 0.0;
if( length == 0.0 )
s = 0.0;
else if( length == crv_length )
s = 1.0;
else
s = length / crv_length;

// Get the parameter of the point on the curve that is a
// prescribed arc length from the start of the curve.
double t = 0.0;
if( crv->GetNormalizedArcLengthPoint(s, &t) )
{
ON_3dPoint pt = crv->PointAt( t );