# Triangulating Polygons

This guide demonstrates how to triangulate polygons using C/C++.

## Overview

Rhino’s mesh representation, ON_Mesh, only support three and four sided faces. This can pose a problem when trying to write an import plugin for a mesh file format that supports n-sided polygons. If you search the Internet, you can probably find a number of algorithms that will triangulate n-sided polygons so they can be used with ON_Mesh. The Rhino C/C++ SDK also includes a tool for doing this.

The RhinoTriangulate3dPolygon SDK function will triangulate an n-sided polygon. The polygon must project onto a plane and the projected polygon must be a simple closed curve. For more information on the RhinoTriangulate3dPolygon, see the comments in rhinoSdkMeshUtilities.h.

## Sample

The following sample code demonstrates how to triangulate a closed planar polygon that has more than three sides using the RhinoTriangulate3dPolygon function. Although this sample demonstrates the function on polyline curves, the code could be easily converted to work on mesh vertices.

CRhinoCommand::result CCommandTest::RunCommand( const CRhinoCommandContext& context )
{
CRhinoGetObject go;
go.SetCommandPrompt( L"Select closed planar polygon to triangulate" );
go.SetGeometryFilter( CRhinoGetObject::curve_object );
go.SetGeometryFilter( CRhinoGetObject::closed_curve );
go.EnableSubObjectSelect( FALSE );
go.GetObjects( 1, 1 );
if( go.CommandResult() != success )
return go.CommandResult();

const CRhinoObjRef& ref = go.Object(0);

ON_3dPointArray vertices;

const ON_PolylineCurve* pc = ON_PolylineCurve::Cast( ref.Curve() );
if( pc )
{
vertices = pc->m_pline;
}
else
{
const ON_NurbsCurve* nc = ON_NurbsCurve::Cast( ref.Curve() );
if( nc )
nc->IsPolyline( &vertices );
}

if( vertices.Count() < 5 )
{
RhinoApp().Print( L"Curve not polygon with at least four sides.\n" );
return nothing;
}

int* triangles = (int*)onmalloc( (vertices.Count()-3) * sizeof(int) * 3 );
if( 0 == triangles )
return failure; // out of memory

memset( triangles, 0, (vertices.Count()-3) * sizeof(int) * 3 );

int rc = RhinoTriangulate3dPolygon( vertices.Count()-1, 3, (const double*)vertices.Array(), 3, triangles);
if( 0 == rc )
{
int i;
for( i = 0; i < vertices.Count()-3; i++ )
{
ON_Polyline pline;
pline.Append( vertices[triangles[i * 3]] );
pline.Append( vertices[triangles[i * 3 + 1]] );
pline.Append( vertices[triangles[i * 3 + 2]] );
pline.Append( pline );