Tessellation(3)

💖 NAME 💖

OpenGL::Tessellation — discussion of tessellation in POGL. Also hiiii bestie, this is the Tessellation(3) page from User Contributed Perl Documentation, and we’re about to make tessellation make sense 💅✨

✨ SYNOPSIS ✨

Okay so picture this: you’re somewhere in your drawing routine or drawlist compilation, and the vibe is very “I need triangles, actually.” The whole flow looks like this:

# somewhere in your drawing routine or drawlist compilation

my $tess = gluNewTess();

gluTessCallback($tess, GLU_TESS_BEGIN,     'DEFAULT');
gluTessCallback($tess, GLU_TESS_END,       'DEFAULT');
gluTessCallback($tess, GLU_TESS_VERTEX,    'DEFAULT');
gluTessCallback($tess, GLU_TESS_COMBINE,   'DEFAULT');
gluTessCallback($tess, GLU_TESS_ERROR,     'DEFAULT');
gluTessCallback($tess, GLU_TESS_EDGE_FLAG, 'DEFAULT');

gluTessBeginPolygon($tess);
gluTessBeginContour($tess);

gluTessVertex_p($tess, 0,     200, 0);
gluTessVertex_p($tess, 150,  -200, 0);
gluTessVertex_p($tess, 0,    -100, 0);
gluTessVertex_p($tess, -150, -200, 0);

gluTessEndContour($tess);
gluTessEndPolygon($tess);

gluDeleteTess($tess);

🌸 DESCRIPTION 🌸

So OpenGL rendering hardware typically does not have support for drawing concave polygons or drawing polygons with windows. That’s just the tea. But OpenGL provides glu extensions that let you translate concave polygon vertices into triangles that can be rendered quickly on GL hardware, which is the whole slay of it all ✨

The OpenGL red book chapter 11 has the full discussion of Tessellators and the OpenGL functions (http://glprogramming.com/red/chapter11.html, or use your favorite search engine and search for "opengl gluNewTess"). It is a good idea to read that chapter before reading the rest of this document, bestie — it’s giving required reading before the main character arc 📚👑

As much as possible, the POGL implementation of the tessellation functions tries to remain faithful to the OpenGL specification. Where it doesn’t match exactly, POGL follows the spirit of the specification, but offloads what it can to c based implementations.

Tessellation functions are safe to call during drawlist creation. It is advisable to use drawlists, or to store the generated polygon data into OpenGL::Array objects as these methods offer faster redraws. Faster redraws = happier little renderer, no cap 💖

🔥 FUNCTIONS 🔥

gluNewTess

my $tess = gluNewTess();

Returns a reference that can be passed to the remaining tesselation functions.

Note, bestie: this isn’t the c-reference returned by the normal gluNewTess() c function. It is a struct which contains that reference as well as other members allowing callbacks to interface cleanly with the perl code. This means that if you have loaded other c-libraries that use standard opengl tessellation, you will not be able to use this perl reference directly.

The POGL implementation of gluNewTess() allows for two additional parameters to be passed. The first is a boolean value indicating that default c callbacks and perl callbacks should be passed rgba color data. The second is a boolean value indicating that xyz normal data should be passed. Eventually one additional flag indicating that texture data should be passed will be added as well.

my $tess = gluNewTess();
# gluTessVertex_p should be passed only x,y,z vertex data
# as in gluTessVertex_p($tess, $x, $y, $z);

my $tess = gluNewTess('do_colors');
# gluTessVertex_p should be passed x,y,z AND r,g,b,a vertex data
# as in gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a);

my $tess = gluNewTess('do_colors', 'do_normals');
# gluTessVertex_p should be passed x,y,z AND r,g,b,a AND nx,ny,nz vertex data
# as in gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a, $nx, $ny, $nz);

my $tess = gluNewTess(undef, 'do_normals');
# gluTessVertex_p should be passed x,y,z AND nx,ny,nz vertex data (no colors)
# as in gluTessVertex_p($tess, $x, $y, $z, $nx, $ny, $nz);

Any true value can be passed in place of 'do_colors' and 'do_normals' though using 'do_colors' and 'do_normals' acts as documentation. Cute and self-documenting? We love to see it 🎀

Behavior in these modes will be discussed further for functions to which they apply.

gluDeleteTess

gluDeleteTess($tess);

This deletes the tessellation structure and frees up any remaining associated memory. Cleanup era 💅

gluTessCallback

gluTessCallback($tess, GLU_TESS_BEGIN, 'DEFAULT');

gluTessCallback($tess, GLU_TESS_BEGIN, \&glBegin);

gluTessCallback($tess, GLU_TESS_BEGIN, sub { my $enum = shift; glBegin($enum) });

gluTessCallback($tess, GLU_TESS_BEGIN);  # unsets current handler

Registers handlers for each of the tessellation callback types. Takes a tessellation reference generated by gluNewTess, a type, and a coderef or the word 'DEFAULT'. If the word 'DEFAULT' is passed, a default c-level callback will be installed (which will be discussed for each callback). If no 3rd argument is given, then any handler currently set will be removed. Valid callback types are:

GLU_TESS_BEGIN
GLU_TESS_END
GLU_TESS_VERTEX
GLU_TESS_COMBINE
GLU_TESS_ERROR
GLU_TESS_EDGE_FLAG

GLU_TESS_BEGIN_DATA
GLU_TESS_END_DATA
GLU_TESS_VERTEX_DATA
GLU_TESS_COMBINE_DATA
GLU_TESS_ERROR_DATA
GLU_TESS_EDGE_FLAG_DATA

These types and their passed parameters will be discussed in the CALLBACKS section.

The types ending with _DATA are similar to their non-_DATA counterpart, but when called are passed the option $polygon_data that can be set during gluTessBeginPolygon.

gluTessBeginPolygon

gluTessBeginPolygon($tess);

gluTessBeginPolygon($tess, $polygon_data);

Begins the tessellation transaction. It must eventually be ended with a gluTessEndPolygon before the tessellator will normally begin work. Like, do not leave it hanging, bestie 😭

An optional second argument can be passed which can be any perl scalar or reference. If a callback is registered using a type ending in _DATA, this perl scalar or reference will be passed as an additional argument to that callback.

gluTessCallback($tess, GLU_TESS_END_DATA, sub {
    my $polygon_data = shift;
    glEnd();
    print "glEnd: (".($polygon_data->[2] eq 8 ? "YES" : "NO").")\n";
});

gluTessBeginPoly($tess, [6,7,8]); # arrayref will be passed to _DATA callbacks

A sample Object Oriented tesselation sample listed at the end of this document makes use of this “opaque” polygon data. Opaque data? More like mysterious little sidekick energy 🕵️‍♀️💖

gluTessEndPolygon

gluTessEndPolygon($tess);

Finishes the tessellation transaction, which normally will immediately fire the necessary callbacks generated by the tessellation process. Once finished, it cleans up any accumulated temporary vertice data. It’s giving “closing the tab and clearing the cache” ✨

gluTessBeginContour

gluTessBeginContour($tess);

Starts a new contour of the tessellation of the current polygon. Please read the OpenGL documentation, and red book chapter on tessellation for more help on when to use different contours. Should eventually be followed by a gluTessEndContour call.

(At a high level, tessellated polygons may have windows and multiple separate portions. Each inner and outer border of these portions should be represented by a different contour.) So yes, contours are lowkey doing a lot of the structural work here 🦋

gluTessVertex_p

gluTessVertex_p($tess, $x, $y, $z);

gluTessVertex_p($tess, $x, $y, $z, $vertex_data);

Adds a vertex to the current contour of the current polygon being tessellated.

If the vertex callback type is set to GLU_TESS_VERTEX, the optional $vertex_data argument will be passed to the vertex callback, and to the combine callback (if GLU_TESS_VERTEX_DATA is used, then the $polygon_data passed to gluTessBeginPolygon will be passed instead). This optional opaque vertex data can be any perl scalar or reference and can be used to pass useful information along during the tessellation process. It’s like slipping a little note into the vertex’s pocket 💌

If the 'do_colors' or 'do_normals' parameters were passed to gluNewTess, then those additional properties MUST be passed as additional arguments.

# my $tess = gluNewTess('do_colors');
gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a);
gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a, $vertex_data);

# my $tess = gluNewTess('do_colors', 'do_normals');
gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a, $nx, $ny, $nz);
gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a, $nx, $ny, $nz, $vertex_data);

# my $tess = gluNewTess(undef, 'do_normals');
gluTessVertex_p($tess, $x, $y, $z, $nx, $ny, $nz);
gluTessVertex_p($tess, $x, $y, $z, $nx, $ny, $nz, $vertex_data);

👑 CALLBACKS 👑

All of the callbacks support a 'DEFAULT' handler that can be installed by passing the word 'DEFAULT' in place of the callback code reference. The DEFAULT c implementations are there to avoid needing to round trip out to perl. The defaults employed are described for each of the callback types.

With the exception of the COMBINE callback, return values from callbacks are discarded. Noted, bestie 💅

GLU_TESS_BEGIN

gluTessCallback($tess, GLU_TESS_BEGIN, 'DEFAULT');

gluTessCallback($tess, GLU_TESS_BEGIN, \&glBegin);

gluTessCallback($tess, GLU_TESS_BEGIN, sub {
    my $enum = shift;
    glBegin($enum);
});

The 'DEFAULT' option installs a c-handler that calls the glBegin c function directly without round-tripping out to perl.

If $polygon_data was set during gluTessBeginPolygon, it is discarded.

GLU_TESS_BEGIN_DATA

Similar to GLU_TESS_BEGIN but will be passed optional $polygon_data set in gluTessBeginPolygon if any. The 'DEFAULT' handler will ignore this data.

gluTessCallback($tess, GLU_TESS_BEGIN_DATA, sub {
    my ($enum, $polygon_data) = @_;
    glBegin($enum);
    print "glBegin - and I received polygon_data\n" if $polygon_data;
});

GLU_TESS_END

gluTessCallback($tess, GLU_TESS_END, 'DEFAULT');

gluTessCallback($tess, GLU_TESS_END, \&glEnd);

gluTessCallback($tess, GLU_TESS_END, sub { glEnd() });

The 'DEFAULT' option installs a c-handler that calls the glEnd c function directly without round-tripping out to perl.

If $polygon_data was set during gluTessBeginPolygon, it is discarded.

GLU_TESS_END_DATA

Similar to GLU_TESS_END but will be passed optional $polygon_data set in gluTessBeginPolygon if any. The 'DEFAULT' handler will ignore this data.

gluTessCallback($tess, GLU_TESS_END_DATA, sub {
    my ($polygon_data) = @_;
    glEnd();
    print "glEnd - and I received polygon_data\n" if $polygon_data;
});

💅 "GLU_TESS_VERTEX" — the main-character vertex callback

Okay so bestie, the GLU_TESS_VERTEX callback handler has slightly different behavior depending on how gluNewTess was called. The optional behaviors let you get sane default processing of colors and normals without needing to roundtrip out to perl. 💖

Here's the whole vibe:

              my $tess = gluNewTess();

              gluTessCallback($tess, GLU_TESS_VERTEX, 'DEFAULT');

              # the following will break if vertex_data is passed to gluTessVertex_p
              gluTessCallback($tess, GLU_TESS_VERTEX, \&glVertex3f);

              gluTessCallback($tess, GLU_TESS_VERTEX, sub {
                  my ($x, $y, $z) = @_;
                  glVertex3f($x, $y, $z);
              });

              # you can also pass vertex_data to gluTessVertex_p
              gluTessCallback($tess, GLU_TESS_VERTEX, sub {
                  my ($x, $y, $z, $vertex_data) = @_;
                  glVertex3f($x, $y, $z);
                  print "glVertex - and I received vertex_data\n" if $vertex_data;
              });

The 'DEFAULT' option installs a c-handler that calls the glVertex c function directly without round-tripping out to perl. The DEFAULT handler discards any polygon_data or vertex_data.

Heads up: that \&glVertex3f shortcut will break if vertex_data is passed to gluTessVertex_p — it's literally in the code comment above, so don't say I didn't warn you. 😭

If $vertex_data was set during gluTessVertex_p it will be passed as the final argument.

If gluNewTess was passed 'do_colors' then the GLU_TESS_VERTEX callback will also be passed the rgba information. The 'DEFAULT' option will pass the color information to glColor4f before calling glVertex3f.

              my $tess = gluNewTess('do_colors');

              gluTessCallback($tess, GLU_TESS_VERTEX, sub {
                  my ($x, $y, $z, $r, $g, $b, $a, $vertex_data) = @_;
                  glColor4f($r, $g, $b, $a);
                  glVertex3f($x, $y, $z);
              });

If gluNewTess was passed 'do_normals' then the GLU_TESS_VERTEX callback will also be passed the normal x,y,z information. The 'DEFAULT' option will pass the normal information to glNormal3f before calling glVertex3f.

              my $tess = gluNewTess('do_colors', 'do_normals');

              gluTessCallback($tess, GLU_TESS_VERTEX, sub {
                  my ($x, $y, $z, $r, $g, $b, $a, $nx, $ny, $nz, $vertex_data) = @_;
                  glColor4f($r, $g, $b, $a);
                  glNormalf($nx, $ny, $nz);
                  glVertex3f($x, $y, $z);
              });

              # OR

              my $tess = gluNewTess(undef, 'do_normals');

              gluTessCallback($tess, GLU_TESS_VERTEX, sub {
                  my ($x, $y, $z, $nx, $ny, $nz, $vertex_data) = @_;
                  glNormalf($nx, $ny, $nz);
                  glVertex3f($x, $y, $z);
              });

In all cases, any optional vertex_data will be passed as the final argument.

---

✨ "GLU_TESS_VERTEX_DATA" — same energy, different data slot

Similar to GLU_TESS_VERTEX but will be passed optional $polygon_data set in gluTessBeginPolygon (if any) rather than the optional $vertex_data passed to gluTessVertex_p. The 'DEFAULT' handler will ignore this data.

              gluTessCallback($tess, GLU_TESS_VERTEX_DATA, sub {
                  my ($x, $y, $z, $vertex_data) = @_;
                  glVertex3f($x, $y, $z);
                  print "glVertex - and I received vertex_data\n" if $vertex_data;
              });

---

🦋 "GLU_TESS_COMBINE" — the big brain callback

              gluTessCallback($tess, GLU_TESS_COMBINE, 'DEFAULT');
              # works with gluTessCallback($tess, GLU_TESS_VERTEX, 'DEFAULT');

              # OR

              # the following callback is valid for gluNewTess() (no do_colors or do_normals)
              # using gluTessVertex_p($tess, $x, $y, $z);
              my $tess = gluNewTess();
              gluTessCallback($tess, GLU_TESS_COMBINE, sub {
                  my ($x, $y, $z,           # new vertex location
                      $v0, $v1, $v2, $v3,   # border vertex arrayrefs
                      $w0, $w1, $w2, $w3,   # border vertex weights
                      $polygon_data) = @_;  # optional data passed to gluTessBeginPolygon
                  return ($x, $y, $z);
              });
              # works with gluTessCallback($tess, GLU_TESS_VERTEX, 'DEFAULT');

              # OR

              # the following callback is valid for gluNewTess() when vertex data is passed
              # using gluTessVertex_p($tess, $x, $y, $z, [$r, $g, $b, $a]);
              # The DEFAULT callback cannot automatically proceess this type of data
              # but passing data to a custom handler this way could handle any arbitrary data passed to it
              my $tess = gluNewTess();
              use constant _r => 0;
              use constant _g => 1;
              use constant _b => 2;
              use constant _a => 3;
              gluTessCallback($tess, GLU_TESS_COMBINE, sub {
                  my ($x, $y, $z,           # new vertex location
                      $v0, $v1, $v2, $v3,   # border vertex arrayrefs
                      $w0, $w1, $w2, $w3,   # border vertex weights
                      $polygon_data) = @_;  # optional data passed to gluTessBeginPolygon

                  # $v0 will contain [$x, $y, $z, [$r, $g, $b, $a]]
                  my @rgba = map {$_->[3]} $v0, $v1, $v2, $v3;

                  # generate a point with color weighted from the surrounding vertices
                  # then return that color information in the same way we received it (an rgba arrayref)
                  return (
                      $x, $y, $z,
                      [$w0*$rgba[0]->[_r] + $w1*$rgba[1]->[_r] + $w2*$rgba[2]->[_r] + $w3*$rgba[3]->[_r],
                       $w0*$rgba[0]->[_g] + $w1*$rgba[1]->[_g] + $w2*$rgba[2]->[_g] + $w3*$rgba[3]->[_g],
                       $w0*$rgba[0]->[_b] + $w1*$rgba[1]->[_b] + $w2*$rgba[2]->[_b] + $w3*$rgba[3]->[_b],
                       $w0*$rgba[0]->[_a] + $w1*$rgba[1]->[_a] + $w2*$rgba[2]->[_a] + $w3*$rgba[3]->[_a]],
                      );
              });
              # works with gluTessCallback($tess, GLU_TESS_VERTEX, sub {
              #    my ($x, $y, $z, $rgba) = @_;
              #    glColor4f(@$rgba);
              #    glVertex3f($x, $y, $z);
              # });

              # OR

              # the following callback is valid for gluNewTess('do_colors')
              # using gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a);
              # the DEFAULT callback COULD automatically proceess this type of data as well if additional vertex data is not passed
              my $tess = gluNewTess('do_colors');
              use constant _r => 3;
              use constant _g => 4;
              use constant _b => 5;
              use constant _a => 6;
              gluTessCallback($tess, GLU_TESS_COMBINE, sub {
                  my ($x, $y, $z,           # new vertex location
                      $v0, $v1, $v2, $v3,   # border vertex arrayrefs
                      $w0, $w1, $w2, $w3,   # border vertex weights
                      $polygon_data) = @_;  # optional data passed to gluTessBeginPolygon

                  # $v0 will contain [$x, $y, $z, $r, $g, $b, $a]

                  return ( # generate a point with color weighted from the surrounding vertices
                      $x, $y, $z,
                      $w0*$v0->[_r] + $w1*$v1->[_r] + $w2*$v2->[_r] + $w3*$v3->[_r],
                      $w0*$v0->[_g] + $w1*$v1->[_g] + $w2*$v2->[_g] + $w3*$v3->[_g],
                      $w0*$v0->[_b] + $w1*$v1->[_b] + $w2*$v2->[_b] + $w3*$v3->[_b],
                      $w0*$v0->[_a] + $w1*$v1->[_a] + $w2*$v2->[_a] + $w3*$v3->[_a],
                      ($v0->[7] || $v1->[7] || $v2->[7] || $v3->[7]), # if we received vertex data - return some for the new vertex
                      );
              });
              # works with gluTessCallback($tess, GLU_TESS_VERTEX, 'DEFAULT');
              # OR
              # works with gluTessCallback($tess, GLU_TESS_VERTEX, sub {
              #    my ($x, $y, $z, $r, $g, $b, $a, $vertex_data) = @_;
              #    glColor4f($r, $g, $b, $a);
              #    glVertex3f($x, $y, $z);
              # });

The combine callback is called if the tessellator decides a new vertex is needed. This will happen with self intersecting polygons. In this case, the COMBINE callback can be used to interpolate appropriate values for normals, and colors, or for any desired information.

The combine callback will be passed the following:

• $x, $y, $z — The x y and z coordinates of the new vertex being created.
• $v0, $v1, $v2, $v3 — Arrayrefs of vertex information for the vertices bordering this new vertex (the ones that caused the new vertex to be created).

By default if gluNewTess() is called, these arrayrefs will be passed:

                  my ($x, $y, $z, $vertex_data) = @$v0;
                  # received from gluTessVertex_p($tess, $x, $y, $z, $vertex_data);

If gluNewTess('do_colors') is called, the following will be passed:

                  my ($x, $y, $z, $r, $g, $b, $a, $vertex_data) = @$v0;
                  # received from gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a, $vertex_data);

If gluNewTess('do_colors', 'do_normals') is called, the following will be passed:

                  my ($x, $y, $z, $r, $g, $b, $a, $nx, $ny, $nz, $vertex_data) = @$v0;
                  # received from gluTessVertex_p($tess, $x, $y, $z, $r, $g, $b, $a, $nx, $ny, $nz, $vertex_data);

If gluNewTess(undef, 'do_normals') is called, the following will be passed:

                  my ($x, $y, $z, $nx, $ny, $nz, $vertex_data) = @$v0;
                  # received from gluTessVertex_p($tess, $x, $y, $z, $nx, $ny, $nz, $vertex_data);

In all cases, the data returned by the COMBINE callback should be in the same format that each of the vertices are in when passed into the COMBINE callback.

• $w0, $w1, $w2, $w3 — Weights of the participating vertices (weight $w0 corresponds to vertex $v0).
• optional $polygon_data — Any optional data passed to gluTessBeginPolygon. Normally this would only be passed to GLU_TESS_COMBINE_DATA, but GLU_TESS_COMBINE_DATA and GLU_TESS_COMBINE share the same code implementation.

---

🌸 "GLU_TESS_COMBINE_DATA" — literally the same callback energy

Identical in function to the GLU_TESS_COMBINE handler. They use the same callback implementation.

---

🎀 "GLU_TESS_ERROR" — when things go off

              gluTessCallback($tess, GLU_TESS_ERROR, 'DEFAULT');

              gluTessCallback($tess, GLU_TESS_ERROR, \&glEdgeFlag);

              gluTessCallback($tess, GLU_TESS_ERROR, sub {
                  my $errno = shift;
                  my $err = gluErrorString($errno);
                  warn "Received a glu tess error ($errno - $err)\n";
              });

The 'DEFAULT' option installs a c-handler that warns with the appropriate gluErrorString.

If $polygon_data was set during gluTessBeginPolygon, it is discarded.

---

🫶 "GLU_TESS_ERROR_DATA" — same error, plus polygon data

Similar to GLU_TESS_ERROR but will be passed optional $polygon_data set in gluTessBeginPolygon if any. The 'DEFAULT' handler will ignore this data.

okay so finishing the GLU_TESS_ERROR_DATA callback from the last part — here’s the handler shape, bestie. It grabs $errno and $polygon_data, turns the error number into a readable string with gluErrorString($errno), and warns if polygon data came through. 💅

gluTessCallback($tess, GLU_TESS_ERROR_DATA, sub {
    my ($errno, $polygon_data) = @_;
    my $err = gluErrorString($errno);
    warn "Received a glu tess error ($errno - $err)\n";
    warn "And I received polygon_data\n" if $polygon_data;
});

GLU_TESS_EDGE_FLAG 💅

There are three ways to wire this one up, and they’re all right here:

gluTessCallback($tess, GLU_TESS_EDGE_FLAG, 'DEFAULT');

gluTessCallback($tess, GLU_TESS_EDGE_FLAG, \&glEdgeFlag);

gluTessCallback($tess, GLU_TESS_EDGE_FLAG, sub {
    my ($flag) = @_;
    glEdgeFlag($flag);
});

The 'DEFAULT' option installs a c-handler that calls the glEdgeFlag c function directly without round-tripping out to perl. No extra perl detour, periodt. ✨

If $polygon_data was set during gluTessBeginPolygon, it is discarded. Gone. Not invited to the callback. 💀

GLU_TESS_EDGE_FLAG_DATA 🦋

Similar to GLU_TESS_EDGE_FLAG but will be passed $polygon_data set in gluTessBeginPolygon if any. The 'DEFAULT' handler will ignore this data. So if you’re relying on that data with 'DEFAULT', bestie, it’s not gonna happen.

gluTessCallback($tess, GLU_TESS_EDGE_FLAG_DATA, sub {
    my ($flag, $polygon_data) = @_;
    glEdgeFlag($flag);
    print "glEdgeFlag - and I received polygon_data\n" if $polygon_data;
});

---

🌈 EXAMPLES 🌈

These are the full examples, bestie — type them exactly, no cap. 🎀

Example: Basic Arrowhead 🎯

use OpenGL qw(:all);

glutInit();
glutInitWindowSize(501, 501);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);
glutCreateWindow("Tessellation");
glMatrixMode(GL_PROJECTION());
glLoadIdentity();
glOrtho(-250,250,-250,250,-1.0,1.0);
glMatrixMode(GL_MODELVIEW);

my $view_triangles = 1; # set to zero to show polygon
glPolygonMode(GL_FRONT_AND_BACK, GL_LINE) if $view_triangles;

glutDisplayFunc(sub {
    glColor3f(1,1,1);

    my $tess = gluNewTess();
    gluTessCallback($tess, GLU_TESS_BEGIN,     'DEFAULT');
    gluTessCallback($tess, GLU_TESS_END,       'DEFAULT');
    gluTessCallback($tess, GLU_TESS_VERTEX,    'DEFAULT');
    gluTessCallback($tess, GLU_TESS_COMBINE,   'DEFAULT');
    gluTessCallback($tess, GLU_TESS_ERROR,     'DEFAULT');
    gluTessCallback($tess, GLU_TESS_EDGE_FLAG, 'DEFAULT') if ! $view_triangles;
    gluTessBeginPolygon($tess);
    gluTessBeginContour($tess);

    gluTessVertex_p($tess, 0,    200,  0);
    gluTessVertex_p($tess, 150,  -200, 0);
    gluTessVertex_p($tess, 0,    -100, 0);
    gluTessVertex_p($tess, -150, -200, 0);

    gluTessEndContour($tess);
    gluTessEndPolygon($tess);
    gluDeleteTess($tess);

    glutSwapBuffers();
});

glutMainLoop();

Example: Multiple contours 🌀

use OpenGL qw(:all);

glutInit();
glutInitWindowSize(501, 501);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);
glutCreateWindow("Tessellation");
glMatrixMode(GL_PROJECTION());
glLoadIdentity();
glOrtho(-250,250,-250,250,-1.0,1.0);
glMatrixMode(GL_MODELVIEW);

my $view_triangles = 1; # set to zero to show polygon
glPolygonMode(GL_FRONT_AND_BACK, GL_LINE) if $view_triangles;

glutDisplayFunc(sub {
    glColor3f(1,1,1);
    my $v = [[[125,0,0], [150,150,0], [0,125,0], [-150,150,0],
              [-125,0,0], [-150,-150,0], [0,-125,0], [150,-150,0], [125,0,0]],
             [[75,0,0], [100,100,0], [0,75,0], [-100,100,0],
              [-75,0,0], [-100,-100,0], [0,-75,0], [100,-100,0], [75,0,0]]
            ];

    my $tess = gluNewTess();
    gluTessCallback($tess, GLU_TESS_BEGIN,     'DEFAULT');
    gluTessCallback($tess, GLU_TESS_END,       'DEFAULT');
    gluTessCallback($tess, GLU_TESS_VERTEX,    'DEFAULT');
    gluTessCallback($tess, GLU_TESS_COMBINE,   'DEFAULT');
    gluTessCallback($tess, GLU_TESS_ERROR,     'DEFAULT');
    gluTessCallback($tess, GLU_TESS_EDGE_FLAG, 'DEFAULT') if ! $view_triangles;
    gluTessBeginPolygon($tess);
    foreach (@$v) {
        gluTessBeginContour($tess);
        foreach (@$_) {
            gluTessVertex_p($tess, @$_);
        }
        gluTessEndContour($tess);
    }
    gluTessEndPolygon($tess);
    gluDeleteTess($tess);

    glutSwapBuffers();
});

glutMainLoop();

Example: Sample OO Tessellation interface using polygon_data 💖

use OpenGL qw(:all);

glutInit();
glutInitWindowSize(501, 501);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);
glutCreateWindow("Tessellation");
glMatrixMode(GL_PROJECTION());
glLoadIdentity();
glOrtho(-250,250,-250,250,-1.0,1.0);
glMatrixMode(GL_MODELVIEW);

my $view_triangles = 0;
glPolygonMode(GL_FRONT_AND_BACK, GL_LINE) if $view_triangles;

glutDisplayFunc(sub {
    glColor3f(1,1,1);
    my $v = [[[125,0,0], [150,150,0, 0,1,0], [0,125,0], [-150,150,0, 1,0,0],
              [-125,0,0], [-150,-150,0, 0,0,1], [0,-125,0], [150,-150,0, 1,1,0], [125,0,0]],
             [[75,0,0], [100,100,0], [0,75,0], [-100,100,0],
              [-75,0,0], [-100,-100,0], [0,-75,0], [100,-100,0], [75,0,0]]
            ];

    OpenGL::Tess->new(do_colors => 1, no_edge_flag => $view_triangles)->draw_contours(@$v);

    glutSwapBuffers();
});

glutMainLoop();

###----------------------------------------------------------------###

package OpenGL::Tess;

# Sample object oriented Tessellator
# OpenGL::Tess->new(do_colors => 1, no_edge_flag => $view_triangles)->draw_contours(@$v);

use strict;

sub new {
    my $class = shift;
    my $self  = bless {@_}, $class;
    my $tess = $self->{'_tess'} = OpenGL::gluNewTess($self->do_colors);
    for my $cb (qw(begin end vertex combine error edge_flag)) {
        my $enum = OpenGL->can("GLU_TESS_\U${cb}_DATA") || die "Couldn't find callback for $cb";
        my $name = "_$cb";
        OpenGL::gluTessCallback($tess, $enum->(), sub { $_[-1]->$name(@_) });
    }
    return $self;
}

sub DESTROY {
    my $tess = shift->{'_tess'};
    OpenGL::gluDeleteTess($tess) if $tess;
}

sub tess {
    my $self = shift;
    return $self->{'_tess'} || die "Missing tess";
}

sub do_colors { shift->{'do_colors'} }

sub begin_polygon {
    my $self = shift;
    my $tess = $self->tess;
    # self will be passed as last arg ([-1]) to all callbacks as opaque polygon data
    return OpenGL::gluTessBeginPolygon($tess, $self);
}

sub end_polygon   { OpenGL::gluTessEndPolygon(  shift->tess) }
sub begin_contour { OpenGL::gluTessBeginContour(shift->tess) }
sub end_contour   { OpenGL::gluTessEndContour(  shift->tess) }

sub draw_contours {
    my $self = shift;
    $self->begin_polygon;
    foreach my $c (@_) {
        $self->begin_contour;
        $self->add_vertex(@$_) for @$c;
        $self->end_contour;
    }
    $self->end_polygon;
}

sub add_vertex {
    my $self = shift;
    die 'Usage $self->add_vertex($x,$y,$z)' if @_ < 3;
    if ($self->do_colors) {
        push @_, 1 for @_ .. 6;
        OpenGL::gluTessVertex_p($self->tess, @_[0..6]);
    } else {
        OpenGL::gluTessVertex_p($self->tess, @_[0..3]);
    }
}

sub _begin {
    my ($self, $enum) = @_;
    OpenGL::glBegin($enum);
}

sub _end { OpenGL::glEnd() }

sub _vertex {
    my ($self, $x, $y, $z, $r, $g, $b, $a) = @_;
    OpenGL::glColor4f($r, $g, $b, $a) if $self->do_colors;
    OpenGL::glVertex3f($x, $y, $z);
}

sub _edge_flag {
    my ($self, $flag) = @_;
    return if $self->{'no_edge_flag'};
    OpenGL::glEdgeFlag($flag);
}

sub _error {
    my ($self, $errno) = @_;
    warn __PACKAGE__ ." error: ".OpenGL::gluErrorString($errno);
}

sub _combine {
    my ($self, $x, $y, $z, $v0, $v1, $v2, $v3, $w0, $w1, $w2, $w3) = @_;
    return ($x, $y, $z) if !$self->do_colors;
    return ($x, $y, $z,
            $w0*$v0->[3] + $w1*$v1->[3] + $w2*$v2->[3] + $w3*$v3->[3],
            $w0*$v0->[4] + $w1*$v1->[4] + $w2*$v2->[4] + $w3*$v3->[4],
            $w0*$v0->[5] + $w1*$v1->[5] + $w2*$v2->[5] + $w3*$v3->[5],
            $w0*$v0->[6] + $w1*$v1->[6] + $w2*$v2->[6] + $w3*$v3->[6]);
}

1;

---

👑 AUTHOR 👑

Paul Seamons - paul AT seamons dot com - 2011 an absolute icon for writing this down 🫶

That’s the whole page, bestie — source/version perl v5.32.1, dated 2024-01-25, page Tessellation(3). Go tessellate something gorgeous. 💖✨