07-tessellation.md

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Tessellation

• Simple Polygon:
  • Edges intersect only at vertices
  • No duplicate vertices
  • Exactly two edges meet at any vertex
• Tessellation — surface subdivision into simpler polygons, used for:
  • Display of concave polygons
  • Polygons containing holes
  • Polygons with intersecting edges
• Winding Number — the signed number of revolutions we make around that point while travelling once around the contour
  • Counterclockwise is positive
  • Clockwise is negative
• Winding Rule — classifies which region is "inside" a polygon (aka filled) given the winding number of a point
  • e.g. if a point is "3" and the winding rule is "odd" then, it will be filled

Tessellation in OpenGL

• gluNewTess() — creates a new tessellation object
• gluTessCallback() — used to register callback functions to perform operations during tessellation
• gluTessProperty() — specify properties
  • Create and render tessellated polygons by specifing the countours of one or more closed polygons
• gluDeleteTess() — to delete a tessellation object

Example

Inside the display() method:

GLUtessellator tobj = glu.gluNewTess();

// vertexCallback
glu.gluTessCallback(tobj, GLU.GLU_TESS_VERTEX, tessCallback);
// beginCallback
glu.gluTessCallback(tobj, GLU.GLU_TESS_BEGIN, tessCallback);
// endCallBack
glu.gluTessCallback(tobj, GLU.GLU_TESS_END, tessCallback);
// errorCallback
glu.gluTessCallback(tobj, GLU.GLU_TESS_ERROR, tessCallback);
// combineCallback
glu.gluTessCallback(tobj, GLU.GLU_TESS_COMBINE, tessCallback);

// Rectangle with triangular hole inside

gl.glNewList(startList, GL2.GL_COMPILE);
gl.glShadeModel(GL2.GL_FLAT);
glu.gluTessBeginPolygon(tobj, null);

// draw rectangle
glu.gluTessBeginContour(tobj);
glu.gluTessVertex(tobj, rect[0], 0, rect[0]);
glu.gluTessVertex(tobj, rect[1], 0, rect[1]);
glu.gluTessVertex(tobj, rect[2], 0, rect[2]);
glu.gluTessVertex(tobj, rect[3], 0, rect[3]);
glu.gluTessEndContour(tobj);

// draw triangle
glu.gluTessBeginContour(tobj);
glu.gluTessVertex(tobj, tri[0], 0, tri[0]);
glu.gluTessVertex(tobj, tri[1], 0, tri[1]);
glu.gluTessVertex(tobj, tri[2], 0, tri[2]);
glu.gluTessEndContour(tobj);

glu.gluTessEndPolygon(tobj);
gl.glEndList();