Triangulation

• A question Robert asked:
  • void glShadeModel(GLenum mode);
  • mode: GL_FLAT and GL_SMOOTH.
  • GL_SMOOTH is the default.
  • Smooth shading each pixel color is computed
  • Flat: only one color per triangle is computed.
• We have done most of chapter 7, probably worth a read anyway.
• Chapter 8, triangulation
  • Suppose Τ is a collections of triangles whose union is an object X. Then Τ is said to be a triangulation of X if, given any two triangles t₁ and t₂ from Τ, exactly one of the following three is true:
    1. t₁ and t₂ are disjoint. ie there is no intersection.
    2. t₁ and t₂ intersect at a common vertex.
    3. t₁ and t₂ intersect at a common edge.
  • This means the triangles intersect "nicely"
  • He gives some examples and non examples:
  • 
  • Does this definition make sense?
  • He gives an example program
    • invalidTriangultion.cpp which demostrates that the picture will change depending on the order of the triangles.
    • 
    • Why?
  • He says that long thin triangles, slivers are bad.
    • If all triangles are roughly the same size, this is good.
    • He provides a lighting example of lighing over a long strip
      1. Where it is composed of two triangles
      2. Where it is composed of a trinangle strip.
• Apparently OpenGL will draw a polygon as a triangle fan.
  • Which means The order of the points is very important for non-convex polygons.
  • 
  • 
• I found a really helpful example for tesselation of a plane
  • It was here.
  • I modified it slightly

        for(int y = 0; y < YDIM; y++) {
            for(int x = 0; x < XDIM; x++) {
              indices[i++] = y * (XDIM+1) + x;
              indices[i++] = y * (XDIM+1) + x + 1;
              indices[i++] = (y + 1) * (XDIM+1) + x+1;
    
              indices[i++] = y * (XDIM+1) + x;
              indices[i++] = (y + 1) * (XDIM+1) + x+1;
              indices[i++] = (y + 1) * (XDIM+1) + x;
              indexCount += 6;
           }
        }
    	 

  • It would be reasonable to compute surface normals at this point as well.
    • An array of three vectors initialized to 0.
    • Use the Cross product to compute a normal for the triangle
    • Add that to each of the vertex normal postions
    • Once all points have been generated, normalize the individual vertex normals.
• Some notes on glDrawElements

     glEnableClientState(GL_VERTEX_ARRAY);
     glEnableClientState(GL_NORMAL_ARRAY);
  
     glVertexPointer(3, GL_FLOAT, 6*sizeof(GLfloat), vertices);
     glNormalPointer(GL_FLOAT, 6*sizeof(GLfloat), &(vertices[0].nx));
     glDrawElements(GL_TRIANGLES, indexCount, GL_UNSIGNED_SHORT, indices);
  
     glDisableClientState(GL_VERTEX_ARRAY);
     glDisableClientState(GL_NORMAL_ARRAY)
      

  • oh, and glPolygonMode(GL_FRONT, GL_FILL), not GL_POLYGON as posted in a previous set of notes.