• Control Points:
  • Let \(p_{ij}\) denote control point \((i,j)\)
  • The patch will be in the convex hull of the control points
• Blending Polynomials:
  • We have one array of blending polynomials for each parameter
• The Bézier Patch:
  • \(p(u,v) = \sum_{i=0}^{n} \sum_{j=0}^{m} b_{i}(u) b_{j}(v) p_{ij}\)

• Evaluators:
  • Are used in the same way as for Bézier curves (i.e., to compute the values for the Bernstein polynomials)
• For Uniform Meshes:
  • glMapGrid2f()
  • glEvalMesh2()

openglexamples/surfaces/shade.c (Fragment: surface)

          //
  // The evaluator
  glMap2f(GL_MAP2_VERTEX_3, 0, 1, 3, uSize, 0, 1, uSize * 3, vSize,
          &points[0][0][0]);

  // Fill the surface
  glEvalMesh2(GL_FILL, 0, gridSize, 0, gridSize);

        

openglexamples/surfaces/shade.c (Fragment: setup)

          // Enable the 2-dimensional evaluator
  glEnable(GL_MAP2_VERTEX_3);
  glMapGrid2f(gridSize, 0.0, 1.0, gridSize, 0.0, 1.0);
        

openglexamples/textures/surface.c (Fragment: init)

        /**
 * Initializations
 */
void init() {
  glClearColor(1.0, 1.0, 1.0, 1.0);
  glShadeModel(GL_FLAT);
  glEnable(GL_DEPTH_TEST);

  // Read the images
  GLbyte image[256][256][3];
  readRAWImage("oak.raw", image);

  // Get "names" for the textures
  glGenTextures(1, &textureName);

  glBindTexture(GL_TEXTURE_2D, textureName);

  // Set the parameters
  glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
  glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
  glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
  glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);

  // Create the texture object
  glTexImage2D(GL_TEXTURE_2D, 0, 3, 256, 256, 0, GL_RGB, GL_UNSIGNED_BYTE,
               image);

  // Map the texture
  glMap2f(GL_MAP2_TEXTURE_COORD_2, 0, 1, 2, 2, 0, 1, 4, 2,
          &textureControlPoints[0][0][0]);

  // Create the surface
  glMap2f(GL_MAP2_VERTEX_3, 0, 1, 3, uSize, 0, 1, uSize * 3, vSize,
          &points[0][0][0]);
  glMapGrid2f(gridSize, 0.0, 1.0, gridSize, 0.0, 1.0);

  // Enable everything
  glEnable(GL_MAP2_TEXTURE_COORD_2);
  glEnable(GL_MAP2_VERTEX_3);
}
        

openglexamples/textures/surface.c (Fragment: render)

        /**
 * The display callback.
 */
void display() {
  // Clear the screen
  glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

  // Set the color
  glColor3f(1.0, 1.0, 1.0);

  // Enable textures
  glEnable(GL_TEXTURE_2D);

  // Select the texture object
  glBindTexture(GL_TEXTURE_2D, textureName);

  // Draw the surface
  glEvalMesh2(GL_FILL, 0, 20, 0, 20);

  // Disable textures (in case you want to render something else)
  glDisable(GL_TEXTURE_2D);

  // Force the rendering (off-screen)
  glFlush();

  // Handle the double buffering
  glutSwapBuffers();
}