• "Simple" materials can be rendered reasonably well using simple lighting and shading models
• More "complex" materials (e.g., bricks, stones, singles) could be rendered the same way if each component (e.g., each brick) were a polygon but this increases the complexity of the model and the time required to render it
• Texture mapping essentially attaches an image (e.g., a photograph of a brick wall) to a polygon (e.g., representing a wall)

• Texture:
  • A rectangular array of colors
• Texel:
  • An individual element in a texture

• Texture Space to Object Space:
  • The texel at \([u, v]\) maps to a point at \([x, y, z, 1]\)
• Object Space to "Screen" Space:
  • A projection/viewing transform

• A Problem:
  • As the textured object is moved it may appear to change abruptly
  • Sometimes called the "minification problem"
• A Solution:
  • Multum In Parvo - Many things in a small place (i.e., multiple textures at different levels of resolution)
  • Sometimes called "image pyramids"

openglexamples/textures/stripes.c (Fragment: stripes)

        /**
 * Fill the given matrix with a striped texture.
 *
 * @param stripeWidth   The width of each stripe
 * @param colorA        The color of one stripe
 * @param colorB        The color of the other stripe
 * @param smooth        0 for sharp stripes; otherwise for smooth
 * @param data          The matrix to fill
 */
void createStripedTexture(int stripeWidth, int* colorA, int* colorB, int smooth,
                          GLbyte data[256][256][3]) {
  int u, v;
  float s, t;

  for (u = 0; u < 256; u++) {
    for (v = 0; v < 256; v++) {
      s = sin(PI * u / stripeWidth);

      if (smooth) {
        t = (1.0 + s) / 2.0;
      } else {
        if (s > 0)
          t = 1.0;
        else
          t = 0.0;
      }

      data[u][v][0] = (GLbyte) ((1.0 - t) * colorA[0] + t * colorB[0]);
      data[u][v][1] = (GLbyte) ((1.0 - t) * colorA[1] + t * colorB[1]);
      data[u][v][2] = (GLbyte) ((1.0 - t) * colorA[2] + t * colorB[2]);
    }
  }
}

  // Create the striped "image"
  int stripeWidth = 32;
  GLbyte image[256][256][3];
  createStripedTexture(stripeWidth, purple, gold, 1, image);
        

• Perlin Noise (Perlin, 1985):
  • "White noise" (i.e., a random value for each texel) looks like static
  • Perlin noise is a (non-linear) interpolation of random vectors
• Sums of Sinusoidal Functions:
  • Peachey (1985) developed a marble texture
  • Gardner (1984, 1985) developed terrain and cloud textures