Mapping Vertices to Texels

A texture looks like it has been pasted or wrapped onto the surface model. In truth, the opposite happens. The 3D models gets flattened onto the 2D texture. Each vertex lands on a location within the bounds of the texture. The 2D coordinates of the location are called texture coordinates, and they are stored as an additional vertex attribute.

Sometimes multiple resolutions of a texture are provided. When the viewer is close to the texture or when the graphics card is a beast, a high-resolution version of the texture is used. When the viewer is too far away from the texture to see detail or if the graphics card is an underachiever, a low-resolution version is used. So that the same texture coordinates can be applied to either resolution, the coordinates are stored not as absolute indices but as proportions in [0, 1].

Consider this square, whose spatial positions span [-1, 1] but whose texture coordinates span [0.2, 0.8]:

content_copyconst positions = [
  -1, -1, 0,
   1, -1, 0,
   1,  1, 0,
  -1,  1, 0,
];

const texPositions = [
  0.2, 0.2,
  0.8, 0.2,
  0.8, 0.8,
  0.2, 0.8, 
];

const attributes = new VertexAttributes();
attributes.addAttribute('position', 4, 3, positions);
attributes.addAttribute('texPosition', 4, 2, texPositions);

const positions = [
  -1, -1, 0,
   1, -1, 0,
   1,  1, 0,
  -1,  1, 0,
];

const texPositions = [
  0.2, 0.2,
  0.8, 0.2,
  0.8, 0.8,
  0.2, 0.8, 
];

const attributes = new VertexAttributes();
attributes.addAttribute('position', 4, 3, positions);
attributes.addAttribute('texPosition', 4, 2, texPositions);

The texture-mapped square appears in the left panel of this renderer, and the complete texture is shown in the right panel:

The wireframe shows the unwrapping of the square onto the texture. Note how the texture coordinates of 0.2 and 0.8 inset the unwrapping by 20% on each side. Drag the vertices around to alter the texture coordinates and see how the textured view changes. In particular, try the following:

• unwrap the square to the entire crate texture
• make the square's two triangles coincide on the texture
• collapse one of the triangles to a line
• unwrap the square to a small corner of the crate texture

Observe that changing a vertex's texture coordinates has no impact on its spatial position. The square steadfastly remains a square, even if its unwrapping is not a square.

Unwrapping a square onto a texture does not require much effort or imagination since it is already flat. Sophisticated models require a more surgical approach and are usually unwrapped in a 3D modeling application, where a mixture of algorithms and manual editing are used to place vertices on the texture.