Texture mapping basics

1. Per-Vertex UVs: Each mesh vertex carries a texture coordinate (u,v) (assigned in modeling or by a function).

2. Barycentric Interpolation: During rasterization, compute each pixel’s (u,v) by interpolating the three vertices’ UVs with barycentric weights \alpha,\beta,\gamma.

3. Sampling: Use that per-pixel (u,v) to look up (and bilinearly filter) the texture.

4. Addressing Modes (when \(u,v\not\in[0,1]\)):

   
   

   • Repeat: wrap around (tile).

   • Mirror: reflect every other tile.

   • Clamp: clamp to edge texel.

   • Border: return a constant border color.

   
   

1. Interpolating texture coordinates in screenspace results in incorrect perspectives

2. Carry out correction through division by homogeneous coordinates

• A texture that encodes per-pixel normals instead of just color.

• Used to fake small-scale surface detail by perturbing the shading normal, so lighting shows bumps and dents without extra geometry.

• Adds rich surface detail (tiny bumps, grooves) in the lighting without increasing the mesh’s triangle count—high visual fidelity at low geometric cost.

1. Sample the normal map at the fragment’s UV coordinate to get a “bump” normal.

2. Transform it from tangent space into world (or eye) space.

3. Use this perturbed normal in your lighting calculations (diffuse, specular) instead of the interpolated mesh normal.

• A displacement map is a 2D texture that stores per-texel offsets along the surface normal.

• Unlike bump/normal maps, which only perturb shading normals (no real geometry change), displacement maps actually move each surface point by the stored offset.

• Effects:

  
  

  • Produces correct self-shadowing and silhouettes.

  • Requires modifying vertex positions (e.g. in a tessellation or height-map pass) or adjusting the Z-value in a software rasterizer.

  
  

• Benefit: Real geometric detail at low memory cost; true depth and occlusion without extra modeling.

• An environment map is a texture (e.g., a spherical or cubemap) that represents the surrounding scene.

• For each shaded point a, compute the reflection vector b

• Use b to index into the environment map (convert b into UV coordinates) to fetch the reflected color.

• This fakes specular reflections of the entire environment (not just light sources) with minimal cost.

• Cube Map: A form of environment map stored as six square textures—one for each face of a virtual cube surrounding the scene.

• Generation: Place a camera at the environment’s center (with only background objects), render six 90°-FOV images looking along +X, –X, +Y, –Y, +Z, –Z, and store each in its corresponding cube face.

• Application: For each reflective surface point, compute the world-space reflection vector r, determine which cube face r points into, and use its 2D (s,t) coordinates on that face to sample the cube map—automatically providing correct reflections (for the original capture point).

You need 6 render passes and then one independent of that one object to render the scene

d2 > d1

Can have more passes with more light sources

• Definition: Rendering the same scene multiple times off-screen (into intermediate textures), each pass computing a different effect (e.g. shadows, reflections, highlights, lighting passes).

For each texture multiple resolutions versions are pre-computed. Depending on the camera distance, the the appropriate level of detail is chosen for texturing

• if camera is close, high resolution textures

provide details

• if camera is far, low resolution textures are good

enough (fine details will not be visible anyway)

• this always provides optimal rendering

performance