Texture Mapping

Software Methodologies

  • A method for adding surface details

  • Aims at increasing realism

    • Relying on mesh geometry to create such details is expensive

    • Lighting/shading models are not enough

  • Associate 2D information with 3D surface

Texture and 3D object

  • Texture image: 2D array of colour values (Texels)

  • Assigning texture coordinates (s,t) at vertex with object coordinates (x,y,z,w)

    • Use interpolated (s,t) for texel lookup at each pixel

    • Use the retrieved colour value to modify a polygon’s colour (or other surface properties)

    • Can be done manually or automatically

Texture Atlas
A large image containing a collection of sub-images, each of which is a texture for some part of an object

Types of texture mapping methods

Identify the correspondence between a texel and a screen pixel

There are two types of mapping methods

Forward texture mapping
Compute 3D positions of the texture points and then project them onto the image plane
Inverse Texture Mapping
Select every pixel in the image plane and identify which point of the texture image is projected there

Coordinate systems in CG application

Parametric Coordinates
A logical coordinate system for processing the surface and the internal space of a 3D object
Texture Coordinates
Used to identify points in the image to be mapped
Local or World Coordinates
Used to position 3D objects
Window Coordinates
Where the final output image is really produced

Types of texture mapping

Forward Texture Mapping

Mapping from texture coordinates to points on a surface, need three functions:

$$x=x(s,t)$$ $$y=y(s,t)$$ $$z=z(s,t)$$

Main Problem - Adjacent texture points may project onto non adjacent image points, thus creating a non coloured image area

Backwards texture mapping

Given a point on an object, we identify to which point in the texture map it corresponds, need a map of the form

$$s=s(x,y,z)$$ $$t=t(x,y,z)$$

Good - Make sure every object has a corresponding texel, particularly visibility of an object point is considered.

Bad - Such functions are difficult to find in general

Two part mapping process

Map a texture image to a complicated shape to create texture mapping coordinates (UV map is difficult)

Break the texture mapping into two parts

  • Map the texture to a simple intermediate surface

  • The textured intermediate surface is then mapped to the object

Second mapping

Map from intermediate object

  • Normals from intermediate to actual

  • Normals from actual to intermediate

  • Vectors from centre of intermediate

MIP Mapping

Use an image pyramid to precompute coarse versions of a texture, store the whole pyramid in a single block of memory. This helps with aliasing.

Advantages of MIP mapping

  • Reduce memory consumption of running application

  • Support anti aliasing, offering better output quality of a CG application

  • Only 1/3 more space required

Normal Mapping

Normal vectors encoded as an image. Generate visually 3D effect by applying lighting to perturbed normal vectors on the object surface.

Bump mapping

  • Treat the texture as a single valued height function

  • Compute the normal from the partial derivatives in the texture

  • The heights encode the amount by which to perturb N in the (u,v) directions of the parametric space describing the object surface

Normal Map vs Bump Map

Bump Map:

  • Texture (greyscale) encodes height

  • Modifies the geometric normal

  • Harder to implement

  • Easier to specify

Normal map:

  • Texture (RGB) encodes normal directly

  • Replaces the normal

  • Easier to implement

  • Harder to specify

Displacement Mapping

  • Use texture map to actually move surface points

  • Geometry must be displaced before visibility is determined

  • Done as a preprocess or with complicated vertex/fragment shader implementation

Environment Maps

  • We can simulate reflections by using the direction of the reflected ray to index a spherical texture map at “infinity”

  • Assumes that all reflected rays begin from the same point

Light mapping

  • Realistic lighting can be achieved

  • Every single bit of expensive lighting calculation is done pre-process time, avoiding overhead

  • At run times, all calculations are done by hardware and so is very fast

  • Visual quality of the lighting is directly dependent on the size of the light map texture(s)

  • For every triangle, a diffuse texture map is applied first and then a light map is usually modulated with it

Fog maps

  • Dynamic modification of light maps

  • Put fog objects into the scene

  • Compute where they intersect with geometry and paint the fog density into a dynamic light map

  • Apply the fog map as with a light map