Texture mapping


Texture mapping is a method for defining high frequency detail, surface texture, or color information on a computer-generated graphic or 3D model. The original technique was pioneered by Edwin Catmull in 1974.
Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface. In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene.
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1: Untextured sphere, 2: Texture and bump maps, 3: Texture map only, 4: Opacity and texture maps

Texture maps

A is an image applied to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3d model formats or material definitions, and assembled into resource bundles.
They may have 1-3 dimensions, although 2 dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping.
They usually contain RGB color data, and sometimes an additional channel for alpha blending especially for billboards and decal overlay textures. It is possible to use the alpha channel for other uses such as specularity.
Multiple texture maps may be combined for control over specularity, normals, displacement, or subsurface scattering e.g. for skin rendering.
Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware.. Modern hardware often supports cube map textures with multiple faces for environment mapping.

Creation

Texture maps may be acquired by scanning/digital photography, designed in image manipulation software such as GIMP, Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or zbrush.

Texture application

This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate.
This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3d space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion.
These coordinates are interpolated across the faces of polygons to sample the texture map during rendering.
Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface.

Texture space

Texture mapping maps the model surface into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations.

Multitexturing

Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps may add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in recent video games, as graphics hardware has become powerful enough to accommodate it in real-time.

Texture filtering

The way that samples are calculated from the texels is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles.

Baking

As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process into a surface texture. Baking is also known as render mapping. This technique is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps.
Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering.

Rasterisation algorithms

Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility and performance.

Forward texture mapping

Some hardware systems e.g. Sega Saturn and the NV1 traverse texture coordinates directly, interpolating the projected position in screen space through texture space and splatting the texels into a frame buffer.. Sega provided tools for baking suitable per-quad texture tiles from UV mapped models.
This has the advantage that texture maps are read in a simple linear fashion.
Forward texture mapping may also sometimes produce more natural looking results than affine texture mapping if the primitives are aligned with prominent texture directions. This provides a limited form of perspective correction. However, perspective distortion is still visible for primitives near the camera.
This technique is not used in modern hardware because UV coordinates have proved more versatile for modelling and more consistent for clipping.

Inverse texture mapping

Most approaches use inverse texture mapping, which traverses the rendering primitives in screen space whilst interpolating texture coordinates for sampling. This interpolation may be affine or perspective correct. One advantage is that each output pixel is guaranteed to only be traversed once; generally the source texture map data is stored in some lower bit-depth or compressed form whilst the frame buffer uses a higher bit-depth. Another is greater versatility for UV mapping. A texture cache becomes important for buffering reads, since the memory access pattern in texture space is more complex.

Affine texture mapping

Affine texture mapping linearly interpolates texture coordinates across a surface, and so is the fastest form of texture mapping. Some software and hardware project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed point UV coordinates, or by an incremental error algorithm akin to Bresenham's line algorithm.
In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations, especially as primitives near the camera. Such distortion may be reduced with the subdivision of the polygon into smaller ones.
renders vertical and horizontal spans with affine texture mapping, and is therefore unable to draw ramped floors or slanted walls.

Perspective correctness

Perspective correct texturing accounts for the vertices' positions in 3D space, rather than simply interpolating coordinates in 2D screen space. This achieves the correct visual effect but it is more expensive to calculate.
To perform perspective correction of the texture coordinates and, we can take advantage of the fact that the values, and are linear in screen space, being the depth component from the viewer's point of view. We can therefore linearly interpolate these reciprocals and at each pixel then compute the corrected values from them as, and.
This correction makes it so that in parts of the polygon that are closer to the viewer the difference from pixel to pixel between texture coordinates is smaller and in parts that are farther away this difference is larger.
All modern 3D graphics hardware implements perspective correct texturing.
Various techniques have evolved for rendering texture mapped geometry into images with different quality/precision tradeoffs, which can be applied to both software and hardware.
Classic software texture mappers generally did only simple mapping with at most one lighting effect, and the perspective correctness was about 16 times more expensive.

Restricted camera rotation

The Doom engine restricted the world to vertical walls and horizontal floors/ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors/ceilings would have a constant depth along a horizontal line. A fast affine mapping could be used along those lines because it would be correct. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom whilst using the same rendering technique.
Some engines were able to render texture mapped Heightmaps via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives.

Subdivision for perspective correction

Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals. First, keeping the arithmetic mill busy at all times. Second, producing faster arithmetic results.

World space subdivision

For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony Playstation made extensive use of this because it only supported affine mapping in hardware but had a relatively high triangle throughput compared to its peers.

Screen space subdivision

Software renderers generally preferred screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up and thus again the overhead.
A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. The polygons are rendered independently, hence it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z but the effort seems not to be worth it.

Other techniques

Another technique was approximating the perspective with a faster calculation, such as a polynomial. Still another technique uses 1/z value of the last two drawn pixels to linearly extrapolate the next value. The division is then done starting from those values so that only a small remainder has to be divided but the amount of bookkeeping makes this method too slow on most systems.
Finally, the Build engine extended the constant distance trick used for Doom by finding the line of constant distance for arbitrary polygons and rendering along it.

Hardware implementations

Texture mapping hardware was originally developed for simulation, and professional graphics workstations such as Silicon Graphics, broadcast digital video effects machines such as the Ampex ADO and later appeared in Arcade cabinets, consumer video game consoles, and PC video cards in the mid 1990s. In flight simulation, texture mapping provided important motion cues.
Modern graphics processing units provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU.
Some hardware combines texture mapping with hidden-surface determination in tile based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the Z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting.

Applications

Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks:

Tomography

It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results

User interfaces

Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Expose in Mac OS X.

Software