Texture Mapping
Texture mapping is a method for adding detail, surface texture, or
colour to a
computer-generated graphic or
3D model. Its application to 3D graphics was pioneered by Dr
Edwin
Catmull in his Ph.D. thesis of 1974.
Contents
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1 Texture
mapping
-
2 Perspective
correctness
-
3 See also
-
4 References
-
5 External links
Texture mapping
A texture map is applied (mapped) to the surface of a shape, or
polygon. This process is akin to applying patterned paper to a plain white box.
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. 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, such as tree bark or rough concrete, 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.
Examples of multitexturing
1. Untextured sphere 2. Texture and bump maps 3. Texture map only 4.
Opacity and texture maps
The way the resulting
pixels on the
screen are calculated from the
texels (texture pixels) is governed by
texture filtering. The fastest 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.
Perspective correctness
Because affine texture mapping does not take into account the depth
information about a polygon's vertices, where the polygon is not
perpendicular to the viewer it produces a noticeable defect.
Texture coordinates are specified at each vertex of a given triangle (for
graphics hardware, polygons are generally broken down into triangles for
rendering), and these coordinates are interpolated using an extended
Bresenham's line algorithm. If these texture coordinates are
linearly interpolated across the screen, the result is affine texture
mapping. This is a fast calculation, but there can be a noticeable
discontinuity between adjacent triangles when these triangles are at an angle to
the plane of the screen (see figure at right).
Perspective correct texturing accounts for the vertices' positions in
3D space, rather than simply interpolating a 2D triangle. This achieves the
correct visual effect, but it is slower to calculate. Instead of interpolating
the texture coordinates directly, the coordinates are divided by their depth
(relative to the viewer), and the reciprocal of the depth value is also
interpolated and used to recover the perspective-correct coordinate. 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
(stretching the texture wider), and in parts that are farther away this
difference is larger (compressing the texture).
- Affine texture mapping directly interpolates a texture coordinate
between two endpoints
and
:
-
where
![](/images/textile/textile-fibers/t7.png)
- Perspective correct mapping interpolates after dividing by depth
,
then uses its interpolated reciprocal to recover the correct coordinate:
Most modern graphics hardware implements perspective correct texturing, but when
games still relied on software rendering, perspective correct texturing had to
be used sparingly because of its computational expense. Several different
techniques were developed to hide the defect of affine texture mapping. For
instance, ,
Doom restricted the world to vertical walls and horizontal
floors/ceilings. This meant the walls would be a constant distance along a
vertical line and the floors/ceilings would be a constant distance along a
horizontal line. A fast affine mapping could be used along those lines because
it would be correct. 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, producing a compromise between
the speed of affine texturing and perspective correctness.
Another technique was subdividing the polygons into smaller polygons and
using an affine mapping on them. The distortion of affine mapping becomes much
less noticeable on smaller polygons. Yet another technique was approximating the
perspective with a faster calculation such as a polynomial. Finally, some
programmers extended the constant distance trick used for Doom by finding the
line of constant distance for arbitrary polygons and rendering along it.
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