3D graphics eBook - Course Materials Repository

Texture mapping 215
Perspective correctness
Texture coordinates are specified at
each vertex of a given triangle, 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 – textures (the checker boxes) appear bent).
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.
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
Perspective correct mapping interpolates after dividing by depth , then uses its interpolated reciprocal to
recover the correct coordinate:
All modern 3D graphics hardware implements perspective correct texturing.
Classic texture mappers generally did only simple mapping with at
most one lighting effect, and the perspective correctness was about 16
times more expensive. To achieve two goals - faster arithmetic results,
and keeping the arithmetic mill busy at all times - every triangle is
further subdivided into groups of about 16 pixels. For perspective
texture mapping without hardware support, a triangle is broken down
into smaller triangles for rendering, which improves details in
non-architectural applications. 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
(compared to 2d affine interpolation) and thus again the overhead (also
affine texture-mapping does not fit into the low number of registers of
Doom renders vertical spans (walls) with affine
texture mapping.
the x86 CPU; the 68000 or any RISC is much more suited). For instance, Doom restricted the world to vertical walls
and horizontal floors/ceilings. This meant the walls would be a