3D graphics eBook - Course Materials Repository

Shadow mapping 179
In order to test a point against the depth map, its position in the scene
coordinates must be transformed into the equivalent position as seen by the
light. This is accomplished by a matrix multiplication. The location of the
object on the screen is determined by the usual coordinate transformation, but
a second set of coordinates must be generated to locate the object in light
space.
The matrix used to transform the world coordinates into the light's viewing
coordinates is the same as the one used to render the shadow map in the first
step (under OpenGL this is the product of the modelview and projection
matrices). This will produce a set of homogeneous coordinates that need a
Visualization of the depth map projected
onto the scene
perspective division (see 3D projection) to become normalized device coordinates, in which each component (x, y,
or z) falls between −1 and 1 (if it is visible from the light view). Many implementations (such as OpenGL and
Direct3D) require an additional scale and bias matrix multiplication to map those −1 to 1 values to 0 to 1, which are
more usual coordinates for depth map (texture map) lookup. This scaling can be done before the perspective
division, and is easily folded into the previous transformation calculation by multiplying that matrix with the
following:
If done with a shader, or other graphics hardware extension, this transformation is usually applied at the vertex level,
and the generated value is interpolated between other vertices, and passed to the fragment level.
Depth map test
Once the light-space coordinates are found, the x and y values usually
correspond to a location in the depth map texture, and the z value corresponds
to its associated depth, which can now be tested against the depth map.
If the z value is greater than the value stored in the depth map at the
appropriate (x,y) location, the object is considered to be behind an occluding
object, and should be marked as a failure, to be drawn in shadow by the
drawing process. Otherwise it should be drawn lit.
If the (x,y) location falls outside the depth map, the programmer must either
decide that the surface should be lit or shadowed by default (usually lit).
Depth map test failures.
In a shader implementation, this test would be done at the fragment level. Also, care needs to be taken when
selecting the type of texture map storage to be used by the hardware: if interpolation cannot be done, the shadow will
appear to have a sharp jagged edge (an effect that can be reduced with greater shadow map resolution).
It is possible to modify the depth map test to produce shadows with a soft edge by using a range of values (based on
the proximity to the edge of the shadow) rather than simply pass or fail.
The shadow mapping technique can also be modified to draw a texture onto the lit regions, simulating the effect of a
projector. The picture above, captioned "visualization of the depth map projected onto the scene" is an example of
such a process.