Shadow mapping

Method to draw shadows in computer graphic images

Shadow mapping or shadowing projection is a process by which shadows are added to 3D computer graphics. This concept was introduced by Lance Williams in 1978, in a paper entitled "Casting curved shadows on curved surfaces." Since then, it has been used both in pre rendered and realtime scenes in many console and PC games. Shadows are created by testing whether a pixel is visible from the light source, by comparing the pixel to a z buffer or depth image of the light source's view, stored in the form of a texture.

If you looked out from a source of light, all the objects you can see would appear in light. Anything behind those objects, however, would be in shadow. This is the basic principle used to create a shadow map. The light's view is rendered, storing the depth of every surface it sees (the shadow map). Next, the regular scene is rendered comparing the depth of every point drawn (as if it were being seen by the light, rather than the eye) to this depth map. This technique is less accurate than shadow volumes, but the shadow map can be a faster alternative depending on how much fill time is required for either technique in a particular application and therefore may be more suitable to real time applications. In addition, shadow maps do not require the use of an additional stencil buffer and can be modified to produce shadows with a soft edge. Unlike shadow volumes, however, the accuracy of a shadow map is limited by its resolution.

Rendering a shadowed scene involves two major drawing steps. The first produces the shadow map itself, and the second applies it to the scene. Depending on the implementation (and the number of lights), this may require two or more drawing passes.

The first step renders the scene from the light's point of view. For a point light source, the view should be a perspective projection as wide as its desired angle of effect (it will be a sort of square spotlight). For directional light (e. g., that from the Sun), an orthographic projection should be used. From this rendering, the depth buffer is extracted and saved. Because only the depth information is relevant, it is common to avoid updating the color buffers and disable all lighting and texture calculations for this rendering, to save drawing time. This depth map is often stored as a texture in graphics memory. This depth map must be updated any time there are changes to either the light or the objects in the scene, but can be reused in other situations, such as those where only the viewing camera moves. (If there are multiple lights, a separate depth map must be used for each light.) In many implementations, it is practical to render only a subset of the objects in the scene to the shadow map to save some of the time it takes to redraw the map. Also, a depth offset which shifts the objects away from the light may be applied to the shadow map rendering in an attempt to resolve stitching problems where the depth map value is close to the depth of a surface being drawn (i. e., the shadow casting surface) in the next step. Alternatively, culling front faces and only rendering the back of objects to the shadow map is sometimes used for a similar result.

The second step is to draw the scene from the usual camera viewpoint, applying the shadow map. This process has three major components. The first step is to find the coordinates of the object as seen from the light, as a 3D object only uses 2D coordinates with axis X and Y to represent its geometric shape on screen, these vertex coordinates will match up with the corresponding edges of the shadow parts within the shadow map (depth map) itself. The second step is the depth test which compares the object z values against the z values from the depth map, and finally, once accomplished, the object must be drawn either in shadow or in light.

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 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.

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). 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.

One of the key disadvantages of real time shadow mapping is that the size and depth of the shadow map determine the quality of the final shadows. This is usually visible as aliasing or shadow continuity glitches. A simple way to overcome this limitation is to increase the shadow map size, but due to memory, computational or hardware constraints, it is not always possible. Commonly used techniques for real time shadow mapping have been developed to circumvent this limitation. These include Cascaded Shadow Maps, Trapezoidal Shadow Maps, Light Space Perspective Shadow maps, or Parallel Split Shadow maps. Also notable is that generated shadows, even if aliasing free, have hard edges, which is not always desirable. In order to emulate real world soft shadows, several solutions have been developed, either by doing several lookups on the shadow map, generating geometry meant to emulate the soft edge or creating non standard depth shadow maps. Notable examples of these are Percentage Closer Filtering, Smoothies, and Variance Shadow maps.

PSSM "Parallel Split" https://developer. nvidia. com/gpugems/GPUGems3/gpugems3 ch10. html
CSM "Cascaded" http://developer. download. nvidia. com/SDK/10.5/opengl/src/cascaded shadow maps/doc/cascaded shadow maps. pdf

LiSPSM "Light Space Perspective" https://www. cg. tuwien. ac. at/research/vr/lispsm/
TSM "Trapezoid" http://www. comp. nus. edu. sg/~tants/tsm. html
PSM "Perspective" http://www sop. inria. fr/reves/Marc. Stamminger/psm/
CSSM "Camera Space" http://bib. irb. hr/datoteka/570987.12 CSSM. pdf

PCF "Percentage Closer Filtering" https://developer. nvidia. com/gpugems/GPUGems/gpugems ch11. html

ESM "Exponential" https://discovery. ucl. ac. uk/id/eprint/10001/1/10001. pdf
CSM "Convolution" https://doclib. uhasselt. be/dspace/bitstream/1942/8040/1/3227. pdf
VSM "Variance" http://citeseerx. ist. psu. edu/viewdoc/download?doi=10.1.1.104.2569&rep=rep1&type=pdf
SAVSM "Summed Area Variance" https://developer. nvidia. com/gpugems/gpugems3/part ii light and shadows/chapter 8 summed area variance shadow maps
SMSR "Shadow Map Silhouette Revectorization" http://bondarev. nl/?p=326

PCSS "Percentage Closer" http://developer. download. nvidia. com/shaderlibrary/docs/shadow PCSS. pdf
VSSM "Variance Soft Shadow Mapping" https://jankautz. com/publications/VSSM PG2010. pdf
SSSS "Screen space soft shadows" http://www. crcnetbase. com/doi/abs/10.1201/b10648 36
FIV "Fullsphere Irradiance Vector" http://getlab. org/publications/FIV/