This week the topic I will be covering will be shadows
Radiosity
Direct illumination is not realistic but radiosity is more. With
radiosity you are not cutting off at shadows directly but with it shadows do
not have sharp edges. The edges are soft and blurry which gives it a feel or
realistic and ambient light. Windows and other edges will gain light as it can
now be lit through reflected light instead of relying on direct contribution.
Add power to everything for reflection and set the power to
zero except for the light sources, you then sort everything in order of how
much power it has. Then you thrust some of the power to all the triangles you
see, rinse and repeat.
Shadows
Shadows are used as a form of visual information that allows
us to discern the position of objects at a distance as well as how the light is
a scene operates. From shadows we can discern the strength and direction of
light.
Shadows also give realism to a scene. If there are no
shadows then a scene will look off. Not only this but shadows give us an idea
of the space an object occupies, if something does not have a shadow, or if the
shadow is far away then it looks like it is floating, but if the object is
connected to its shadow then it looks like it is on the ground.
Shadow Mapping
With shadow mapping you want to render the scene twice. The
first time you render the scene it is from the lights point of view. From this
we can get the depth values of all the objects from the light point of view.
This will create what is called a shadow map. You then render the scene from
the cameras view. The newly created shadow map is then projected onto the scene
after being compared to objects depth transformed to the lights position. Areas
that are further away from the light than indicated by the mapping are then
shaded.
This can create a few problems, the first problem being
aliasing. Since all you are doing is overlaying a texture the edges could be
jagged.
We could always raise the texture resolution but there are other ways
to fix this issue. The first way would be to compare multiple samples of the
same map and then filter them. The second way would be to smooth the edges by
using the UV offset of the texture to weight the mapping. If we pull ourselves
off the grid system then we can use non-uniform sampling. While error is still
there we can randomize our samples. Our offsets can be coded in; we can store
two per vector for optimum efficiency. You have to be careful because
constantly changing you offsets will give you undesirable results. You can
pre-compute your values in the screen and based on your already aligned
textures.
Depth Masking
There is always a problem though. If an object is behind
another one, we still calculate the lighting and shading, even if we cannot see
it. This leads to a large amount of unnecessary calculations. In this kind of
scene we try not to use edge mapping, instead we use depth mapping, where, if
there is an edge, we do a minimum and maximum depths for the region, this
prevents us from having to do shading for multiple objects that we cannot see.
Shadow Silhouettes
Silhouette mapping is a way of increasing the qualities of
our shadows without having to increase the size of our textures. The map
contains new positions for the centers of each texel. To do this there is a
three step process, first we start out by rendering our shadow map, after that
we render our silhouette map. We offset our mapping centers in order to
represent our edges better. Finally we do our lighting pass. Through the
silhouette we chose which shadow map texel to pull data from.
To do this we find the location of the current pixel. We
then grab the data of its neighbouring pixels as well. Using this data we find
out which area quadrant the sub location is.
There is one large limitation for silhouette mapping. There
cannot be overlapping silhouettes, doing so creates artifacts. Despite these
limitations silhouette mapping provides a much higher quality than regular shadow
mapping.
Bias
Bias is an increase of the depth values of your shadow map.
You use this when you get incorrect depth values while shading you scene, a
problem caused by the limited precision of depth maps as well as differences in
the sampling rates of shadow maps and the sampling rate of the scene. If you
have to little bias then you get artifacts along the orders of you shadow but
if you give too much bias the shadows will become disjointed from the body
itself.
A bias has two components, numeric and geometric. The
numeric component is simply the shadow map component. The geometric component
is the fact that when a shadow map is applied to an area of a scene, they only
represent a single depth value, this means that a low resolution map, or a highly
sloped scene will affect precision.
To understand bias we need to understand depth textures.
These are what shadow maps use and, are themselves, essentially shadow maps.
These maps hold data from the scene that holds the depth of each piece of geometry.
Through rendering into the depth map we are able to not only save memory, but
render any sized depth texture. These take care or memory issues and slope based
bias without any additional cost. We use depth textures for depth of field,
semi-transparent objects, lens flares and fog.
As you can see above, the light is hitting the plane at an
angle. This causes shadow disconnect. What we want instead is a flattened, untangled
shadow map. For this we need to know how the depth of the terrain changes based
on the texture coordinates.
To do this we need to get the derivative of the texture
coordinates based on the screen, or view, coordinates. This creates a
transformation matrix which transforms information in the screen space to the
texture space, this allows for proper mapping.
