# shadow mapping and linear depth

I'm implementing ominidirectional shadow mapping for point lights. I want to use a linear depth which will be stored in the color textures (cube map). A program will contain two filtering techniques: software pcf (because hardware pcf works only with depth textures) and variance shadow mapping. I found two ways of storing linear depth:

const float linearDepthConstant = 1.0 / (zFar - zNear);
//first
float moment1 = -viewSpace.z * linearDepthConstant;
float moment2 = moment1 * moment1;
outColor = vec2(moment1, moment2);
//second
float moment1 = length(viewSpace) * linearDepthConstant;
float moment2 = moment1 * moment1;
outColor = vec2(moment1, moment2);


What are differences between them ? Are both ways correct ?

For the standard shadow mapping with software pcf a shadow test will depend on the linear depth format. What about variance shadow mapping ?

I implemented omnidirectional shadow mapping for points light using a non-linear depth and hardware pcf. In that case a shadow test looks like this:

vec3 lightToPixel = worldSpacePos - worldSpaceLightPos;
vec3 aPos = abs(lightToPixel);
float fZ = -max(aPos.x, max(aPos.y, aPos.z));
vec4 clip = pLightProjection * vec4(0.0, 0.0, fZ, 1.0);
float depth = (clip.z / clip.w) * 0.5 + 0.5;


I also implemented standard shadow mapping without pcf which using second format of linear depth: (Edit 1: i.e. distance to the light + some offset to fix shadow acne)

vec3 lightToPixel = worldSpacePos - worldSpaceLightPos;
const float linearDepthConstant = 1.0 / (zFar - zNear);
float fZ = length(lightToPixel) * linearDepthConstant;
if(depth <= fZ)
{
}
else
{
}


but I have no idea how to do that for the first format of linear depth. Is it possible ?

Edit 2: For non-linear depth I used glPolygonOffset to fix shadow acne. For linear depth and distance to the light some offset should be add in the shader. I'm trying to implement standard shadow mapping without pcf using a linear depth (-viewSpace.z * linearDepthConstant + offset) but following shadow test doesn't produce correct results:

vec3 lightToPixel = worldSpacePos - worldSpaceLightPos;
vec3 aPos = abs(lightToPixel);
float fZ = -max(aPos.x, max(aPos.y, aPos.z));
vec4 clip = pLightProjection * vec4(0.0, 0.0, fZ, 1.0);
float fDepth = (clip.z / clip.w) * 0.5 + 0.5;
if(depth <= fDepth)
{
}
else
{
}


How to fix that ?

The method with viewSpace.z is storing depth, while the method with length(viewSpace) is storing distance to the light, not depth (which is always measured parallel to a view direction).
Depth is the natural choice as that's what will be generated by the GPU rasterizer when you draw the shadow map. It takes extra work to convert it to distance (you have to set up the viewSpace vector). But I can imagine that distance might give better results in some situations with VSM. You'd have to experiment to see.