why sPos.z is uesd to get texcoord in shadow mapping - directx

Question

why use sPos.z here to get tescoord?
Out.shadowCrd.x = 0.5 * (sPos.z + sPos.x);
Out.shadowCrd.y = 0.5 * (sPos.z - sPos.y);
Out.shadowCrd.z = 0;
Out.shadowCrd.w = sPos.z;
It is a shader which achieves shadow mapping in "Shaders for Game Programming and Artists".
The first pass render depth texture in light space.( light is camera and watch towards the origin )
The second pass get the depth and calculate the shadow.
Before these codes, the model has already been transformed to light space.
Then the texcoord should be calculated to read depth texture.
But I can't understand the algorithm of calculating the texcoord. Why sPos.z will be here?
Here is the whole vertex shader of the second pass
float distanceScale;
float4 lightPos;
float4 view_position;
float4x4 view_proj_matrix;
float4x4 proj_matrix;
float time_0_X;
struct VS_OUTPUT
{
float4 Pos: POSITION;
float3 normal: TEXCOORD0;
float3 lightVec : TEXCOORD1;
float3 viewVec: TEXCOORD2;
float4 shadowCrd: TEXCOORD3;
};
VS_OUTPUT vs_main(float4 inPos: POSITION, float3 inNormal: NORMAL)
{
VS_OUTPUT Out;
// Animate the light position.
float3 lightPos;
lightPos.x = cos(1.321 * time_0_X);
lightPos.z = sin(0.923 * time_0_X);
lightPos.xz = 100 * normalize(lightPos.xz);
lightPos.y = 100;
// Project the object's position
Out.Pos = mul(view_proj_matrix, inPos);
// World-space lighting
Out.normal = inNormal;
Out.lightVec = distanceScale * (lightPos - inPos.xyz);
Out.viewVec = view_position - inPos.xyz;
// Create view vectors for the light, looking at (0,0,0)
float3 dirZ = -normalize(lightPos);
float3 up = float3(0,0,1);
float3 dirX = cross(up, dirZ);
float3 dirY = cross(dirZ, dirX);
// Transform into light's view space.
float4 pos;
inPos.xyz -= lightPos;
pos.x = dot(dirX, inPos);
pos.y = dot(dirY, inPos);
pos.z = dot(dirZ, inPos);
pos.w = 1;
// Project it into light space to determine she shadow
// map position
float4 sPos = mul(proj_matrix, pos);
// Use projective texturing to map the position of each fragment
// to its corresponding texel in the shadow map.
sPos.z += 10;
Out.shadowCrd.x = 0.5 * (sPos.z + sPos.x);
Out.shadowCrd.y = 0.5 * (sPos.z - sPos.y);
Out.shadowCrd.z = 0;
Out.shadowCrd.w = sPos.z;
return Out;
}
Pixel Shader:
float shadowBias;
float backProjectionCut;
float Ka;
float Kd;
float Ks;
float4 modelColor;
sampler ShadowMap;
sampler SpotLight;
float4 ps_main(
float3 inNormal: TEXCOORD0,
float3 lightVec: TEXCOORD1,
float3 viewVec: TEXCOORD2,
float4 shadowCrd: TEXCOORD3) : COLOR
{
// Normalize the normal
inNormal = normalize(inNormal);
// Radial distance and normalize light vector
float depth = length(lightVec);
lightVec /= depth;
// Standard lighting
float diffuse = saturate(dot(lightVec, inNormal));
float specular = pow(saturate(
dot(reflect(-normalize(viewVec), inNormal), lightVec)),
16);
// The depth of the fragment closest to the light
float shadowMap = tex2Dproj(ShadowMap, shadowCrd);
// A spot image of the spotlight
float spotLight = tex2Dproj(SpotLight, shadowCrd);
// If the depth is larger than the stored depth, this fragment
// is not the closest to the light, that is we are in shadow.
// Otherwise, we're lit. Add a bias to avoid precision issues.
float shadow = (depth < shadowMap + shadowBias);
// Cut back-projection, that is, make sure we don't lit
// anything behind the light.
shadow *= (shadowCrd.w > backProjectionCut);
// Modulate with spotlight image
shadow *= spotLight;
// Shadow any light contribution except ambient
return Ka * modelColor +
(Kd * diffuse * modelColor + Ks * specular) * shadow;
}