Spatial-Temporal Query Results

For time slice C_t₁ the x-query S_xC_t₁ = S_x(x₁,x₂)C_t₁ = (u: C_x₁,t₁ < C_x₂,t₁) produces MAT(S_xC_t₁) = (u: a < b)_t₁
The y-query S_yC_t₁ = S_y(y₁,y₂)C_t₁ produces MAT(S_yC_t₁) = (v: b < a)_t₁
The x-t-query S_x (x₁^o, x₂^o) (S_t (t₁, t₂, t₃) R)) = (t: (u: C_x₁,t₁< C_x₂,t₁) < (u: C_x₁,t₂< C_x₂,t₂) < (u:C_x₁,t₃ < C_x₂,t₃)) produces the following result,

MAT(S_x (x₁^o, x₂^o) (S_t (t₁, t₂, t₃) R)) = (t: (u: a< b)_t₁ < (u: a< b)_t₂ < (u:a < b)_t₃)
NOTE: In the 2D space, (S_xR, S_yR) is exactly the same as the pair of symbolic projections (u,v).