The cells of a structured grid are usually saved linearly in memory. For example, in 2D...

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The cells of a structured grid are usually saved linearly in memory. For example, in 2D the cells (i, j) are saved to the linear memory space at indices according to the following scheme: (0,2) (1,2) (2.2) j (0,1) (1,1) (2,1) (0,0) (1,0) (2,0) (0,1) (1,1) (2,1) (0,2) (1,2) (2,2) 0 1 2 3 4 5 6 7 8 l (0,0) (1,0) (2,0) i Let a structured grid in 3D consist of (nx, ny, nz) grid points in each dimension. (a) Find the map (i, j, k) that maps 3D cell indices to linear cell indices. Assume that the first dimension (i) varies fastest in the linear memory space. (b) Find the map (i,j,k) that maps linear cell indices to 3D cell indices. Assume again that the first dimension (i) varies fastest in the linear memory space. The cells of a structured grid are usually saved linearly in memory. For example, in 2D the cells (i, j) are saved to the linear memory space at indices according to the following scheme: (0,2) (1,2) (2.2) j (0,1) (1,1) (2,1) (0,0) (1,0) (2,0) (0,1) (1,1) (2,1) (0,2) (1,2) (2,2) 0 1 2 3 4 5 6 7 8 l (0,0) (1,0) (2,0) i Let a structured grid in 3D consist of (nx, ny, nz) grid points in each dimension. (a) Find the map (i, j, k) that maps 3D cell indices to linear cell indices. Assume that the first dimension (i) varies fastest in the linear memory space. (b) Find the map (i,j,k) that maps linear cell indices to 3D cell indices. Assume again that the first dimension (i) varies fastest in the linear memory space.