Orthographic parallel projection Finding the starting point of

Orthographic (parallel) projection: Finding the starting point of the ray P(0, 0): origin of image plane P(4, 1): image pixel at i=4, j=1 v n u P(0, 0) P(4, 1)

Orthographic (parallel) projection: Finding the starting point of the ray P(0, 0): origin of image plane P(4, 1): image pixel at i=4, j=1 v n u P(0, 0) P(4, 1)

Orthographic (parallel) projection: Finding the starting point of the ray P(0, 0): origin of image plane P(4, 1): image pixel at i=4, j=1 v n u P(0, 0) P(4, 1)

Orthographic (parallel) projection: Casting the ray P(0, 0): origin of image plane P(4, 1): image pixel at i=4, j=1 Q(6): ray sample point at k=6 n n n v n u P(0, 0) Q(6) P(4, 1)

Orthographic (parallel) projection: Casting the ray P(0, 0): origin of image plane P(4, 1): image pixel at i=4, j=1 Q(6): ray sample point at k=6 n n n v n u P(0, 0) Q(6) P(4, 1)

Orthographic (parallel) projection: Casting the ray P(0, 0): origin of image plane P(4, 1): image pixel at i=4, j=1 Q(6): ray sample point at k=6 n n n v n u P(0, 0) Q(6) P(4, 1) (assume)

Orthographic (parallel) projection: Interpolation P(0, 0): origin of image plane P(4, 1): image pixel at i=4, j=1 Q(6): ray sample point at k=6 n n n v n u P(0, 0) Q(6) (assume)

y Orthographic (parallel) projection: Interpolation x z 32 30 13 43 Q(6) 20 24 8 10

Orthographic (parallel) projection: Nearest Neighbor Interpolation y x z 32 30 13 43 Q(6) 20 24 8 10

Orthographic (parallel) projection: Nearest Neighbor Interpolation y x z 32 30 13 43 Q(6) 20 24 8 10

Orthographic (parallel) projection: Nearest Neighbor Interpolation y x z 32 30 13 43 Q(6) 20 24 8 10

Orthographic (parallel) projection: Nearest Neighbor Interpolation y x z 32 30 13 43 Q(6) 20 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: Trilinear Interpolation y x z 32 30 13 ww 43 Q(6) vv 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 1 st linear interpolation: along x y x z 32 30 13 43 Q(6) 20 uu 24 8 10

Orthographic (parallel) projection: 2 nd linear interpolation: along y y x z 32 30 13 43 Q(6) vv 20 24 8 10

Orthographic (parallel) projection: 2 nd linear interpolation: along y y x z 32 30 13 43 Q(6) vv 20 24 8 10

Orthographic (parallel) projection: 2 nd linear interpolation: along y y x z 32 30 13 43 Q(6) vv 20 24 8 10

Orthographic (parallel) projection: 2 nd linear interpolation: along y y x z 32 30 13 43 Q(6) vv 20 24 8 10

Orthographic (parallel) projection: 2 nd linear interpolation: along y y x z 32 30 13 43 Q(6) vv 20 24 8 10

Orthographic (parallel) projection: 2 nd linear interpolation: along y y x z 32 30 13 43 Q(6) vv 20 24 8 10

Orthographic (parallel) projection: 2 nd linear interpolation: along y y x z 32 30 13 43 Q(6) vv 20 24 8 10

Orthographic (parallel) projection: 3 rd linear interpolation: along z y x z 32 Val(Q(6)) 30 13 ww 43 Q(6) 20 24 8 10

Orthographic (parallel) projection: 3 rd linear interpolation: along z y x z 32 Val(Q(6)) 30 13 ww 43 Q(6) 20 24 8 10

Orthographic (parallel) projection: 3 rd linear interpolation: along z y x z 32 Val(Q(6)) 30 13 ww 43 Q(6) 20 24 8 10

Orthographic (parallel) projection: 3 rd linear interpolation: along z y x z 32 Val(Q(6)) 30 13 ww 43 Q(6) 20 24 8 10