Interpolation of Multidimensional Functions - Control of Color Imaging Systems: Analysis and Design - page 257

Tetrahedral 1 Tetrahedral 2 Tetrahedral 3

Tetrahedral 4 Tetrahedral 5 Tetrahedral 6

FIGURE 6.9 Dividing the cube into six tetrahedrals.

(2) If x x 0 > z z 0 > y y 0 , then p is in tetrahedral 2 and

p x ¼ p 100 p 000 , p y ¼ p 111 p 101 , and p z ¼ p 101 p 100 ( 6 : 12 )

(3) If z z 0 > x x 0 > y y 0 , then p is in tetrahedral 3 and

p x ¼ p 101 p 001 , p y ¼ p 111 p 101 , and p z ¼ p 001 p 000 ( 6 : 13 )

(4) If y y 0 > x x 0 > z z 0 , then p is in tetrahedral 4 and

p x ¼ p 110 p 010 , p y ¼ p 010 p 000 , and p z ¼ p 111 p 110 ( 6 : 14 )

(5) If y y 0 > z z 0 > x x 0 , then p is in tetrahedral 5 and

p x ¼ p 111 p 011 , p y ¼ p 010 p 000 , and p z ¼ p 011 p 010 ( 6 : 15 )

(6) If z z 0 > y y 0 > x x 0 , then p is in tetrahedral 6 and

p x ¼ p 111 p 011 , p y ¼ p 011 p 001 , and p z ¼ p 001 p 000 ( 6 : 16 )