Euclidean Distance in a Rectangular Framework

• The Euclidean distance in a rectangular space is given by

D = (xa - xb)2 + (ya - yb)2 +(za - zb)2 .

• A straight line is the minimum distance path between a and b.

• The variables are linearly related by the parametric equations

of a line.

• The equation of the line segment from a to b is given by

x = xa + (x - xb) µ

y = ya + (y - yb) µ

z = za + (z - zb) µ where the parameter µ is in [0, 1].