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I have got discrete time model of the point x movement to point y stated as:

$$z = x + s\left( \frac{y - x}{||y-x||} \right)$$

where

z - is new position s- is some offset for example 0,04 || y - x || - euclidean norm operator z,x,y are points in some m-dimensional R space 

How to use this model (how to calculate) in

  1. two dimensional real space where point x (1, 1) moves to point y (4, 2) with s 0,04
  2. three dimensional real space where point x(1, 1, 1) moves to point y(3, 2, 3) with s 0,04

2 Answers 2