Multimedia maths (E-boek) by Ivo De Pauw & Bieke Masselis

Author:Ivo De Pauw & Bieke Masselis [De Pauw, Ivo]
Language: eng
Format: epub
Publisher: Terra - Lannoo, Uitgeverij
Published: 2016-10-12T07:00:00+00:00

Distance between two points

We are now able to calculate the distance between two given points A and B straightforwardly as the length of their created free vector (see formula (6.2)).

EULER’S METHOD FOR TRAJECTORIES

Especially in game programming, the trajectory by a moving location vector due to an acceleration is often realized via a method named after the Swiss mathematician Leonard Euler (1707–1783). Euler estimates the moving point’s trajectory, given its acceleration function as an initial value problem. For such a problem we know at time zero t0 what we nowadays call the frame data of point S:

the initial location vector

its initial velocity

and the scalar delta time between two successive frames.

Taking off with our initial location and velocity we now try to determine and straightforwardly for the next frame. In case of sufficiently small time intervals Δt, we may assume the instantaneous velocity and acceleration equal to the average velocity and acceleration:

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