Question

I am messing around with some Javascript game development, trying to create a simple Framework for drawing a playing field (for a sports game).

I am horrible at math and really need help with this algorithm.

Say I have these variables:

GAME_WIDTH = 1024;  
FIELD_LENGTH = 170;  
PLAYER_SPEED = 4.72;  
update_duration = 30;  

The first 3 in caps are variable, meaning they can be set by the user. The last is essentially how often my “update” code is called in 1 second.

GAME_WIDTH is pixels, FIELD_LENGTH is meters, PLAYER_SPEED is how many seconds a player can cover 40 meters.

What I want to do, is take those 4 variables and translate that into how many pixels a player can move in 1 “update”. I have never really done any Game Development and I never payed attention to Geometry or Trigonometry in school so I am completely at a loss here.
Can anyone help?

EDIT
This is a 2D top-down game so this algorithm is only dealing with X (right-to-left) coordinates.

Answer 1

You need to embrace the fine art of “Units Conversion”.
http://oakroadsystems.com/math/convert.htm

For example, 12 inches = 1 foot. So you can convert inches to feet like so:

48 inches * (1 foot / 12 inches) = 4 feet. The “inches” cancel out, leaving just feet.

So the answer we want is pixels per update. (Is update_duration in milliseconds? assuming so…)

(40 meters / 4.72 seconds) 
 * (1024 pixels / 170 meters) 
 * (1 second / 1000 ms) 
 * (30 ms / 1 update) = 1.53140578 pixels / update

or if the 30 is updates/second, same idea:

  (40 meters / 4.72 seconds) 
   * (1024 pixels / 170 meters) 
   * (1 second / 30 updates = 1.70156198 pixels / update

(I may have misinterpreted the meaning of your constants… but that’s the technique. The concept is that each of those fractions, a / b, is equivalent to “1”.

This looks better when you write it in full classroom fraction style, all the canceling becomes chalkboard-perfect. Very useful technique to embrace.