Eng:Finding Direction With Velocity

While programming, it is sometimes necessary to find the direction a sprite should point given two velocities (x and y). This article presents the script that will provide the correct direction as well as an explanation of how it works.

The Script
if <(y-vel) = [0]> then if <(x-vel) < [0]> then point in direction (-90 v) else point in direction (90 v) end else if <(y-vel) > [0]> then point in direction ([atan v] of ((x-vel) / (y-vel))) else point in direction ((180) + ([atan v] of ((x-vel) / (y-vel)))) end end

How it Works
The bottom half calculates the direction working on the assumption that y is not zero (which would yield an error when x is divided by y). The mathematical function "atan" which stands for "Arc Tangent" and is the inverse of tangent, a trigonometric function used to determine the ratio of the two legs of a right triangle.

The script essentially treats the x and y axes as the two legs of a right triangle, using "atan" to derive the angle. However, as the angle has to be between -90 and 90, the "y > 0" conditional (or Boolean Block) must be added to point the sprite in the proper direction.

It is notable that typical geometry uses atan(y/x) (rather than x/y) to determine the angle; the flip made in the script is to match with Scratch's unusual degree measurement system (0 is typically right).

The top half of the script is a simple comparison. If y velocity is zero, the only possible directions ignoring the chance that the x velocity could be zero  are right and left (90 and -90 degrees). Should both the x and y velocities be zero, the sprite will face right (90 degrees).

Example Uses

 * Finding out the direction the mouse is moving in
 * Predicting the position of the character in a platformer in a few seconds, maybe as a power up tool.
 * Finding the direction an arrow should point in given an x and y velocity