The black "circle" is created with the approximation. The red circle is a "perfect" circle created with the regular (slow) sqrt equation. Visually, this is what the equation would create if you used it with a speed of 150 and fired projectiles in every direction. The inverse of the square root of 2 is roughly 0.70711, which is where I get the 0.29289 from (1 - 0.29289 = 0.70711). What it does is look at the x and y parts of the vector, and adjust them from 100% to 70.711% based on how close their absolute values are to each other (how diagonal the vector is essentially). Depending on your programming language, using conditionals in place of the abs and max functions will be faster. Ideally, I would like to get rid of the division, but I haven't figured out a way yet. This is faster mainly because it doesn't use a square root function and only uses one division instead of 2. Here is an approximation that I came up with for the unit vector: You probably don't need perfectly-accurate calculations for your game, so it is often better to use an approximation that is faster. This is all fine and good, but the square root function and the two divisions can slow things down if you're using it a lot every frame (and the trigonometry version is slower yet).
The above will give you a vector from player to enemy that will travel 12 per iteration, regardless of the angle of the vector or how far away enemy was from player. Divide by magnitude and multiply by desired speed The speed you want the projectile to travel In 2D gaming, you often use unit vectors along with multipliers to calculate a projectile's vector based on the speed you want it to travel at.
DETERMINE ANGLE VECTOR 2D CODE
You can also use trigonometry to calculate it, but it is slower:īoth code blocks above will give you the same unit vector. To get a unit vector, the easiest and most accurate way is to divide each part of the vector by the vector's magnitude (length). Think about the actual length of the line (it's magnitude) and you'll understand why (1,1) is not a unit vector. Notice that while (1,0) is a unit vector, (1,1) is not. Unit vector and normalized vector are often used interchangeably. To get a unit vector from any old vector, you "normalize" that vector, which gives you a new vector with the same direction but a magnitude of 1.
The vector can be pointing in any direction, but the magnitude will always be 1. A unit vector is a vector with a magnitude (distance) of 1. Here's a quick description of a unit vector for those that don't know.
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