How to fix diagonal velocity being greater than axis-aligned?

Question

I have a 2D top-down RPG type game, with movement in 8 directions (N/E/S/W/NE/NW/SE/SW) involving both x and y velocity.

I'm finding when I'm moving in the diagonal directions, I'm building both x and y velocity and it's making my character move faster than they do in a straight line along only x or only y. Is there a fix for this, so no matter which of the 8 directions I travel along, it's the same speed?

My code works like this. I initialize my variables and speed:

vel_x, vel_y=0  
spd=1

Then each frame in my game loop, I apply drag to reduce the velocity:

vel_x*=0.2  
vel_y*=0.2

Then my button presses add/subtract the spd value from their corresponding velocity direction x/y when pressed.

Lastly, I add the vel_x to my sprite's x position and same with vel_y for my sprite's y position.

How would I address this? Would I look at button press actions for when both keys are held, or limits for when vel_x and vel_y are 'high' enough in tandem?

I've done the latter and it helps, but I can't make it accurate.

Images: With velocity removed and just +-1 speed increases/decreases. Left is the proposed adjustment to the vertical movement. Right is no adjustment. Is left moving at same speed all the time and right isn't?

Answer 1

Is there a fix for this so no matter what of the 8 I travel its the same speed?

Yes... You want to apply a total force and split it between x and y

To do this for any angle, you apply ± totalForce * sin(angle) in one direction, and ± totalForce * cos(angle) in the other.

Your case is simpler as the angle is fixed at 45 degrees when moving diagonally, and conveniently both sin(45) and cos(45) are the same ... 0.70710678118 (which happens to be 1/sqrt(2))

So multiply your X and Y forces by 0.70710678118 when moving diagonally, and the total will be the same as when moving in a cardinal direction.

Even better... If you use the formulas above instead of the fixed value, it works for any direction including N/E/S/W.

You can get the angle from the player's current rotation around the Y axis.

How would I address this...?

If I've understood correctly and you're concerned about how forces add up over time...

Usually, you apply some form of damping so that movement decreases over time if there's no input.

You can do this a number of ways, but the simplest is probably to calculate the current speed (eg by checking how far the sprite had travelled in the timespan since the last frame) then multiply that speed by some number just below 1 (say 0.95) and use that as your speed for the next frame.

That way, when you're applying a force, the sprite accelerates and when you let go, it slows down and eventually comes to a stop.

If you can't find a value that feels "just right", there's a lot of research on different ways to damp... Wikipedia's article on Damping might be a good starting point to get some search terms.

Edit:

Is this equivalent to me irl walking straight 1m/s then turning diag and walking 1ms?

Yes

Think in terms of a 2D grid. We'll draw a triangle with the base being how far we travel in X and the side being how far we travel in y.

The hypotenuse is the resulting motion.

Moving Straight up?

• x stays at zero
• y increments by 1

No need to do any fancy calculations as that's obviously 1 unit.

Now let's move diagonally NE...

• x increases by 0.70710678118
• y increases by 0.70710678118

How long is the hypotenuse? Well, from Pythagoras, it should be

sqrt(x ^ 2 + y ^ 2)
or
sqrt(0.70710678118 ^ 2 + 0.70710678118 ^ 2)

(Remember I said 0.70710678118 is equivalent to 1/sqrt(2)? This is one reason that's helpful to know ...).

1 / sqrt(2) ^ 2 simplifies to 1/2 or 0.5

So we get

sqrt(0.5 + 0.5)
or
sqrt(1)

Which is -of course- 1

So yes, it's moving at the same speed of 1 unit/s.

Answer 2

You use trigonometry. Here we can just use the Pythagorean theorem:

a² + b² = c²

If the player is moving at a 45° angle, a and b are the same, so we can simplify to

2a² = c²
a² = c²/2
a = sqrt(c²/2)

Let's say that your desired movement speed is 10.

2a² = 10²
a² = 100 / 2
a = sqrt(50)
a = 7.071

So if you want the player to move diagonally at a total speed of 10 units/second, move them 7.071 units along X and 7.071 units along Y.

Answer 3

Think intuitively first.

orthogonal speed is a 2D Vector with an X and Y component.

if that Vector was (1,1). Then that makes the multiplier for x and y both 1. That means that diagonally, you're still going to be traversing the grid at 1 /ms in both directions.

Anytime we accelerate / decelerate we modify the speed vector.

the speed vector gets multiplied by the amount of time that has elapsed since the last frame in this case.

You then simply add / subtract the position vector.