根据对象的角度移动对象

Question

I am trying moving an object based on its rotation, and I have 4 methods:

• forward
• backward
• up
• down

Of the 4 methods, only forward and backward seem to be working properly. The other two seem to have a different effect based on the rotation. When it is set to a 90 degree rotation it acts the same as forward (forward is down the screen at this rotation), but in reality the desired affect is for it to move right.

These two methods seem to be working properly:

public get forward(): Vector2 {
    return new Vector2(
        Math.cos(this.rotation.degrees * (Math.PI / 180)),
        Math.sin(this.rotation.degrees * (Math.PI / 180))
    );
}

public get backward(): Vector2 {
    return new Vector2(
        -Math.cos(this.rotation.degrees * (Math.PI / 180)),
        -Math.sin(this.rotation.degrees * (Math.PI / 180))
    );
}

These two however are not working properly. I can not seem to figure out what is causing this, I assumed the math would be similar, maybe I am wrong on that?

public get up(): Vector2 {
    return new Vector2(
        Math.cos(this.rotation.degrees * (Math.PI / 180)),
        -Math.sin(this.rotation.degrees * (Math.PI / 180))
    );
}

public get down(): Vector2 {
    return new Vector2(
        -Math.cos(this.rotation.degrees * (Math.PI / 180)),
        Math.sin(this.rotation.degrees * (Math.PI / 180))
    );
}

Answer 1

You should calculate it this way: up is +90 degrees from forward , down is -90 degrees from forward (and backward is just 180 degrees from forward ).

In other words:

public get up(): Vector2 {
    const phi = (this.rotation.degrees + 90) * (Math.PI / 180);
    return new Vector2(
        Math.cos(phi),
        Math.sin(phi)
    );
}

Negating cos / sin without the other clearly isn't correct. Just -cos , for example, just means "move in the opposite direction in the x axis and keep the y axis velocity the same". The case where forward points North-Northeast, for example, would create a vector going North-Northwest.

Answer 2

If you calculate cos and sin for main direction once, then vector components are:

forward:            cos,   sin
backward:          -cos,   -sin
up(really left):   -sin,    cos
down(really right): sin,   -cos