Gamemaker - Maintain relative position between objects during rotation

Question

I have a large object and a small object - the small object updates its x and y position every step to match the x and y of the larger object. It is easy to keep it in the same position on the larger object without any rotation, as follows (in this instance, slightly above and to the right of the centre of the larger object, here called Owner:

x = Owner.x + 50
y = Owner.y - 50

However, this all goes pearshaped if the larger object is rotated from its sprite's initial position!

How can I maintain the relative position of the two objects even when rotated?

Answer 1

You need to use lengthdir_x and lengthdir_y functions, like:

x = owner.x + lengthdir_x(distance, owner.image_angle); // or owner.direction
y = owner.y + lengthdir_y(distance, owner.image_angle);

Also see answer for similar question, with an example and special tool for calculate values.

P.S. And remember that you need do it in End Step event, and not simple Step

Answer 2

I don't know about GameMaker, but usually you need to rotate second object with an angle of the first one like this:

// Distances between two object are needed
dx = 50;
dy = 50;

// Cosinus and Sinus are needed
cos = Cos(angle);
sin = Sin(angle);

// Calculate rotation
x = cos * dx - sin * dy + Owner.x;
y = cos * dy + sin * dx + Owner.y;

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You can also check Wikipedia article about rotation.