GameMaker: Bezier curve/path simulation

Bezier curve/path simulation in GameMaker

If you are working with GameMaker, you might have wandered, how to make paths similar to standard ones but in 3 dimensions, or how to efficiently draw path of non-1px width, or other things not covered by path functions.

For this reason, I have made the following function:

(technically, it is a port of my AS3 function, which in turn was built around explanation by xot)

/// bezier(position, ordinates:ds_list)
var _list, _pos, _length, _index, p, c, n;
_list = argument1
_length = ds_list_size(_list)
_pos = max(0, min(1, argument0)) * _length;
_index = min(floor(_pos), _length - 1);
_pos -= _index // _pos is now (0..1)
// previous\current\next value:
p = ds_list_find_value(_list, max(_index - 1, 0))
c = ds_list_find_value(_list, _index)
n = ds_list_find_value(_list, min(_length - 1, _index + 1))
// actual calculations (yes, you need to know the formula for these):
return .5 * (((p - 2 * c + n) * _pos + 2 * (c - p)) * _pos + p + c)


  • argument0 'position' is position in list (0..1). Script also handles 'out of range' problems just in case you forget to make sure it's in valid range.
  • argument1 'points' is a pointer (index) of ds_list containing list of point coordinates (or rather, values, since this is a 1-dimensional array, but anyway). Normally you would want a single list and script call per each axis (2d = 2 lists, 3d = 3 lists, etc.).

How to use it: first, you will need several ds_list's, which will contain your values. Then, for each point, add point's coordinates into according lists. The following code would convert a existing 2d path into two ds_list's:
list_x = ds_list_create()
list_y = ds_list_create()
path = path_test;
for (i = 0; i < path_get_number(path); i += 1) {
    ds_list_add(list_x, path_get_point_x(path, i))
    ds_list_add(list_y, path_get_point_y(path, i))

If you want to simulate exact GameMaker's behavior relating to number of points, set for-loop step to 1 / (length << precision), where length is number of points in path, and precision is 'precision' parameter of path. Initial value of loop variable should be set to half of step value.

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5 thoughts on “GameMaker: Bezier curve/path simulation

  1. this is a most useful game maker tutorial page i’ve found.
    Thanks Yallll
    now i can go on making my game with your tut :)

  2. Thanks for the code.
    I’m expanding the script to work with closed paths, but I want understand the formula, how did you get the mathematical expression?, is really a Bézier curve?

    • I cannot easily locate the source material that I have used for formula, but I believe that it was a modification of cubic bézier curve formula. GameMaker’ curves are slighlty non-standard due to “handle points” being decided automatically, which probably means that you cannot particularly classify them as bezier curves of any given order.

      As per closed paths, I believe that you need to taking last point’s ordientate when calculating for the first and vice versa to have that working correctly.

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