Calculate the vector perpendicular to a triangle (GML).

triangle_normals.gml

function triangle_normal(x1, y1, z1, x2, y2, z2, x3, y3, z3) {
    gml_pragma("forceinline");
    var v1x = x2 - x1;
    var v1y = y2 - y1;
    var v1z = z2 - z1;
    var v2x = x3 - x1;
    var v2y = y3 - y1;
    var v2z = z3 - z1;
    var cx = v1y * v2z - v1z * v2y;
    var cy = -v1x * v2z + v1z * v2x;
    var cz = v1x * v2y - v1y * v2x;
    
    // if this is zero, the triangle has zero area and won't be visible anyway
    var cpl = point_distance_3d(0, 0, 0, cx, cy, cz);
    
    if (cpl != 0) return [cx / cpl, cy / cpl, cz / cpl];
    return [0, 0, 1];
}

triangle_normals_legacy.gml

/// @param x1
/// @param y1
/// @param z1
/// @param x2
/// @param y2
/// @param z2
/// @param x3
/// @param y3
/// @param z3
/// @return a three-element array containing the x, y, and z component of the triangle's normal.

gml_pragma("forceinline");

var v1x = argument3 - argument0;
var v1y = argument4 - argument1;
var v1z = argument5 - argument2;
var v2x = argument6 - argument0;
var v2y = argument7 - argument1;
var v2z = argument8 - argument2;

var cx = v1y * v2z - v1z * v2y;
var cy = -v1x * v2z + v1z * v2x;
var cz = v1x * v2y - v1y * v2x;

var cpl = point_distance_3d(0, 0, 0, cx, cy, cz);

if (cpl != 0) {
    return [cx / cpl, cy / cpl, cz / cpl];
}

return [0, 0, 1];

Just saw your comment. Here's the reminder ;).

Edit: anyways, it was already revamped. Thanks Dragonite for the always really useful (well not always always) content.