Pixel-Composer/scripts/curve_bezier_function/curve_bezier_function.gml

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//curve format [-cx0, -cy0, x0, y0, +cx0, +cy0, -cx1, -cy1, x1, y1, +cx1, +cy1]
//segment format [y0, +cx0, +cy0, -cx1, -cy1, y1];
#macro CURVE_DEF_01 [0, 0, 0, 0, 1/3, 1/3, /**/ -1/3, -1/3, 1, 1, 0, 0]
#macro CURVE_DEF_10 [0, 0, 0, 1, 1/3, -1/3, /**/ -1/3, 1/3, 1, 0, 0, 0]
#macro CURVE_DEF_11 [0, 0, 0, 1, 1/3, 0, /**/ -1/3, 0, 1, 1, 0, 0]
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function draw_curve(x0, y0, _w, _h, _bz, miny = 0, maxy = 1) {
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var segments = array_length(_bz) / 6 - 1;
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for( var i = 0; i < segments; i++ ) {
var ind = i * 6;
var _x0 = _bz[ind + 2];
var _y0 = _bz[ind + 3];
//var bx0 = _x0 + _bz[ind + 0];
//var by0 = _y0 + _bz[ind + 1];
var ax0 = _x0 + _bz[ind + 4];
var ay0 = _y0 + _bz[ind + 5];
var _x1 = _bz[ind + 6 + 2];
var _y1 = _bz[ind + 6 + 3];
var bx1 = _x1 + _bz[ind + 6 + 0];
var by1 = _y1 + _bz[ind + 6 + 1];
//var ax1 = _x1 + _bz[ind + 6 + 4];
//var ay1 = _y1 + _bz[ind + 6 + 5];
var dx0 = x0 + _w * _x0;
var dx1 = x0 + _w * _x1;
var dw = dx1 - dx0;
var smp = ceil((_x1 - _x0) * 32);
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draw_curve_segment(dx0, y0, dw, _h, [_y0, ax0, ay0, bx1, by1, _y1], smp, miny, maxy);
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}
}
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function draw_curve_segment(x0, y0, _w, _h, _bz, SAMPLE = 32, miny = 0, maxy = 1) {
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var _ox, _oy;
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for(var i = 0; i <= SAMPLE; i++) {
var t = i / SAMPLE;
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var _r = eval_curve_segment_t_position(t, _bz);
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var _rx = _r[0], _ry = _r[1];
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_ry = (_ry - miny) / (maxy - miny);
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var _nx = _rx * _w + x0;
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var _ny = (_h? _ry : 1 - _ry) * abs(_h) + y0;
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if(i)
draw_line(_ox, _oy, _nx, _ny);
_ox = _nx;
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_oy = _ny;
}
}
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function eval_curve_segment_t_position(t, _bz) {
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return [
power(1 - t, 3) * 0
+ 3 * power(1 - t, 2) * t * _bz[1]
+ 3 * (1 - t) * power(t, 2) * _bz[3]
+ power(t, 3) * 1,
power(1 - t, 3) * _bz[0]
+ 3 * power(1 - t, 2) * t * _bz[2]
+ 3 * (1 - t) * power(t, 2) * _bz[4]
+ power(t, 3) * _bz[5]
];
}
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function eval_curve_segment_t(_bz, t) {
return power(1 - t, 3) * _bz[0]
+ 3 * power(1 - t, 2) * t * _bz[2]
+ 3 * (1 - t) * power(t, 2) * _bz[4]
+ power(t, 3) * _bz[5];
}
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function eval_curve_x(_bz, _x, _prec = 0.00001) {
static _CURVE_DEF_01 = [0, 0, 0, 0, 1/3, 1/3, /**/ -1/3, -1/3, 1, 1, 0, 0];
static _CURVE_DEF_10 = [0, 0, 0, 1, 1/3, -1/3, /**/ -1/3, 1/3, 1, 0, 0, 0];
static _CURVE_DEF_11 = [0, 0, 0, 1, 1/3, 0, /**/ -1/3, 0, 1, 1, 0, 0];
if(array_equals(_bz, _CURVE_DEF_11)) return 1;
if(array_equals(_bz, _CURVE_DEF_01)) return _x;
if(array_equals(_bz, _CURVE_DEF_10)) return 1 - _x;
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var segments = array_length(_bz) / 6 - 1;
_x = clamp(_x, 0, 1);
for( var i = 0; i < segments; i++ ) {
var ind = i * 6;
var _x0 = _bz[ind + 2];
var _y0 = _bz[ind + 3];
//var bx0 = _x0 + _bz[ind + 0];
//var by0 = _y0 + _bz[ind + 1];
var ax0 = _x0 + _bz[ind + 4];
var ay0 = _y0 + _bz[ind + 5];
var _x1 = _bz[ind + 6 + 2];
var _y1 = _bz[ind + 6 + 3];
var bx1 = _x1 + _bz[ind + 6 + 0];
var by1 = _y1 + _bz[ind + 6 + 1];
//var ax1 = _x1 + _bz[ind + 6 + 4];
//var ay1 = _y1 + _bz[ind + 6 + 5];
if(_x < _x0) continue;
if(_x > _x1) continue;
return eval_curve_segment_x([_y0, ax0, ay0, bx1, by1, _y1], (_x - _x0) / (_x1 - _x0));
}
return array_safe_get(_bz, array_length(_bz) - 3);
}
function eval_curve_segment_x(_bz, _x, _prec = 0.00001) {
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var st = 0;
var ed = 1;
var _xt = _x;
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var _binRep = 8;
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if(_x <= 0) return _bz[0];
if(_x >= 1) return _bz[5];
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if(_bz[0] == _bz[2] && _bz[0] == _bz[4] && _bz[0] == _bz[5]) return _bz[0];
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repeat(_binRep) {
var _ftx = power(1 - _xt, 3) * 0
+ 3 * power(1 - _xt, 2) * _xt * _bz[1]
+ 3 * (1 - _xt) * power(_xt, 2) * _bz[3]
+ power(_xt, 3) * 1;
if(abs(_ftx - _x) < _prec)
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return eval_curve_segment_t(_bz, _xt);
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if(_xt < _x)
st = _xt;
else
ed = _xt;
_xt = (st + ed) / 2;
}
var _newRep = 8;
repeat(_newRep) {
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var slope = ( 9 * _bz[1] - 9 * _bz[3] + 3) * _xt * _xt
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+ (-12 * _bz[1] + 6 * _bz[3]) * _xt
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+ 3 * _bz[1];
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var _ftx = power(1 - _xt, 3) * 0
+ 3 * power(1 - _xt, 2) * _xt * _bz[1]
+ 3 * (1 - _xt) * power(_xt, 2) * _bz[3]
+ power(_xt, 3) * 1
- _x;
_xt -= _ftx / slope;
if(abs(_ftx) < _prec)
break;
}
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_xt = clamp(_xt, 0, 1);
return eval_curve_segment_t(_bz, _xt);
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}
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function bezier_range(bz) {
return [ min(bz[0], bz[2], bz[4], bz[5]), max(bz[0], bz[2], bz[4], bz[5]) ];
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}
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function ease_cubic_in(rat) {
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return power(rat, 3);
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}
function ease_cubic_out(rat) {
return 1 - power(1 - rat, 3);
}
function ease_cubic_inout(rat) {
return rat < 0.5 ? 4 * power(rat, 3) : 1 - power(-2 * rat + 2, 3) / 2;
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}