How to calculate width, height and position of bezier curve -


i have bezier curve defined start point, end point , 2 control points (parameters of this: http://www.w3schools.com/tags/canvas_beziercurveto.asp). first, need calculate width , height of curve. if make rectangle around curve, width , height need. need start point (x,y of left top corner) of rectangle.

how can calculate ? thanks.

i found approximate solution in other topic (i don't remember one) here simple js function calculate it:

function getcurveboundary(ax, ay, bx, by, cx, cy, dx, dy) {         var tobx = bx - ax;         var toby = - ay;         var tocx = cx - bx;         var tocy = cy - by;         var todx = dx - cx;         var tody = dy - cy;         var step = 1 / 40;    // precission         var d, px, py, qx, qy, rx, ry, tx, ty, sx, sy, x, y, i, minx, miny, maxx, maxy;         function min(num1, num2) {             if (num1 > num2)                 return num2;             if (num1 < num2)                 return num1;             return num1;         }         function max(num1, num2) {             if (num1 > num2)                 return num1;             if (num1 < num2)                 return num2;             return num1;         }         (var = 0; < 41; i++)         {             d = * step;             px = ax + d * tobx;             py = ay + d * toby;             qx = bx + d * tocx;             qy = + d * tocy;             rx = cx + d * todx;             ry = cy + d * tody;             toqx = qx - px;             toqy = qy - py;             torx = rx - qx;             tory = ry - qy;              sx = px + d * toqx;             sy = py + d * toqy;             tx = qx + d * torx;             ty = qy + d * tory;             totx = tx - sx;             toty = ty - sy;              x = sx + d * totx;             y = sy + d * toty;             if (i == 0)             {                 minx = x;                 miny = y;                 maxx = x;                 maxy = y;             }             else             {                 minx = min(minx, x);                 miny = min(miny, y);                 maxx = max(maxx, x);                 maxy = max(maxy, y);             }         }         return {x: math.round(minx), y: math.round(miny), width: math.round(maxx - minx), height: math.round(maxy - miny)};     }

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