在二次贝塞尔曲线上找到控制点

Question

I drew a Quadratic Bezier curve. Here A(0, 1.39) and B(30, 1.42) are two points and curves drawn with a single control point (15.02, 6.07).

I want to move point B along the curve. But When I move the curve shape changes. So I want to move the control point also with respect to point B.

Pic: Point moved but not control point moved so curve disoriented.

Pic: Point and Control point moved, so the curve is in proper shape.

The blue shape is for reference. Kindly help me to find the control point on moving point B.

Answer 1

You need to subdivide curve onto two new smaller curves. To calculate control point of "left" new curve, when you subdivide large curve at parameter t (in range 0..1):

left_P[1] = large_P[0] * (1-t) + large_P[1] * t

All points of left curve:

left_P[0] = large_P[0]   //initial point
left_P[1] = large_P[0] * (1-t) + large_P[1] * t   //control point
left_P[2] = large_P[0] * (1-t)^2 + 2*large_P[1] * t*(1-t) + large_P[2] * t^2   //last point, coincides with your moving point

For your example t is about 0.7, and

new_C = 0.3*A + 0.7*C