# Cubic Bezier Curve - General Questions

A bezier curve B(t) has 4 control points P0 = (0,0,0) , P1 = (1,0,0), P2 = (1,1,1) , P3 = (0,1,1). Which of the following are correct:

a) B(-2) is not defined
b) B(-1) = (-1,-1,-1)
c) B(t) , t in [0,1] is in the plane that P0,P1,P2 define.

I don't know if t can have values in a range not in [0,1]. The Bezier curves are parametric relations in general. We can define parametric equations that describe curves and t not in [0,1], but i never have read about Bezier Curves with t not in [0,1] so i am confused. For c) i believe that the Bezier Curve is in the plain that ALL control points define and not in some of them.

Again we have a Bezier curve B(t) with 4 control points but now in 2-dimensions.

The P0 = (1,0) and the P3 = (0,1) The curve must be tangent at P0 in y-axis and tangent at P3 at x-axis [*]. When t = 0.5 must pass from the point A(4,4).

Find control points P1 and P2.

In the equation that describe the cubic Bezier curve we set t =0.5. Then we create two relations one for the x and one for the y. But if P1(x1,y1) and P2 = (x2,y2) we have 4 unknowns and 2 relations. So we need another 2. Here i am confused about the *. Especially * means that derivative of the equation that describe the cubic bezier curve must be 0 in x coordinate, for t = 0 ? How i can create the other two equations that we help me to solve the problem ?

• RE: "For c) i believe that the Bezier Curve is in the plain that ALL control points define and not a some of them." A quadratic Bezier lies in the plane of the 3 control points. A cubic allows the curve not be constrained to a plane (assuming the control points are non-planar). Jul 21 at 9:51