A cubic Bézier curve is defined by four points: P₀, P₁, P₂ and P₃.

The curve is constructed as follows:
On the segments P₀P₁, P₁P₂ and P₂P₃ the points Q₀,Q₁ and Q₂ are drawn such that
P₀Q₀ / P₀P₁ = P₁Q₁ / P₁P₂ = P₂Q₂ / P₂P₃ = t (t in [0,1]).
On the segments Q₀Q₁ and Q₁Q₂ the points R₀ and R₁ are drawn such that
Q₀R₀ / Q₀Q₁ = Q₁R₁ / Q₁Q₂ = t for the same value of t.
On the segment R₀R₁ the point B is drawn such that R₀B / R₀R₁ = t for the same value of t.
The Bézier curve defined by the points P₀, P₁, P₂, P₃ is the locus of B as Q₀ takes all possible positions on the segment P₀P₁.
(Please note that for all points the value of t is the same.)

At this (external) web address you will find an applet that allows you to drag the points P₀, P₁, P₂ and P₃ to see what the Bézier curve (green curve) defined by those points looks like. You can also drag the point Q₀ along the segment P₀P₁.

From the construction it is clear that the Bézier curve will be tangent to the segments P₀P₁ in P₀ and P₂P₃ in P₃.

A cubic Bézier curve with P₀=(1,0), P₁=(1,v), P₂=(v,1) and P₃=(0,1) is used to approximate a quarter circle.
The value v > 0 is chosen such that the area enclosed by the lines OP₀, OP₃ and the curve is equal to ^π/₄ (the area of the quarter circle).