Composite Bezier Cubic Curve:
![1645_Composite Bezier Cubic Curve.png](https://www.expertsmind.com/CMSImages/1645_Composite%20Bezier%20Cubic%20Curve.png)
where
![1512_Composite Bezier Cubic Curve1.png](https://www.expertsmind.com/CMSImages/1512_Composite%20Bezier%20Cubic%20Curve1.png)
Continuity of curve implies
![28_Composite Bezier Cubic Curve2.png](https://www.expertsmind.com/CMSImages/28_Composite%20Bezier%20Cubic%20Curve2.png)
Continuity of slope implies
![1198_Composite Bezier Cubic Curve3.png](https://www.expertsmind.com/CMSImages/1198_Composite%20Bezier%20Cubic%20Curve3.png)
Thus the three points
must be collinear.
Now
![1565_Composite Bezier Cubic Curve5.png](https://www.expertsmind.com/CMSImages/1565_Composite%20Bezier%20Cubic%20Curve5.png)
i.e.
![174_Composite Bezier Cubic Curve6.png](https://www.expertsmind.com/CMSImages/174_Composite%20Bezier%20Cubic%20Curve6.png)
Therefore
is also determined from
and
.
The only free vertex in
is
. Also from the above requirements illustrated that
are all coplanar. But the curve may yet be 3D as
and may be defined freely.