Describe the difference between the explicit formula, a closed form and a parametric form for a curve in two dimensions. Give illustrations to describe your answer.
Describe the term mathematical continuity (Cn) when joining the two curves.
Give the formulation of the cubic Bezier curve in two dimensions, describing the role of the parameter and control points.
Consider the joint between the two cubic Bezier curves. Define and prove the constraints on their control points to make sure:
a) C0 continuity at the joint
b) C1 continuity at the joint
c) C2 continuity at the joint
Describe the implications of requiring C3 continuity at joint between the two cubic Bezier curves.