Two cubic bezier curves

Question

Question 1:

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.

Question 2:

Describe the term mathematical continuity (C_n) when joining the two curves.

Question 3:

Give the formulation of the cubic Bezier curve in two dimensions, describing the role of the parameter and control points.

Question 4:

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

Question 5:

Describe the implications of requiring C₃ continuity at joint between the two cubic Bezier curves.