Week 1 - curves

Question 1

Bezier vs BSpline curves

Answer 1

Bezier: Very flexible and computationally cheap to generate. They are not robust to changes, changing one control point can drastically change the entire shape.

B-Spline: Less flexible, essentially a chain of repeated curves (using one of the curve equations) that are “glued” together. Because it is segmented, only neighbouring nodes will be affected.

Question 2

True or false: In Bezier, the degree of the polynomial defining the curve segment is one less than the number of defining polygon points

Answer 2

Very true

Question 3

Why are there more than one type of curve?

Answer 3

As with any problem, there are multiple ways to ‘solve’ a curve. Some offer more accuracy over what you need to model, some are more scalable and do not require solving high degree polynomials, but require different data structures and are more robust.

E.g. Whilst you can technically draw a curve by using the equation of a circle and drawing arcs or similarly polynomial curves, is that really useful for visual artists that want to create curved surfaces? They would always have to find the parameters for the equation and so on.