Curves & Surfaces

Last Updated February 22, 2010

How can a parametric equation of a surface be used to render that surface in a system like OpenGL
Derive the parametric equation of a sphere?
What is a ruled surface? Give an example.
Derive a parametric equation in two variables for a sphere of radius R centered at the origin
Derive a parametric equation in two variables for a Torus centred at the origin whose Outer radius is R and Inner radius is r.
Describe an algorithm for building a polygon mesh using the explicit method for a sphere.
Write a detailed note about Bezier curves. How would you represent them parametrically?
Describe Bezier curves in terms of their properties, advantages and disadvantages
With respect to Bezier curves, what is “end-point interpolation”?
Why does a Bezier curve always say inside it’s convex hull?
What is the role of the Blending function in Bezier curves.
Given a curve, p(t), defined on the x-z plane, describe how you would rotate it around z-axis to generate a volume of rotation. Show the parametric equation for the resulting shape. How can this equation be used to build a polygon mesh.
Describe (geometrically) how a Bezier curve of 3 control points is generated.
How is this extended to n-control points.
How is the general Bezier curve described parametrically.
A Bezier curve is defined by the following control points; {(1,1), (2,2), (3,2)}. Find the location of the curve at t=0.5.