Computer Graphics Through OpenGL, 2nd Edition

Chapter 17

Hermite

Our objective in this chapter is to learn a method of interpolating a set of control points, in other words, finding a curve (or surface) that passes through each. Bézier curves, as we know, mandatorily interpolate only their first and last control points, while Bézier surfaces only the four corner control points. B-spline curves and surfaces of quadratic and higher degree do not necessarily interpolate any of their control points. Nevertheless, we learned in Section 16.2.5 how to force a B-spline curve to interpolate a control point by raising the multiplicity of a knot. In fact, the so-called standard knot vector, with repeated end knots, is often used to ensure the interpolation of end control points.

However, if a designer ...