A curve with continuity is a curve that is smooth and without kinks or breaks. A curve with discontinuity is a curve that has kinks and breaks in it. Discontinuities can be added to a curve to change its shape. Adding discontinuities to a curve by adding control points is discussed under the heading "Adding control points" on page 84.
A C0 discontinuity is an actual break in the curve, and a C1 discontinuity is a change in the tangent (a kink in the curve). You get a Cn discontinuity in a curve when the knot vector contains the same value k - n times in a row. Figure 41 shows a cubic curve with the knot vector [00001222344445555]. The C1 discontinuity occurs at 2 (k1 = 3 twos in a row), and the C0 discontinuity occurs at 4 (k0 = 4 fours in a row).
The following functions let you get and make discontinuities:
- TCurve::GetNextDiscontinuity returns the next discontinuity of the type requested (C0, C1, Corder1).
- TCurve::MakeDiscontinuity adds a Cn discontinuity at parametric location u without changing the shape of the curve.
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