Joining curves

You can join two adjoining curves and then smooth out the join between them. The knot vectors provide a straightforward mechanism for doing this. For example, you might have two pinned uniform cubic curves with knot vectors starting at zero that meet at a common point. Follow the steps outlined below and shown in Figure 44 to join the curves. The curves being joined are both order four (k=4) curves.

  1. Add the last value in the knot vector of the first curve to all of the knots in the second curve.
  2. Remove the first control point and the k first knots from the second curve where k = order. Remove the last knot from the first curve and concatenate the control points and the knot vector of the second curve.
  3. To smooth the join, space apart the knots where the two knot vectors were joined. This removes the discontinuity. As they are moved further apart, the join becomes less sharp.

The TCurve::Concatenation function joins the curve passed to it to the end of the calling curve.

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