Interpolating Points and Curve Continuity

By default, the control points are interpolated with a curve of cubic order, using a uniform BSpline curve knot vector. This creates a curve that has 2nd order continuity at both the geometric and parametric levels. One way of understanding the effect of cubic interpolation using a uniform knot vector is to think about there being the same length of curve between each of the control points. When two control points become quite close, as the span of curve has to put somewhere, loops can often appear.

4. Using the previous example, move two of the control points close together. A loop should form as a result. In the image below, a sharp point or loop has formed as a result of the close proximaty of two control points.

A closer inspection of the two control points show the shape of the loop in the curve.

Interpolating control points using a uniform knot vector often results in undesirable undulations in the curve shape in order to achieve C2 continuity. The undesirable loops and undulations can be removed by intepolating the control points using a non-uniform knot vector based on chord length.

5. Change the interpolation technique to use a non-uniform knot vector based on the distance between control points (Chord Length), (Right-Click -> X-Topology Curve -> Cubic Spline Knot Vector based on Chord Length).

The loop in the curve should now be smooth out.

The overal shape of the curve should now be improved. However, the curve will no longer be C2 continuous and this is one of the compromises in using these mathematics. C2 continuous curves can be created but to ensure a desirable shape the control points must be placed in the right locations. In practice, this is not always possible and this feature allows a fair curve shape to be obtained athough the shape may not be fully C2 continuous.

Applying Constraints to X-Topology Curve Control Points >>>