 Quartic treble-knot representation of a quadratic B-spline

For a uniform quadratic B-spline with interior control points $P_i$, label its $i$th span $[i,i+1]$. A quartic B-spline with interior spline knot sequence ${\tau }_{3i}={\tau }_{3i+1}={\tau }_{3i+2}=i$ represents the identical curve whenTo verify this, raise each quadratic Bézier curve span twice by degree elevation of Bernstein coefficients. The three interior quartic controls are the displayed points. One additional knot insertion at each interior knot supplies the shared endpoint as the mean of its two neighboring controls, recovering all five quartic Bézier curve controls. Thus the knot multiplicity is three, giving $C^1$ joins rather than imposing unwanted extra smoothness.