= 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 when
$$
Q_{3i-1}=\frac{P_{i-1}+3P_i}{4},\quad Q_{3i}=\frac{P_{i-1}+10P_i+P_{i+1}}{12},\quad Q_{3i+1}=\frac{3P_i+P_{i+1}}4.
$$
To 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.
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