Curves

de Casteljau Quadratic

Build one quadratic Bezier point by interpolating between control points, then interpolating again.

Example

Build a quadratic Bezier point by repeated linear interpolation.

highlighted = computed this step

Step 1 — Set up

Set up the exact input values.

control points and t(((0, 0), (2, 4), (6, 0)), 1/2)\begin{array}{c|c}\text{control points and t}&\text{(((0, 0), (2, 4), (6, 0)), 1/2)}\end{array}
de Casteljau quadraticLinear interpolations reveal the quadratic point.P0P1P2

Step 2 — First edge

Compute the highlighted value.

first edge point(1, 2)\begin{array}{c|c}\text{first edge point}&\hlmath{\text{(1, 2)}}\end{array}
de Casteljau quadraticLinear interpolations reveal the quadratic point.P0P1P2Q0

Step 3 — Second edge

Compute the highlighted value.

second edge point(4, 2)\begin{array}{c|c}\text{second edge point}&\hlmath{\text{(4, 2)}}\end{array}
de Casteljau quadraticLinear interpolations reveal the quadratic point.P0P1P2Q0Q1

Step 4 — Curve point

Compute the highlighted value.

R(5/2, 2)\begin{array}{c|c}\text{R}&\hlmath{\text{(5/2, 2)}}\end{array}
de Casteljau quadraticLinear interpolations reveal the quadratic point.P0P1P2Q0Q1R
de-casteljau-quadratic de Casteljau's algorithm turns a curve point into repeated exact linear interpolation.