Curves

de Casteljau Cubic

Build one cubic Bezier point through three exact interpolation levels.

de-casteljau-cubic A cubic Bezier point is found by interpolating four controls down to three points, then two points, then one point.

Example

Build a cubic Bezier point through three interpolation levels.

highlighted = computed this step

Step 1 — Set up

Set up the exact input values.

control points and t(((0, 0), (1, 3), (4, 3), (6, 0)), 1/3)\begin{array}{c|c}\text{control points and t}&\text{(((0, 0), (1, 3), (4, 3), (6, 0)), 1/3)}\end{array}
de Casteljau cubicThree interpolation levels reveal the cubic point.P0P1P2P3

Step 2 — First level

Compute the highlighted value.

level one((1/3, 1), (2, 3), (14/3, 2))\begin{array}{c|c}\text{level one}&\hlmath{\text{((1/3, 1), (2, 3), (14/3, 2))}}\end{array}
de Casteljau cubicThree interpolation levels reveal the cubic point.P0P1P2P3A1B1C1

Step 3 — Second level

Compute the highlighted value.

level two((8/9, 5/3), (26/9, 8/3))\begin{array}{c|c}\text{level two}&\hlmath{\text{((8/9, 5/3), (26/9, 8/3))}}\end{array}
de Casteljau cubicThree interpolation levels reveal the cubic point.P0P1P2P3A1B1C1DE

Step 4 — Cubic point

Compute the highlighted value.

curve point(14/9, 2)\begin{array}{c|c}\text{curve point}&\hlmath{\text{(14/9, 2)}}\end{array}
de Casteljau cubicThree interpolation levels reveal the cubic point.P0P1P2P3A1B1C1DEF