Cubic Bézier curve (§13 "Bézier"), traversed with the parameter advancing linearly in time (u = t / duration).
u = t / duration
B(u) = (1−u)³·p0 + 3(1−u)²u·p1 + 3(1−u)u²·p2 + u³·p3 B'(u) = 3(1−u)²(p1−p0) + 6(1−u)u(p2−p1) + 3u²(p3−p2) B''(u) = 6(1−u)(p2−2p1+p0) + 6u(p3−2p2+p1) Copy
B(u) = (1−u)³·p0 + 3(1−u)²u·p1 + 3(1−u)u²·p2 + u³·p3 B'(u) = 3(1−u)²(p1−p0) + 6(1−u)u(p2−p1) + 3u²(p3−p2) B''(u) = 6(1−u)(p2−2p1+p0) + 6u(p3−2p2+p1)
Velocity is B'(u) / duration and acceleration B''(u) / duration² by the chain rule. The parameter is uniform, not arc length, so the speed along the curve varies with the control-point spacing.
B'(u) / duration
B''(u) / duration²
Readonly
Natural extent of the path in seconds. See the module note on extrapolation.
Second derivative of position at time, per second squared. Writes into out when given.
time
out
Optional
Position at time seconds. Writes into out when given.
First derivative of position at time, per second. Writes into out when given.
Cubic Bézier curve (§13 "Bézier"), traversed with the parameter advancing linearly in time (
u = t / duration).Velocity is
B'(u) / durationand accelerationB''(u) / duration²by the chain rule. The parameter is uniform, not arc length, so the speed along the curve varies with the control-point spacing.