\[B(t)=(1-t)^3P_0+3(1-t)^2tP_1+3(1-t)t^2P_2+t^3P_3\]
Variables
B(t)curve point
tparameter (0 to 1)
P0start point
P1control point 1
P2control point 2
P3end point
Description
What is this formula?
This formula defines a cubic Bézier curve, which is a parametric curve widely used in computer graphics and geometric modeling.
When to use it
Use this formula when designing smooth curves defined by control points in graphics, animation or CAD systems.
Example
For t=0.5, the curve is evaluated by blending all control points using cubic weights.
Applications
Computer graphics
Font design
Animation paths
CAD modeling
UI/UX design
Game development