bezierCubic

a cubic Bezier curve and returns both value and derivative.

Parameters

Name	Type	Description
t	f32	Parameter along the curve (0-1).
p0	f32	First control point.
p1	f32	Second control point.
p2	f32	Third control point.
p3	f32	Fourth control point.

Returns

vec2<f32>value and derivative (tangent).

WGSL Code

fn bezierCubic(t: f32, p0: f32, p1: f32, p2: f32, p3: f32) -> vec2<f32> {
  // Clamp t to [0,1]
  let tt = clamp(t, 0.0, 1.0);
  
  // Calculate curve value using cubic Bezier formula
  // P(t) = (1-t)³P₀ + 3(1-t)²tP₁ + 3(1-t)t²P₂ + t³P₃
  let t1 = 1.0 - tt;
  let t1Squared = t1 * t1;
  let t1Cubed = t1Squared * t1;
  let tSquared = tt * tt;
  let tCubed = tSquared * tt;
  
  let value = t1Cubed * p0 + 
             3.0 * t1Squared * tt * p1 + 
             3.0 * t1 * tSquared * p2 + 
             tCubed * p3;
  
  // Calculate derivative for tangent information
  // P'(t) = 3(1-t)²(P₁-P₀) + 6(1-t)t(P₂-P₁) + 3t²(P₃-P₂)
  let derivative = 3.0 * t1Squared * (p1 - p0) +
                  6.0 * t1 * tt * (p2 - p1) +
                  3.0 * tSquared * (p3 - p2);
  
  return vec2<f32>(value, derivative);
}