splines/bezier

Beziér splines

Beziér splines are useful for drawing strokes and shapes and are often the dominant parametric curve exposed by graphical editors.

Types

Bezier

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A generic n-ary Beziér spline over the domain a. Most users will want the simpler versions produced by new_2d or new_3d.

If you construct the spline yourself, you must supply an Interpolator function for the domain. The number of points in the domain determines both the order and the computational-complexity of sampling the domain using the de Castlejau algorithm.

Number of points	Order	Complexity
2	Linear	1 step
3	Quadratic	3 steps
4*	Cubic	6 steps
5	Quartic	10 steps
…	…	…

If you use new_2d or new_3d, and you pass 4 points, this will create instead the CubicBezier variant automatically. Sampling of this variant will use the matrix-multiplication formulation instead of de Casteljau’s method.

pub type Bezier(a) {
  Bezier(points: List(a), interpolator: fn(a, a, Float) -> a)
  CubicBezier(
    points: vec4.Vec4(a),
    scale: fn(a, Float) -> a,
    sum: fn(List(a)) -> a,
  )
}

Constructors

Bezier(points: List(a), interpolator: fn(a, a, Float) -> a)

CubicBezier(
  points: vec4.Vec4(a),
  scale: fn(a, Float) -> a,
  sum: fn(List(a)) -> a,
)

Special case of the most common kind of Bezier curve

Values

new_2d

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pub fn new_2d(
  points: List(vec2.Vec2(Float)),
) -> Bezier(vec2.Vec2(Float))

Constructs an n-ary Bezier spline in two dimensions. This spline should include at least two points, but that constraint is not checked.

new_3d

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pub fn new_3d(
  points: List(vec3.Vec3(Float)),
) -> Bezier(vec3.Vec3(Float))

Constructs an n-ary Beziér spline in three dimensions. This spline should include at least two points, but that constraint is not checked.

sample

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pub fn sample(b: Bezier(a), t: Float) -> a

Samples the Beziér spline at time t using the recursive de Castlejau algorithm.

Panics if the curve contains no points.