bezier

An array of three or four vectors, the start point, the endpoint, the first control point and optionally a second control point if the bezier is cubic.

The following functions are in the bezier module.

quadratic-point

quadratic-point(
a: vector,b: vector,c: vector,t: float,
) 

Get the point on quadratic bezier at position t.

a:

vector

Start point

b:

vector

End point

c:

vector

Control point

t:

float

Position on curve

quadratic-derivative

quadratic-derivative(
a: vector,b: vector,c: vector,t: float,
) 

Get the derivative (dx/dt) of a quadratic bezier at position t.

a:

vector

Start point

b:

vector

End point

c:

vector

Control point

t:

float

Position on curve [0, 1]

cubic-point

cubic-point(
a: vector,b: vector,c1: vector,c2: vector,t: float,
) 

Get the point on a cubic bezier curve at position t.

a:

vector

Start point

b:

vector

End point

c1:

vector

Control point 1

c2:

vector

Control point 2

t:

float

Position on curve [0, 1]

cubic-derivative

cubic-derivative(
a: vector,b: vector,c1: vector,c2: vector,t: float,
) 

Get the derivative (dx/dt) of a cubic bezier at position t.

a:

vector

Start point

b:

vector

End point

c1:

vector

Control point 1

c2:

vector

Control point 2

t:

float

Position on curve [0, 1]

to-abc

to-abc(
s: vector,e: vector,B: vector,t: float,deg: int,
) 

Get a bezier curve’s ABC coordinates. Returns them as a respective array</Type> of vector</Type>s.

       /A\  <-- Control point of quadratic bezier
      / | <br />     /  |  <br />    /.-B-.\  <-- Point on curve
   ,'   |   ',
  /     |     <br /> s------C------e  <-- Point on line between s and e

s:

vector

Curve start

e:

vector

Curve end

B:

vector

Point on curve

t:

float

Position on curve

deg:

int

Bezier degree (2 or 3)

quadratic-through-3points

quadratic-through-3points(
s: vector,e: vector,B: vector,
) 

Compute the control points for a quadratic bezier through 3 points.

s:

vector

Curve start

e:

vector

Curve end

B:

vector

A point which the curve passes through

quadratic-to-cubic

quadratic-to-cubic(
s: vector,e: vector,c: vector,
) 

Convert a quadratic bezier to a cubic bezier.

s:

vector

Curve start

e:

vector

Curve end

c:

vector

Control point

cubic-through-3points

cubic-through-3points(
s: vector,e: vector,B: vector,
) 

Compute the control points for a cubic bezier through 3 points.

s:

vector

Curve start

e:

vector

Curve end

B:

vector

A point which the curve passes through

split

split(
s: vector,e: vector,c1: vector,c2: vector,t: float,
) 

Split a cubic bezier into two cubic beziers at the point t. Returns an array</Type> of two bezier</Type>. The first holds the original curve start s, and the second holds the original curve end e.

s:

vector

Curve start

e:

vector

Curve end

c1:

vector

Control point 1

c2:

vector

Control point 2

t:

float

The point on the bezier to split,

cubic-arclen

cubic-arclen(
s: vector,e: vector,c1: vector,c2: vector,
) 

Get the approximate cubic curve length

s:

vector

Curve start

e:

vector

Curve end

c1:

vector

Control point 1

c2:

vector

Control point 2

cubic-shorten-linear

cubic-shorten-linear(
s: vector,e: vector,c1: vector,c2: vector,d: float,
) 

Shorten the curve by offsetting s and c1 or e and c2 by distance d. If d is positive the curve gets shortened by moving s and c1 closer to e, if d is negative, e and c2 get moved closer to s.

s:

vector

Curve start

e:

vector

Curve end

c1:

vector

Control point 1

c2:

vector

Control point 2

d:

float

Distance to shorten by

cubic-t-for-distance

cubic-t-for-distance(
s: vector,e: vector,c1: vector,c2: vector,d: float,
) 

Approximate bezier interval t for a given distance d. If d is positive, the functions starts from the curve’s start s, if d is negative, it starts form the curve’s end e.

s:

vector

Curve start

e:

vector

Curve end

c1:

vector

Control point 1

c2:

vector

Control point 2

d:

float

The distance along the bezier to find t.

cubic-shorten

cubic-shorten(
s: vector,e: vector,c1: vector,c2: vector,d: float,samples: int,
) 

Shorten curve by distance d. This keeps the curvature of the curve by finding new values along the original curve. If d is positive the curve gets shortened by moving s closer to e, if d is negative, e is moved closer to s. The points s and e are moved along the curve, keeping the curve’s curvature the same (the control points get recalculated).

s:

vector

Curve start

e:

vector

Curve end

c1:

vector

Control point 1

c2:

vector

Control point 2

d:

float

Distance to shorten by

samples:

int

Maximum of samples/steps to use

cubic-extrema

cubic-extrema(
s: vector,e: vector,c1: vector,c2: vector,
) 

Find cubic curve extrema by calculating the roots of the curve’s first derivative. Returns an array</Type> of vector</Type> ordered by distance along the curve from the start to its end.

s:

vector

Curve start

e:

vector

Curve end

c1:

vector

Control point 1

c2:

vector

Control point 2

cubic-aabb

cubic-aabb(
s: vector,e: vector,c1: vector,c2: vector,
) 

Returns axis aligned bounding box coordinates (bottom-left, top-right) for a cubic bezier curve.

s:

vector

Curve start

e:

vector

Curve end

c1:

vector

Control point 1

c2:

vector

Control point 2

catmull-to-cubic

catmull-to-cubic(
points: array,k: float,close: bool,
) 

Returns an array of cubic bezier</Type> for a catmull curve through an array of points.

points:

array

Array of 2d points

k:

float

Strength between 0 and 1

close:

bool

line-cubic-intersections

line-cubic-intersections(
s: vector,e: vector,c1: vector,c2: vector,la: vector,lb: vector,ray: bool,
) 

Calculate the intersection points between a 2D cubic-bezier and a straight line. Returns an array of vector</Type>

s:

vector

Bezier start point

e:

vector

Bezier end point

c1:

vector

Bezier control point 1

c2:

vector

Bezier control point 2

la:

vector

Line start point

lb:

vector

Line end point

ray:

bool

If set to true, ignore line length