Curve

Construct curves from a set of points.

The problem of drawing a line through a set of points is actually quite tricky. Should the curve be smooth? Should the ends be connected? This module gives many options for drawing lines through points.

Supports all the curves defined by D3 Shape.

Linear

linear : List (Vec2 Float) -> SubPath

Draw straight lines between the data points.

linearClosed : List (Vec2 Float) -> SubPath

Draw a straigt line between the data points, connecting the ends.

Bezier

cubicBezier : Vec2 Float -> List (Vec3 (Vec2 Float)) -> SubPath

Shorthand to draw a sequence of cubic bezier segments

smoothCubicBezier :

Vec2 Float

-> Vec3 (Vec2 Float)

-> List (Vec2 (Vec2 Float))

-> SubPath

Shorthand to draw a sequence of smooth cubic bezier segments

quadraticBezier : Vec2 Float -> List (Vec2 (Vec2 Float)) -> SubPath

Shorthand to draw a sequence of quadratic bezier segments

smoothQuadraticBezier : Vec2 Float -> Vec2 (Vec2 Float) -> List (Vec2 Float) -> SubPath

Shorthand to draw a sequence of smooth quadratic bezier segments

Step

step : Float -> List (Vec2 Float) -> SubPath

Step goes some distance to the right, then to the y-coordinate of the next data point, and then draws to the next point.

The first argument determines where the step is.

step 1 points is stepAfter
step 0 points is stepBefore
step 0.5 points steps exactly in the middle

stepBefore : List (Vec2 Float) -> SubPath

stepAfter : List (Vec2 Float) -> SubPath

Basis

basis : List (Vec2 Float) -> SubPath

Basis interpolation (also known as B-spline)

basisClosed : List (Vec2 Float) -> SubPath

Closed Basis interpolation (also known as B-spline)

basisOpen : List (Vec2 Float) -> SubPath

bundle : Float -> List (Vec2 Float) -> SubPath

Cardinal

cardinal : Float -> List (Vec2 Float) -> SubPath

cardinalClosed : Float -> List (Vec2 Float) -> SubPath

cardinalOpen : Float -> List (Vec2 Float) -> SubPath

Catmull-Rom

Catmull-Rom splines are a special case of cardinal splines. These curves are great for animation, because the data points are hit exactly and the curve is smooth.

catmullRom : Float -> List (Vec2 Float) -> SubPath

catmullRomClosed : Float -> List (Vec2 Float) -> SubPath

catmullRomOpen : Float -> List (Vec2 Float) -> SubPath

Monotone

The monotone curves can only be increasing (staying flat or becoming higher) or decreasing (staying flat or becoming lower) between any two adjacent points. It cannot first go down and then go up.

Notice that around 0.45, the cubic interpolation dives below the y-coordinate of the next point, whereas the monotone interpolation does not.

A nice consequence is that there are no weird bumps in the curve between the data points.

monotoneX : List (Vec2 Float) -> SubPath

Draw a curve monotone in y assuming the points are monotone in x.

Note, does not deal well with coincident points

monotoneY : List (Vec2 Float) -> SubPath

Draw a curve monotone in y assuming the points are monotone in x.

Natural

natural : List (Vec2 Float) -> SubPath

Transformations

repeatFirstPoint : List a -> List a

Repeat the first element of a list

This is sometimes useful for curves that don't go through their first control point (catmullRom, cardinal). Repeating the first point makes the curve actually hit the first control point.

repeatFinalPoint : List a -> List a

Repeat the final element of a list

Similar to repeatFirstPoint, this can be used to make some curves hit their final control point.

radial : Vec2 Float -> List (Vec2 Float) -> SubPath

Interpret a 2D vector as a (angle, radius) pair. The angle is in radians. The first argument is the center.

toPolarWithCenter : Vec2 Float -> List (Vec2 Float) -> List (Vec2 Float)

Convert (angle, radius) pairs to (x, y) coordinates, relative to the given vector.

This function is used by radial and can be used to use radial with different interpolations, for instance.

radialNatural  : Vec2 Float -> List (Vec2 Float) -> SubPath
radialNatural ( x, y ) =
    natural << toPolarWithCenter ( x, y )

WIP TEST

naturalControlPoints : List (Vec2 Float) -> List (Vec3 (Vec2 Float))

calculate the control points for natural spline interpolation

folkertdev/one-true-path-experiment/2.0.0