The four types of segments.

Make a line segment

Make a quadratic bezier segment

Make a cubic bezier segment

Make an elliptic arc segment

Get the location at a point on the curve, only defined in the range [0, 1].

at 0.5 (line (0,0) (10, 0)) --> ( 5, 0 )


at 0.5 (quadratic (0,0) (5, 10) (10, 0)) --> ( 5, 5 )

The signed angle (in radians) between the end of segment1 and the start of segment2

a : Segment
a = line ( 0, 0 ) ( 1, 0 )


b : Segment
b = line ( 0, 0 ) ( 0, 1 )


angle a b --> degrees 90


angle b a --> degrees -90

Get the derivative at a point on the curve, only defined in the range [0, 1].

import LowLevel.Command exposing
    ( EllipticalArcArgument
    , largestArc
    , clockwise
    )


derivativeAt 0.5 (line (0,0) (1,1))
    --> (0.7071067811865475,0.7071067811865475)


argument : EllipticalArcArgument
argument =
    { target = ( 10, 0 )
    , radii = ( 5, 5 )
    , xAxisRotate = 0
    , arcFlag = largestArc
    , direction = clockwise
    }


derivativeAt 0.5 (arc (0,0)  argument) --> ( 1, 0)

The derivative at the starting point of the segment

The derivative at the ending point of the segment

Extract the first point from a segment

Extract the final point from a segment

Reverse a line segment

Convert a segment to a drawto instruction. forgets the starting point.

Convert a drawto into a segment

This function needs the previous segment to the starting point and (for bezier curves) the control points

import LowLevel.Command exposing (DrawTo(EllipticalArc), CursorState)


start : CursorState
start = { start = (0,0), cursor = (0,0), previousControlPoint = Nothing }


drawto : DrawTo
drawto =
        EllipticalArc
            [ { target = (10, 0)
              , radii = (5,5)
              , xAxisRotate = 90
              , arcFlag = largestArc
              , direction = clockwise
              }
            ]


expected : List Segment
expected =
     [ Arc
        { start = (0,0)
        , end = (10, 0)
        , radii = (5,5)
        , xAxisRotate = pi / 2
        , arcFlag = largestArc
        , direction = clockwise
        }
      ]


toSegment start drawto --> expected

Convert a Segment to a CursorState

toCursorState (line (0,0) (10, 10))
    --> { start = (0,0) , cursor = (10, 10) , previousControlPoint = Nothing }