Representation of a single SVG path data point

View the Point part of a PathData

Move the Point part of a PathData

Multiplicatively scale a PathData

Project a list of connected PathDatas from one Rect (XY plave) to a new one.

Bounding box for a list of path XYs.

Bounding box for a path info, start and end Points.

Information about an individual arc path.

Specification of an Arc using positional referencing as per SVG standard.

Arc specification based on centroidal interpretation.

See: https://www.w3.org/TR/SVG/implnote.html#ArcConversionEndpointToCenter

convert from an ArcPosition spec to ArcCentroid spec.

See also this

>>> let p = ArcPosition (Point 0 0) (Point 1 0) (ArcInfo (Point 1 0.5) (pi/4) False True)
>>> arcCentroid p
ArcCentroid {centroid = Point 0.20952624903444356 (-0.48412291827592724), radius = Point 1.0 0.5, cphi = 0.7853981633974483, ang0 = 1.3753858999692936, angdiff = -1.823476581936975}

Convert from an ArcCentroid to an ArcPosition specification.

Morally,

arcPosition . arcCentroid == id

Not isomorphic if:

• angle diff is pi and large is True
• radii are less than they should be and thus get scaled up.

compute the bounding box for an arcBox

let p = ArcPosition (Point 0 0) (Point 1 0) (ArcInfo (Point 1 0.5) (pi/4) False True)
arcBox p

Potential arc turning points.

>>> arcDerivs (Point 1 0.5) (pi/4)
(-0.4636476090008061,0.4636476090008062)

Ellipse formulae

>>> ellipse zero (Point 1 2) (pi/6) pi
Point (-0.8660254037844388) (-0.4999999999999997)

Compare this "elegent" definition from stackexchange

\[\dfrac{((x-h)\cos(A)+(y-k)\sin(A))^2}{a^2}+\dfrac{((x-h) \sin(A)-(y-k) \cos(A))^2}{b^2}=1\]

with the haskell code:

c + (rotate phi |. (r * ray theta))

See also: wolfram

Quadratic bezier curve expressed in positional terms.

Quadratic bezier curve with control point expressed in polar terms normalised to the start - end line.

Convert from a polar to a positional representation of a quadratic bezier.

quadPosition . quadPolar == id
quadPolar . quadPosition == id

>>> quadPosition $ quadPolar (QuadPosition (Point 0 0) (Point 1 1) (Point 2 (-1)))
QuadPosition {qposStart = Point 0.0 0.0, qposEnd = Point 1.0 1.0, qposControl = Point 2.0 (-0.9999999999999998)}

Convert from a positional to a polar representation of a cubic bezier.

>>> quadPolar (QuadPosition (Point 0 0) (Point 1 1) (Point 2 (-1)))
QuadPolar {qpolStart = Point 0.0 0.0, qpolEnd = Point 1.0 1.0, qpolControl = Polar {radial = 2.1213203435596424, azimuth = -0.7853981633974483}}

Bounding box for a QuadPosition

>>> quadBox (QuadPosition (Point 0 0) (Point 1 1) (Point 2 (-1)))
Rect 0.0 1.3333333333333335 (-0.33333333333333337) 1.0

The quadratic bezier equation

>>> quadBezier (QuadPosition (Point 0 0) (Point 1 1) (Point 2 (-1))) 0.33333333
Point 0.9999999933333332 (-0.33333333333333326)

QuadPosition turning points.

>>> quadDerivs (QuadPosition (Point 0 0) (Point 1 1) (Point 2 (-1)))
[0.6666666666666666,0.3333333333333333]

Cubic bezier curve

Note that the ordering is different to the svg standard.

A polar representation of a cubic bezier with control points expressed as polar and normalised to the start - end line.

Convert from a polar to a positional representation of a cubic bezier.

cubicPosition . cubicPolar == id
cubicPolar . cubicPosition == id

>>> cubicPosition $ cubicPolar (CubicPosition (Point 0 0) (Point 1 1) (Point 1 (-1)) (Point 0 2))
CubicPosition {cposStart = Point 0.0 0.0, cposEnd = Point 1.0 1.0, cposControl1 = Point 1.0 (-1.0), cposControl2 = Point 1.6653345369377348e-16 2.0}

Convert from a positional to a polar representation of a cubic bezier.

cubicPosition . cubicPolar == id
cubicPolar . cubicPosition == id

>>> cubicPolar (CubicPosition (Point 0 0) (Point 1 1) (Point 1 (-1)) (Point 0 2))
CubicPolar {cpolStart = Point 0.0 0.0, cpolEnd = Point 1.0 1.0, cpolControl1 = Polar {radial = 1.1180339887498947, azimuth = -1.2490457723982544}, cpolControl2 = Polar {radial = 1.1180339887498947, azimuth = 1.8925468811915387}}

Bounding box for a CubicPosition

>>> cubicBox (CubicPosition (Point 0 0) (Point 1 1) (Point 1 (-1)) (Point 0 2))
Rect 0.0 1.0 (-0.20710678118654752) 1.2071067811865475

The cubic bezier equation

>>> cubicBezier (CubicPosition (Point 0 0) (Point 1 1) (Point 1 (-1)) (Point 0 2)) 0.8535533905932737
Point 0.6767766952966369 1.2071067811865475

Turning point positions for a CubicPosition (0,1 or 2)

>>> cubicDerivs (CubicPosition (Point 0 0) (Point 1 1) (Point 1 (-1)) (Point 0 2))
[0.8535533905932737,0.14644660940672624,0.5]

Convert cubic position to path data.

Convert quad position to path data.

Convert arc position to path data.

Convert arc position to a pie slice, with a specific center.