Diagrams: Declarative Vector Graphics in Haskell Brent Yorgey NY - - PowerPoint PPT Presentation

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Diagrams: Declarative Vector Graphics in Haskell Brent Yorgey NY - - PowerPoint PPT Presentation

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Diagrams: Declarative Vector Graphics in Haskell Brent Yorgey NY Haskell Users Group November 25, 2013 Part I: Demo! Part II: Lessons for EDSL design Take home Domain analysis is hard! Take home Domain analysis is hard! Be in it for

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Diagrams: Declarative Vector Graphics in Haskell

Brent Yorgey NY Haskell Users’ Group November 25, 2013

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Part I: Demo!

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Part II: Lessons for EDSL design

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Take home

Domain analysis is hard!

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Take home

Domain analysis is hard! Be in it for the long haul.

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History

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April 2008. Wanted: declarative, programmatic drawing.

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PGF/TikZ

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“How hard could it be?”

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After two weeks of feverish hacking, diagrams was born!

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After two weeks of feverish hacking, diagrams was born! It sucked.

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Paths

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What is a path?

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type Path = [Point ]

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Problem 1

?

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Problem 2

type Path = [(P2, CurveSpec)] ?

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Affine spaces

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Find the bug

type Point = (Double, Double) type Vector = (Double, Double) instance (Num a, Num b) ⇒ Num (a, b) where . . . parallelogram :: Point → Point → Point → Point parallelogram p1 p2 p3 = p1 − p3 − p2

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Affine spaces for programmers

Confusing points and vectors is a type error!

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Affine spaces

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translate (p1 − p2) ≡ translate p1 − translate p2

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translate (p1 − p2) ≡ translate p1 − translate p2 Translations apply to points but not to vectors!

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(ˆ + ˆ) :: Vector → Vector → Vector (. + ˆ) :: Point → Vector → Point (. − .) :: Point → Point → Vector

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. . . Paths Again

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type Path = [Vector ]

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type Path = [Segment ]

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type Path = ([Segment ], Bool) ?

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( , True)?

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( , True)?

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Our solution

data Offset c v where OffsetOpen :: Offset Open v OffsetClosed :: v → Offset Closed v data Segment c v = Linear (Offset c v) | Cubic v v (Offset c v)

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data Trail′ l v where Line :: [Segment Closed v ] → Trail′ Line v Loop :: [Segment Closed v ] → Segment Open v → Trail′ Loop v glueLine :: Trail′ Line v → Trail′ Loop v closeLine :: Trail′ Line v → Trail′ Loop v cutLine :: Trail′ Loop v → Trail′ Line v

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Problem 3

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Problem 3

type Trail = [Segment ] . . . type Path = [(Point, Trail)]

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Our solution

data Located a = Loc {loc :: Point (V a), unLoc :: a} newtype Path v = Path [Located (Trail v)]