>>> :{
haddockRender "Geometry/Core/polar.svg" 100 60 $ \_ -> do
    let angle = deg 30
        p = polar angle 100
    cairoScope $ do
        setColor (mma 1)
        C.arc 0 0 40 0 (getRad angle)
        sketch (Line zero p)
        C.stroke
    cairoScope $ do
        setColor (mma 0)
        sketch (Circle p 3)
        C.fill
:}
Generated file: size 2KB, crc32: 0x7a43a888

>>> :{
haddockRender "Geometry/Core/line_reverse.svg" 180 150 $ \_ -> do
    let line = Line (Vec2 10 10) (Vec2 150 140)
        line' = lineReverse line
    C.setLineWidth 2
    cairoScope $ do
        sketch (Arrow line def)
        C.stroke
    cairoScope $ do
        setColor (mma 1)
        C.translate 20 0
        sketch (Arrow line' def)
        C.stroke
:}
Generated file: size 2KB, crc32: 0x2e031609

>>> :{
haddockRender "Geometry/Core/perpendicular_bisector.svg" 200 160 $ \_ -> do
    let line = Line (Vec2 20 20) (Vec2 190 90)
        bisector = perpendicularBisector line
    C.setLineWidth 2
    sketch line >> C.stroke
    sketch bisector >> setColor (mma 1) >> C.stroke
:}
Generated file: size 2KB, crc32: 0x9940c32d

>>> :{
haddockRender "Geometry/Core/perpendicular_line_through.svg" 170 170 $ \_ -> do
    let line = transform (translate (Vec2 20 20))
                         (Line zero (Vec2 (3*40) (4*20)))
        points =
            [ Vec2 20 110  -- above
            , Vec2 70 90   -- above
            , Vec2 130 20  -- below
            , Vec2 110 80  -- directly on
            , Vec2 130 150 -- beyond
            ]
    C.setLineWidth 2
    sketch line >> C.stroke
    for_ (zip [1..] points) $ \(i, p) -> cairoScope $ do
        setColor (mma i)
        sketch (Arrow (perpendicularLineThrough p line) def)
        C.stroke
        sketch (Circle p 5)
        C.strokePreserve
        setColor (mma i `withOpacity` 0.7)
        C.fill
:}
Generated file: size 6KB, crc32: 0xf5ff8529

>>> :{
haddockRender "Geometry/Core/subdivide_line.svg" 200 150 $ \_ -> do
    let line = Line (Vec2 20 20) (Vec2 190 140)
        subdivisions = subdivideLine 8 line
    cairoScope $ do
        C.setLineWidth 2
        setColor (mma 0)
        sketch line
        C.stroke
    cairoScope $ for_ subdivisions $ \point -> do
        sketch (Circle point 4)
        setColor (mma 1)
        C.fill
:}
Generated file: size 4KB, crc32: 0x527103e6

>>> :{
haddockRender "Geometry/Core/subdivide_line_by_length.svg" 200 150 $ \_ -> do
    let line = Line (Vec2 20 20) (Vec2 190 140)
        subdivisions = subdivideLineByLength 30 line
    cairoScope $ do
        C.setLineWidth 2
        setColor (mma 0)
        sketch line
        C.stroke
    cairoScope $ for_ subdivisions $ \point -> do
        sketch (Circle point 4)
        setColor (mma 1)
        C.fill
:}
Generated file: size 4KB, crc32: 0x6180122d

>>> :{
haddockRender "Geometry/Core/reflection.svg" 520 300 $ \_ -> do
   let mirrorSurface = angledLine (Vec2 10 100) (deg 10) 510
   cairoScope $ do
       C.setLineWidth 2
       setColor (black `withOpacity` 0.5)
       sketch mirrorSurface
       C.stroke
   let angles = [-135,-120.. -10]
   cairoScope $ do
       let rayOrigin = Vec2 180 250
       setColor (hsv 0 1 0.7)
       sketch (Circle rayOrigin 5)
       C.stroke
       for_ angles $ \angleDeg -> do
           let rayRaw = angledLine rayOrigin (deg angleDeg) 100
               Just (Line _ reflectedRayEnd, iPoint, _) = reflection rayRaw mirrorSurface
               ray = Line rayOrigin iPoint
               ray' = Line iPoint reflectedRayEnd
           setColor (flare (lerp (minimum angles, maximum angles) (0.2,0.8) angleDeg))
           sketch ray
           sketch ray'
           C.stroke
   cairoScope $ do
       let rayOrigin = Vec2 350 30
       setColor (hsva 180 1 0.7 1)
       sketch (Circle rayOrigin 5)
       C.stroke
       for_ angles $ \angleDeg -> do
           let rayRaw = angledLine rayOrigin (deg angleDeg) 100
               Just (Line _ reflectedRayEnd, iPoint, _) = reflection rayRaw mirrorSurface
               ray = Line rayOrigin iPoint
               ray' = Line iPoint reflectedRayEnd
           setColor (crest (lerp (minimum angles, maximum angles) (0,1) angleDeg))
           sketch ray
           sketch ray'
           C.stroke
:}
Generated file: size 9KB, crc32: 0x76885f25

>>> :{
haddockRender "Geometry/Core/point_in_polygon.svg" 180 180 $ \_ -> do
    let square = boundingBoxPolygon (shrinkBoundingBox 40 [zero, Vec2 180 180])
        points = subdivideLine 11 (Line (Vec2 20 120) (Vec2 160 60))
    C.setLineWidth 2
    sketch square
    C.stroke
    setColor (mma 1)
    for_ points $ \point -> do
        sketch (Circle point 4)
        if pointInPolygon point square then C.fill else C.stroke
:}
Generated file: size 5KB, crc32: 0xabb5dfc

>>> :{
haddockRender "Geometry/Core/polygon_average.svg" 100 100 $ \_ -> do
    let polygon = Polygon [Vec2 10 10, Vec2 10 90, Vec2 20 70, Vec2 40 60, Vec2 30 40, Vec2 90 90, Vec2 80 20]
        averate = polygonAverage polygon
    sketch polygon
    C.stroke
    setColor (mma 1)
    sketch (Circle averate 5)
    sketch (Cross averate 5)
    C.stroke
:}
Generated file: size 2KB, crc32: 0xcf7a8233

>>> :{
haddockRender "Geometry/Core/polygon_centroid.svg" 100 100 $ \_ -> do
    let polygon = Polygon [Vec2 10 10, Vec2 10 90, Vec2 20 70, Vec2 40 60, Vec2 30 40, Vec2 90 90, Vec2 80 20]
        centroid = polygonCentroid polygon
    sketch polygon
    C.stroke
    setColor (mma 1)
    sketch (Circle centroid 5)
    sketch (Cross centroid 5)
    C.stroke
:}
Generated file: size 2KB, crc32: 0x4453ccc1

>>> :{
haddockRender "Geometry/Core/polygon_edges.svg" 100 100 $ \_ -> do
    let polygon = Polygon [ transform (rotateAround (Vec2 50 50) (deg d)) (Vec2 50 10) | d <- take 5 [0, 360/5 ..] ]
    for_ (zip [0..] (polygonEdges polygon)) $ \(i, edge) -> do
        C.setLineCap C.LineCapRound
        setColor (mma i)
        sketch edge
        C.stroke
:}
Generated file: size 3KB, crc32: 0x9c27134b

>>> :{
haddockRender "Geometry/Core/is_convex.svg" 200 100 $ \_ -> do
    let convex = Polygon [Vec2 10 10, Vec2 10 90, Vec2 90 90, Vec2 90 10]
        concave = Polygon [Vec2 110 10, Vec2 110 90, Vec2 150 50, Vec2 190 90, Vec2 190 10]
    for_ [convex, concave] $ \polygon -> do
        if isConvex polygon
            then setColor (mma 2)
            else setColor (mma 3)
        sketch polygon
        C.stroke
:}
Generated file: size 2KB, crc32: 0x60a3e9a1

>>> :{
haddockRender "Geometry/Core/convex_hull.svg" 200 200 $ \(Vec2 w h) -> do
    points <- C.liftIO $ MWC.withRng [] $ \gen ->
        gaussianDistributedPoints
            gen
            (shrinkBoundingBox 10 [zero, Vec2 w h])
            (30 *. mempty)
            100
    for_ points $ \point -> do
        sketch (Circle point 3)
        C.fill
    setColor (mma 1)
    for_ (polygonEdges (convexHull points)) $ \edge ->
        sketch (Arrow edge def{_arrowheadRelPos=0.5, _arrowheadSize=5})
    C.stroke
:}
Generated file: size 29KB, crc32: 0xe4bf922

>>> :{
haddockRender "Geometry/Core/grow_polygon.svg" 160 230 $ \_ -> do
    let polygon = transform (scale 2) $ Polygon [Vec2 20 40, Vec2 20 80, Vec2 40 60, Vec2 60 80, Vec2 60 40, Vec2 40 20]
    for_ [0,5..25] $ \offset -> cairoScope $ do
        when (offset == 0) (C.setLineWidth 3)
        setColor (icefire (Numerics.Interpolation.lerp (0,25) (0.5, 1) (fromIntegral offset)))
        sketch (growPolygon (fromIntegral offset) polygon)
        C.stroke
:}
Generated file: size 4KB, crc32: 0xd6cd58c1

>>> :{
haddockRender "Geometry/Core/shrink_polygon.svg" 160 230 $ \_ -> do
    let polygon = transform (scale 2) $ Polygon [Vec2 20 40, Vec2 20 80, Vec2 40 60, Vec2 60 80, Vec2 60 40, Vec2 40 20]
    for_ [0,5..25] $ \offset -> cairoScope $ do
        when (offset == 0) (C.setLineWidth 3)
        setColor (icefire (Numerics.Interpolation.lerp (0,25) (0.5, 0) (fromIntegral offset)))
        sketch (shrinkPolygon (fromIntegral offset) polygon)
        C.stroke
:}
Generated file: size 4KB, crc32: 0x4a75ae5c

>>> :{
haddockRender "Geometry/Core/ellipses.svg" 300 300 $ \(Vec2 w h) -> do
    let center = zero
        radius = w/6*0.9
        ellipse = toEllipse (Circle center radius)
        grid i j = C.translate (fromIntegral i*w/3 + w/6) (fromIntegral j*h/3 + w/6)
    let actions =
            [ cairoScope $ do
                grid 0 0
                for_ (take 10 [0..]) $ \i -> do
                    let scaleFactor = lerpID (0,9) (0.1, 1) i
                    sketch (transform (scaleAround center scaleFactor) ellipse)
                    C.stroke
            , cairoScope $ do
                grid 1 0
                for_ (take 10 [0..]) $ \i -> do
                    let scaleFactor = lerpID (0,9) (0.1, 1) i
                    sketch (transform (scaleAround' center scaleFactor 1) ellipse)
                    C.stroke
            , cairoScope $ do
                grid 2 0
                for_ [0..9] $ \i -> do
                    let scaleFactor1 = lerp (0, 9) (1, 0.1) (fromIntegral i)
                        scaleFactor2 = lerp (0, 9) (0.1, 1) (fromIntegral i)
                    sketch (transform (scaleAround' center scaleFactor1 scaleFactor2) ellipse)
                    C.stroke
            , cairoScope $ do
                grid 0 1
                for_ (take 10 [0..]) $ \i -> do
                    let scaleX = scaleAround' center (lerpID (0,9) (0.5,1) (fromIntegral i)) 1
                        scaleY = scaleAround' center 1 (lerpID (0,9) (0.1,1) (fromIntegral i))
                    sketch (transform (scaleX <> scaleY) ellipse)
                    C.stroke
            , cairoScope $ do
                grid 1 1
                for_ (take 10 [0..]) $ \i -> do
                    let angle = deg (lerpID (0,9) (0, 90) i)
                    sketch (transform (rotateAround center angle <> scaleAround' center 1 0.5) ellipse)
                    C.stroke
            , cairoScope $ do
                grid 2 1
                for_ (take 19 [0..]) $ \i -> do
                    let angle = deg (lerpID (0,19) (0, 180) i)
                    sketch (transform (rotateAround center angle <> scaleAround' center 1 0.5) ellipse)
                    C.stroke
            , cairoScope $ do
                grid 0 2
                for_ (take 9 [0..]) $ \i -> do
                    let scaleFactor = lerpID (0,9) (1,0.1) i
                        angle = deg (lerpID (0,9) (90,0) i)
                    sketch (transform (rotateAround center angle <> scaleAround' center 1 scaleFactor) ellipse)
                    C.stroke
            , cairoScope $ do
                grid 1 2
                for_ (take 9 [0..]) $ \i -> do
                    let scaleFactor = lerpID (0,9) (1,0.1) i
                        angle = deg (lerpID (0,9) (0,90) i)
                    sketch (transform (scaleAround center scaleFactor <> rotateAround center angle <> scaleAround' center 1 scaleFactor) ellipse)
                    C.stroke
            , cairoScope $ do
                grid 2 2
                for_ (take 9 [0..]) $ \i -> do
                    let BoundingBox topLeft _ = boundingBox ellipse
                        scaleFactor = lerpID (0,9) (1,0.1) i
                        angle = deg (lerpID (0,9) (0,90) i)
                    sketch (transform (rotateAround center angle <> scaleAround (0.5 *. (topLeft -. center)) scaleFactor) ellipse)
                    C.stroke
            ]
    for_ (zip [0..] actions) $ \(i, action) -> do
        setColor (mma i)
        action
:}
Generated file: size 42KB, crc32: 0xb3cabf7b

>>> :{
haddockRender "Geometry/Core/pseudo_angle.svg" 200 100 $ \_ -> do
    let anglesDeg = takeWhile (< 180) [-180, -175 ..]
        atan2Plot = Polyline $ do
            angleDeg <- anglesDeg
            let Vec2 x y = polar (deg angleDeg) 1
            pure (Vec2 angleDeg (atan2 y x))
        pseudoAtan2Plot = Polyline $ do
            angleDeg <- anglesDeg
            let vec = polar (deg angleDeg) 1
            pure (Vec2 angleDeg (pseudoAngle vec))
        trafo = transformBoundingBox
            [atan2Plot, pseudoAtan2Plot]
            (shrinkBoundingBox 10 [zero, Vec2 200 100])
            def {_bbFitAspect = IgnoreAspect}
    cairoScope $ do
        sketch (transform trafo atan2Plot)
        setColor (mma 0)
        C.stroke
    cairoScope $ do
        sketch (transform trafo pseudoAtan2Plot)
        setColor (mma 1)
        C.stroke
:}
Generated file: size 5KB, crc32: 0xda270ddb

>>> :{
haddockRender "Geometry/Core/translate.svg" 100 50 $ \_ -> do
    let point = Vec2 20 20
        offset = Vec2 70 20
        point' = transform (translate offset) point
    sketch (Circle point 5)
    sketch (Circle point' 5)
    C.fill
    setColor (mma 1)
    sketch (Arrow (Line point point') def) >> C.stroke
:}
Generated file: size 2KB, crc32: 0x5f8c6969

>>> :{
haddockRender "Geometry/Core/rotate.svg" 100 70 $ \_ -> do
    let point = Vec2 90 10
        angle = deg 30
        point' = transform (rotate angle) point
    cairoScope $ do
        sketch (Circle point 5, Circle point' 5)
        C.fill
    setColor (mma 1)
    let line = Line zero point
        line' = Line zero point'
    cairoScope $ do
        C.setDash [1,1] 0
        sketch (line, line')
        C.stroke
    cairoScope $ do
        let angle = angleOfLine line
            angle' = angleOfLine line'
        C.arc 0 0 (lineLength line) (getRad angle) (getRad angle')
        sketch (Arrow (transform (rotateAround point' (deg 15)) (Line point point')) def{_arrowDrawBody=False})
        C.stroke
:}
Generated file: size 2KB, crc32: 0x980f5f

>>> :{
haddockRender "Geometry/Core/scale.svg" 100 100 $ \_ -> do
    let square = Polygon [Vec2 10 10, Vec2 10 45, Vec2 45 45, Vec2 45 10]
        square' = transform (scale 2) square
    sketch square
    C.stroke
    setColor (mma 1)
    sketch square'
    C.stroke
:}
Generated file: size 2KB, crc32: 0x9126ef6

>>> :{
haddockRender "Geometry/Core/shear.svg" 100 100 $ \_ -> do
    let square = Polygon [Vec2 10 10, Vec2 10 80, Vec2 50 80, Vec2 50 10]
        square' = transform (shear 0.5 0.1) square
    sketch square
    C.stroke
    setColor (mma 1)
    sketch square'
    C.stroke
:}
Generated file: size 2KB, crc32: 0xfd1224e4