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# TheSeamau5/CatmullClarkSubdivision2D.elm

Last active August 29, 2015 14:11
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2D Catmull Clark Subdivision in Elm
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 import Graphics.Collage (move, filled, circle, Form, collage) import Graphics.Element (Element) import List (map, map2, (::), head, tail) import Color (rgb) --- GLOBALS YOU CAN MESS WITH pointSize = 3 -- THE SIZE OF THE POINTS pointColor = rgb 255 100 0 -- THE COLOR OF THE POINTS iterations = 5 -- NUMBER OF ITERATIONS OF CATMULL-CLARK SUBDIVISION -- 2D POINT TYPE type alias Point = { x : Float, y : Float } origin = Point 0 0 -- CALCULATES THE MIDPOINT BETWEEN TWO POINTS midpoint : Point -> Point -> Point midpoint p q = Point ((p.x + q.x) / 2) ((p.y + q.y) / 2) -- INTERLEAVE THE ELEMENTS OF A LIST WITHIN ANOTHER LIST interleave : List a -> List a -> List a interleave list1 list2 = case list1 of [] -> list2 x :: xs -> case list2 of [] -> list1 y :: ys -> y :: x :: interleave xs ys -- A SQUARE square : Point -> Float -> List Point square {x, y} size = let halfSize = size / 2 in [Point (x + halfSize) (y + halfSize), Point (x - halfSize) (y + halfSize), Point (x - halfSize) (y - halfSize), Point (x + halfSize) (y - halfSize)] -- A RHOMBUS FROM 30 60 90 TRIANGLES rhombus {x, y} size = let shortHalf = size / 2 longHalf = (sqrt 3) * shortHalf in [Point 0 (y + shortHalf), Point (x - longHalf) 0, Point 0 (y - shortHalf), Point (x + longHalf) 0] -- AN EQUILATERAL TRIANGLE triangle {x, y} size = let halfSize = size / 2 in [Point (x + halfSize * cos 0) (y + halfSize * sin 0), Point (x + halfSize * cos (degrees 120)) (y + halfSize * sin (degrees 120)), Point (x + halfSize * cos (degrees 240)) (y + halfSize * sin (degrees 240))] -- CATMULL CLARK SUBDIVISION: SPLIT THEN REAVERAGE REPEAT split : List Point -> (List Point, List Point) split points = let averages = map2 midpoint points (tail points ++ [head points]) in (points, averages) reAverage : (List Point, List Point) -> (List Point, List Point) reAverage (points, averages) = let newAverages = map2 midpoint averages (tail points ++ [head points]) in (newAverages, averages) join : (List Point, List Point) -> List Point join (points, averages) = interleave points averages subDivide : List Point -> List Point subDivide = split >> reAverage >> join catmullClarkSubdivision : Int -> List Point -> List Point catmullClarkSubdivision iterations = if iterations <= 0 then identity else subDivide >> catmullClarkSubdivision (iterations - 1) -- -- DRAW A POINT drawPoint : Point -> Form drawPoint {x, y} = move (x,y) <| filled pointColor (circle pointSize) -- DRAW A LIST OF POINTS render : List Point -> Element render = collage 400 400 << map drawPoint -- THE MAIN FUNCTION --main = render <| catmullClarkSubdivision iterations <| square origin 200 --main = render <| catmullClarkSubdivision iterations <| rhombus origin 200 main = render <| catmullClarkSubdivision iterations <| triangle origin 200
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