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authorSébastien Dailly <sebastien@chimrod.com>2021-02-05 09:08:39 +0100
committerSébastien Dailly <sebastien@dailly.me>2022-02-07 14:39:30 +0100
commit561d0f0155f4906d90eb7e73a3ff9cb28909126f (patch)
tree9a606c2d7832272ea33d7052512a5fa59805d582 /shapes
parent86ec559f913c389e8dc055b494630f21a45e039b (diff)
Update project structure
Diffstat (limited to 'shapes')
-rwxr-xr-xshapes/bezier.ml228
-rwxr-xr-xshapes/bezier.mli40
-rwxr-xr-xshapes/bspline.ml149
-rwxr-xr-xshapes/bspline.mli24
-rwxr-xr-xshapes/dd_splines.pdfbin184248 -> 0 bytes
-rwxr-xr-xshapes/dune7
-rwxr-xr-xshapes/matrix/EltsI.ml28
-rwxr-xr-xshapes/matrix/Helpers.ml16
-rwxr-xr-xshapes/matrix/Matrix.ml529
-rwxr-xr-xshapes/matrix/MatrixI.ml105
-rwxr-xr-xshapes/matrix/Order.ml2
-rwxr-xr-xshapes/matrix/dune3
-rwxr-xr-xshapes/tools/dune6
-rwxr-xr-xshapes/tools/utils.ml63
-rwxr-xr-xshapes/tools/utils.mli21
15 files changed, 0 insertions, 1221 deletions
diff --git a/shapes/bezier.ml b/shapes/bezier.ml
deleted file mode 100755
index f5f288c..0000000
--- a/shapes/bezier.ml
+++ /dev/null
@@ -1,228 +0,0 @@
-(**
-
- Bezier curve
-*)
-
-module Utils = Tools.Utils
-
-type quadratic =
- { p0:Gg.v2 (* The starting point *)
- ; p1:Gg.v2 (* The end point *)
- ; ctrl:Gg.v2 } (* The control point *)
-
-
-type t =
- { p0:Gg.v2 (* The starting point *)
- ; p1:Gg.v2 (* The end point *)
- ; ctrl0:Gg.v2 (* The control point *)
- ; ctrl1:Gg.v2 } (* The control point *)
-
-
-(**
- Build a control point for a quadratic curve for passing throuht 3 points.
- taken from https://xuhehuan.com/2608.html
-
-
- also look to https://pomax.github.io/bezierinfo/#pointcurves
-*)
-let three_points_quadratic
- : Gg.v2 -> Gg.v2 -> Gg.v2 -> quadratic
- = fun p0 c1 p1 ->
-
- let open Gg.V2 in
-
- let vect_1 = p0 - c1
- and vect_2 = p1 - c1 in
- let norm1 = norm vect_1
- and norm2 = norm vect_2 in
- let v = (Float.sqrt (norm1 *. norm2)) /. 2. in
-
- let ctrl = c1 - v * (( vect_1 / norm1) + (vect_2 / norm2)) in
- {p0; p1; ctrl}
-
-(**
-
- Convert a cubic bezier curve into a quadratic one
-
-*)
-let quadratic_to_cubic
- : quadratic -> t
- = fun {p0; p1; ctrl} ->
-
- let coef = 2. /. 3. in
-
- let open Gg.V2 in
- { p0
- ; p1
- ; ctrl0 = mix p0 ctrl coef
- ; ctrl1 = mix p1 ctrl coef }
-
-
-
-let abc_ratio
- : int -> float -> float
- = fun n t ->
- let n' = Float.of_int n in
- let bottom = (Float.pow t n') +. (Float.pow (1. -. t) n') in
- let top = bottom -. 1. in
- Float.abs (top /. bottom)
-
-let half_cubic_ratio = abc_ratio 3 0.5
-
-exception Not_found
-
-(**
-
- https://pomax.github.io/bezierinfo/#pointcurves
-
-*)
-let three_points_cubic
- : float -> Gg.v2 -> Gg.v2 -> Gg.v2 -> t
- = fun f p0 p1 p2 ->
-
- let open Gg.V2 in
-
- let c = half ( p0 + p2) in
- let a = p1 + ((p1 - c) / half_cubic_ratio) in
-
- let vect1_0 = p1 - p0 in
- let vect2_0 = p2 - p0 in
-
- let d1 = norm vect1_0
- and d2 = norm (p2 - p1) in
- let t = d1 /. (d1 +. d2) in
-
- let angle_1_0 = angle vect1_0
- and angle_2_0 = angle vect2_0 in
-
- (* get our e1-e2 distances *)
- let angle = mod_float
- (Gg.Float.two_pi
- +. angle_2_0
- -. angle_1_0)
- Gg.Float.two_pi in
-
- let distance = (norm vect2_0) *. f in
-
- let bc =
- if angle < 0. || angle > Gg.Float.pi then
- Float.(neg distance)
- else
- distance in
- let de1 = t *. bc
- and de2 = (1. -. t) *. bc in
-
- (* get the circle-aligned slope as normalized dx/dy *)
- let center = Utils.center p0 p1 p2 in
- match center with
- | None -> raise Not_found
- | Some center ->
- let t' = p1 - center in
- let tangent0 = v
- ((x p1) -. (y t'))
- ((y p1) +. (x t'))
- and tangent1 = v
- ((x p1) +. (y t'))
- ((y p1) -. (x t')) in
-
- let d = unit (tangent1 - tangent0) in
-
- (* then set up an e1 and e2 parallel to the baseline *)
- let e1 = p1 + de1 * d
- and e2 = p1 - de2 * d in
-
- (* then use those e1/e2 to derive the new hull coordinates *)
- let v1 = a + (e1 - a) / (1. -. t)
- and v2 = a + (e2 - a) / t in
-
- let ctrl0 = p0 + (v1 - p0) / t
- and ctrl1 = p2 + (v2 -p2) / (1. -. t) in
-
- {p0; p1 = p2; ctrl0; ctrl1}
-
-(** Split a bezier curve in two at a given position *)
-let slice
- : float -> t -> t * t
- = fun t {p0; p1; ctrl0; ctrl1} ->
-
- let mix p1 p2 = Gg.V2.mix p1 p2 t in
-
- let p12 = mix p0 ctrl0
- and p23 = mix ctrl0 ctrl1
- and p34 = mix ctrl1 p1 in
-
- let p123 = mix p12 p23
- and p234 = mix p23 p34 in
-
- let p1234 = mix p123 p234 in
-
- ( { p0
- ; ctrl0 = p12
- ; ctrl1 = p123
- ; p1 = p1234 }
- , { p0 = p1234
- ; ctrl0 = p234
- ; ctrl1 = p34
- ; p1 } )
-
-
-let get_closest_point
- : Gg.v2 -> t -> float * Gg.v2
- = fun point t ->
-
- let rec f min max t =
-
- (* First devide the curve in two *)
- let seq_0, seq_1 = slice 0.5 t in
- let avg = (min +. max) /. 2. in
-
- let p0 = t.p0
- and p1 = t.p1
- and p01 = seq_0.p1 in (* seq_0.p1 = seq_1.p0 *)
-
- let open Gg.V2 in
- let center0 = mix p0 p01 0.5
- and center1 = mix p01 p1 0.5 in
-
- if Tools.Utils.equal_point 0.001 p0 p1 then
- avg, p01
- else if (norm (point - center0)) < (norm (point - center1)) then
- f min avg seq_0
- else
- f avg max seq_1
-
- in f 0. 1. t
-
-let reverse
- : t -> t
- = fun bezier ->
- {
- p0 = bezier.p1
- ; p1 = bezier.p0
- ; ctrl0 = bezier.ctrl1
- ; ctrl1 = bezier.ctrl0 }
-
-(**
-
- see https://github.com/Pomax/BezierInfo-2/blob/master/docs/js/graphics-element/lib/bezierjs/bezier.js#L504
-
- let root
- : t -> 'a
- = fun bezier ->
-
- let accept
- : float -> bool
- = fun t ->
- 0. <= t && t <= 1. in
-
- let cuberoot v =
- if v < 0. then
- Float.pow (Float.neg v) ( 1. /. 3.)
- |> Float.neg
- else Float.pow v (1. /. 3.) in
-
-
-
-
- failwith "Non implemented"
-*)
diff --git a/shapes/bezier.mli b/shapes/bezier.mli
deleted file mode 100755
index 2f5bbcf..0000000
--- a/shapes/bezier.mli
+++ /dev/null
@@ -1,40 +0,0 @@
-type t =
- { p0:Gg.v2 (* The starting point *)
- ; p1:Gg.v2 (* The end point *)
- ; ctrl0:Gg.v2 (* The control point *)
- ; ctrl1:Gg.v2 } (* The control point *)
-
-type quadratic
-
-(**
- Build a control point for a quadratic curve for passing throuht 3 points.
- taken from https://xuhehuan.com/2608.html
-
-
- also look to https://pomax.github.io/bezierinfo/#pointcurves
-*)
-val three_points_quadratic
- : Gg.v2 -> Gg.v2 -> Gg.v2 -> quadratic
-
-(**
- Create a curve from three points.
-
- This is an implementation for
- https://pomax.github.io/bezierinfo/#pointcurves
-
-*)
-val three_points_cubic
- : float -> Gg.v2 -> Gg.v2 -> Gg.v2 -> t
-
-val quadratic_to_cubic
- : quadratic -> t
-
-(** Split a bezier curve in two at a given position *)
-val slice
- : float -> t -> t * t
-
-(** Return the closest point to the curve by approximation *)
-val get_closest_point
- : Gg.v2 -> t -> float * Gg.v2
-
-val reverse: t -> t
diff --git a/shapes/bspline.ml b/shapes/bspline.ml
deleted file mode 100755
index bb60227..0000000
--- a/shapes/bspline.ml
+++ /dev/null
@@ -1,149 +0,0 @@
-open StdLabels
-
-type err = [`InvalidPath ]
-
-module M = Matrix.MakeMatrix (struct
-
- type t = Float.t
-
- let compare a b =
-
- let v = Float.compare a b in
- if v = 0 then Matrix.Order.Equal
- else if v > 0 then Matrix.Order.Greater
- else Matrix.Order.Less
-
- let zero = Float.zero
- let one = Float.one
-
- let divide = (/.)
- let multiply = ( *. )
- let add = (+.)
- let subtract = (-.)
- exception NonElt
-
-
- end)
-
-type t = Gg.v2 list
-
-let from_points
- : Gg.v2 array -> (Gg.v2 array, [> `InvalidPath]) Result.t
- = fun points ->
-
- let n = (Array.length points - 2) in
-
- if n <= 1 then
- Result.error `InvalidPath
- else
-
- (* Create the initial matrix.
-
- The matrix is augmented with two additionals columns, which will be
- populated with the points from the path.
- *)
- let arr = Array.init n ~f:(fun line ->
- Array.init (n +2) ~f:(fun row ->
- match row - line with
- | (-1) -> 1.
- | 0 -> 4.
- | 1 -> 1.
- | _ -> 0.
- )
- ) in
- let matrix = M.from_array arr in
-
- (* Add the points from the augmented matrix *)
- let points_array = points in
- for line = 0 to (n -1) do
-
- let point =
- if line = 0 then
- let p0 = points_array.(0)
- and p1 = points_array.(1) in
- Gg.V2.(6. * p1 - p0)
- else if (line + 1) = n then
- let p_n_2 = points_array.(n)
- and p_n_1 = points_array.(n + 1) in
- Gg.V2.(6. * p_n_2 - p_n_1)
- else
- let n' = line + 1 in
- Gg.V2.(6. * points_array.(n'))
- in
- let x = (Gg.V2.x point)
- and y = (Gg.V2.y point) in
-
-
- M.set_elt matrix (line + 1, n + 1) x;
- M.set_elt matrix (line + 1, n + 2) y;
- done;
-
- (* Resolve the matrix *)
- let res' = M.row_reduce matrix in
-
- (* Extract the result as points *)
- let _, col_x = M.get_column res' (n + 1)
- and _, col_y = M.get_column res' (n + 2) in
-
- (* Build the result *)
- let res = Array.make (n + 2) (Array.get points_array (n + 1) ) in
- for i = 1 to n do
- let point = Gg.V2.v col_x.(i - 1) col_y.(i - 1) in
- Array.set res i point;
- done;
- Array.set res 0 (Array.get points_array 0);
- Result.ok res
-
-let (let*) = Result.bind
-
-(** Build a continue curve from path
-
- see https://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf
-*)
-let to_bezier
- : ?connexion0:Gg.v2 -> ?connexion1:Gg.v2 -> t -> (Bezier.t array, [> `InvalidPath]) Result.t
- = fun ?connexion0 ?connexion1 points ->
-
- let points' = match connexion0 with
- | None -> points
- | Some pt -> pt::points in
-
- let arr_points = match connexion1 with
- | None -> Array.of_list points'
- | Some pt ->
- let arr = Array.make (1 + (List.length points')) pt in
- List.iteri points'
- ~f:(fun i value -> Array.set arr i value);
- arr in
-
- let* bspline_points = from_points arr_points in
-
- let start = match connexion0 with
- | None -> 1
- | Some _ -> 2
- and end_ = match connexion1 with
- | None -> (Array.length bspline_points) - 1
- | Some _ -> (Array.length bspline_points) - 2 in
-
- let result = Array.init (end_ - start + 1) ~f:(fun i ->
-
- let i = i + start in
-
- let prev_b = Array.get bspline_points (i - 1)
- and bpoint = Array.get bspline_points i
- and prev_p = Array.get arr_points (i - 1)
- and point = Array.get arr_points i in
- let ctrl0 = Gg.V2.(mix prev_b bpoint (1. /. 3.))
- and ctrl1 = Gg.V2.(mix prev_b bpoint (2. /. 3.)) in
-
- let bezier =
- { Bezier.p0 = prev_p
- ; Bezier.p1 = point
- ; Bezier.ctrl0
- ; Bezier.ctrl1 } in
-
- bezier
-
- ) in
- Result.Ok result
-
diff --git a/shapes/bspline.mli b/shapes/bspline.mli
deleted file mode 100755
index a36aa22..0000000
--- a/shapes/bspline.mli
+++ /dev/null
@@ -1,24 +0,0 @@
-type t
-
-type err =
- [ `InvalidPath (* Too few points in the path for building the curve *)
- ]
-
-(** Convert a list of points into a beziers curves.
-
- At least 4 points are required for building the path.
-
- [to_bezier ~connexion points] create a list of beziers segments joining all
- the points together.
-
- [connexion0] add a virtual point in the begining for helping to get the
- appropriate tangent when connecting path together
-
- [connexion1] does the same at the end
-
-*)
-val to_bezier
- : ?connexion0:Gg.v2
- -> ?connexion1:Gg.v2
- -> Gg.v2 list
- -> (Bezier.t array, [> err]) Result.t
diff --git a/shapes/dd_splines.pdf b/shapes/dd_splines.pdf
deleted file mode 100755
index 2618162..0000000
--- a/shapes/dd_splines.pdf
+++ /dev/null
Binary files differ
diff --git a/shapes/dune b/shapes/dune
deleted file mode 100755
index d03a217..0000000
--- a/shapes/dune
+++ /dev/null
@@ -1,7 +0,0 @@
-(library
- (name shapes)
- (libraries
- tools
- matrix
- )
- )
diff --git a/shapes/matrix/EltsI.ml b/shapes/matrix/EltsI.ml
deleted file mode 100755
index fcfdb50..0000000
--- a/shapes/matrix/EltsI.ml
+++ /dev/null
@@ -1,28 +0,0 @@
-module type ORDERED_AND_OPERATIONAL =
-sig
-
- (* Exception for from_string. Is raised when from_string is passed something
- * that is not an elt *)
- exception NonElt
-
- type t
-
- (* The zero element *)
- val zero : t
-
- (* The one element *)
- val one: t
-
- (* ts must be comparable *)
- val compare : t -> t -> Order.order
-
- (* Basic mathematical operations must be possible *)
- val add: t -> t -> t
-
- val subtract: t -> t -> t
-
- val multiply: t -> t -> t
-
- val divide: t -> t -> t
-
-end
diff --git a/shapes/matrix/Helpers.ml b/shapes/matrix/Helpers.ml
deleted file mode 100755
index 6980052..0000000
--- a/shapes/matrix/Helpers.ml
+++ /dev/null
@@ -1,16 +0,0 @@
-(* Takes in a string and a separator, and separates the string into a list of
- * substrings where each substring is between two separators or between a
- * separator and the beginning/end of the string *)
-let explode (s: string) (space: string) : string list =
- let rec build (curr: string) (buffer: string) (lst: string list) : string list =
- let len = String.length curr in
- if len = 0 then buffer::lst
- else
- let c = String.sub curr (len - 1) 1 in
- if len = 1 then (c ^ buffer)::lst
- else
- let s' = String.sub curr 0 (len - 1) in
- if c = space then build s' "" (buffer::lst)
- else build s' (c ^ buffer) lst in
- build (String.trim s) "" []
-
diff --git a/shapes/matrix/Matrix.ml b/shapes/matrix/Matrix.ml
deleted file mode 100755
index 7f1d54b..0000000
--- a/shapes/matrix/Matrix.ml
+++ /dev/null
@@ -1,529 +0,0 @@
-open Order
-
-module Order = Order
-
-(*************** Exceptions ***************)
-
-exception NonSquare
-exception ImproperDimensions
-
-(* Functor so we can Abstract away! *)
-module MakeMatrix (C: EltsI.ORDERED_AND_OPERATIONAL) :
- (MatrixI.MATRIX with type elt = C.t) =
-struct
-
-
- (*************** End Exceptions ***************)
-
- (*************** Types ***************)
-
- type elt = C.t
-
- (* A matrix is a pair of dimension (n x p) and a array of arrays
- * the first array is the row (n) and the second the column (p) *)
- type matrix = (int * int) * (elt array array)
-
- (*************** End Types ***************)
-
- (*************** Base Functions ***************)
-
- (* catching negative dimensions AND 0 dimensions and too large
- * of a dimension so we don't have to worry about it later *)
- let empty (rows: int) (columns: int) : matrix =
- if rows > 0 && columns > 0 then
- try
- let m = Array.make_matrix rows columns C.zero in ((rows,columns),m)
- with _ ->
- raise ImproperDimensions
- else (* dimension is negative or 0 *)
- raise ImproperDimensions
-
- (*************** End Base Functions ***************)
-
- (*************** Helper Functions ***************)
-
- (* get's the nth row of a matrix and returns (r, row) where r is the length
- * of the row and row is a COPY of the original row. For example, calling
- * calling get_row m 1 will return (3, |1 3 4 |)
- * ________
- * m = | 1 3 4 |
- * |*2 5 6 |
- *)
- (* aside: we don't check whether n < 1 because of our matrix invariant *)
- let get_row (((n,p),m): matrix) (row: int) : int * elt array =
- if row <= n then
- let row' = Array.map (fun x -> x) m.(row - 1) in
- (p, row')
- else
- raise (Failure "Row out of bounds.")
-
- (* similar to get_row. For m, get_column m 1 will return (2, |1 2|) *)
- let get_column (((n,p),m): matrix) (column: int) : int * elt array =
- if column <= p then
- begin
- let column' = Array.make n C.zero in
- for i = 0 to n - 1 do
- column'.(i) <- m.(i).(column - 1)
- done;
- (n, column')
- end
- else
- raise (Failure "Column out of bounds.")
-
- (* sets the nth row of the matrix m to the specified array a.
- * This is done IN-PLACE. Therefore the function returns unit. You should
- * nonetheless enfore immutability whenever possible. For a clarification on
- * what nth row means, look at comment for get_row above. *)
- let set_row (((n, p), m): matrix) (row: int) (a: elt array) : unit =
- if row <= n then
- begin
- assert(Array.length a = p);
- for i = 0 to p - 1 do
- m.(row - 1).(i) <- a.(i)
- done;
- end
- else
- raise (Failure "Row out of bounds.")
-
- (* Similar to set_row but sets the nth column instead *)
- let set_column (((n,p),m): matrix) (column: int) (a: elt array) : unit =
- if column <= p then
- begin
- assert(Array.length a = n);
- for i = 0 to n - 1 do
- m.(i).(column - 1) <- a.(i)
- done;
- end
- else
- raise (Failure "Column out of bounds.")
-
- (* returns the ij-th element of a matrix (not-zero indexed) *)
- let get_elt (((n,p),m): matrix) ((i,j): int*int) : elt =
- if i <= n && j <= p then
- m.(i - 1).(j - 1)
- else
- raise ImproperDimensions
-
- (* Changes the i,j-th element of a matrix to e. Is not zero-indexed, and
- * changes the matrix in place *)
- let set_elt (((n,p),m): matrix) ((i,j): int*int) (e: elt) : unit =
- if i <= n && j <= p then
- m.(i - 1).(j - 1) <- e
- else
- raise ImproperDimensions
-
- (* similar to map, but applies to function to the entire matrix
- * Returns a new matrix *)
- let map (f: elt -> elt) (mat: matrix) : matrix =
- let (dim,m) = mat in
- (dim, Array.map (Array.map f) m)
-
- (* Just some wrapping of Array.iter made for Matrices! *)
- let iter (f: elt -> unit) (mat: matrix) : unit =
- let _, m = mat in
- Array.iter (Array.iter f) m
-
- (* Just some wrapping of Array.iteri. Useful for pretty
- * printing matrix. The index is (i,j). NOT zero-indexed *)
- let iteri (f: int -> int -> elt -> unit) (mat: matrix) : unit =
- let _, m = mat in
- Array.iteri (fun i row -> Array.iteri (fun j e -> f i j e) row) m
-
- (* folds over each row using base case u and function f *)
- (* could be a bit more efficient? *)
- let reduce (f: 'a -> elt -> 'a) (u: 'a) (((p,q),m): matrix) : 'a =
- let total = ref u in
- for i = 0 to p - 1 do
- for j = 0 to q - 1 do
- total := f (!total) m.(i).(j)
- done;
- done;
- !total
-
- let fold_row ~(f: elt array -> 'b) ((_,m): matrix) : 'b list =
-
- let call_row acc v = (f v)::acc in
- Array.fold_left call_row [] m
- |> List.rev
-
-
-
-
- (* given two arrays, this will calculate their dot product *)
- (* It seems a little funky, but this is done for efficiency's sake.
- * In short, it tries to multiply each element by it's respective
- * element until the one array is indexed out of bounds. If the
- * other array is also out of bounds, then it returns their value.
- * Otherwise, the arrays were the wrong size and raises ImproperDimension
-
- THE ABOVE COMMENT HAS NOT BEEN IMPLEMENTED
-
- Instead we calculate the length before starting
- *)
- let dot (v1: elt array) (v2: elt array) : elt =
- let rec dotting (i: int) (total: elt) : elt =
- if i = 0 then total
- else
- let curr = C.multiply v1.(i-1) v2.(i-1) in
- dotting (i - 1) (C.add curr total) in
- let len1, len2 = Array.length v1, Array.length v2 in
- if len1 = len2 then dotting len1 C.zero
- else raise ImproperDimensions
-
- (* function to expose the dimensions of a matrix *)
- let get_dimensions (m: matrix) : (int * int) =
- let ((x,y), _) = m in (x,y)
-
- (*************** End Helper Functions ***************)
-
-
- (*************** Primary Matrix Functions ***************)
-
- (* scales a matrix by the appropriate factor *)
- let scale (m: matrix) (sc: elt) : matrix = map (C.multiply sc) m
-
- (* Generates a matrix from a list of lists. The inners lists are the rows *)
- let from_list (lsts : elt list list) : matrix =
- let check_length (length: int) (lst: elt list) : int =
- if List.length lst = length then length
- else raise ImproperDimensions in
- let p = List.length lsts in
- match lsts with
- | [] -> raise ImproperDimensions
- | hd::tl ->
- let len = List.length hd in
- if List.fold_left check_length len tl = len then
- ((p,len),Array.map Array.of_list (Array.of_list lsts))
- else
- raise ImproperDimensions
-
- (* Generates a matrix from a list of lists. The inners lists are the rows *)
- let from_array (arrs : elt array array) : matrix =
- let check_length (length: int) (arr: elt array) : unit =
- if Array.length arr = length then ()
- else raise ImproperDimensions in
- let p = Array.length arrs in
- match Array.length arrs with
- | 0 -> raise ImproperDimensions
- | _ ->
- let len = Array.length (Array.get arrs 0) in
- Array.iter (check_length len) arrs;
- ((p, len), arrs)
-
- (* Adds two matrices. They must have the same dimensions *)
- let add ((dim1,m1): matrix) ((dim2,m2): matrix) : matrix =
- if dim1 = dim2 then
- let n, p = dim1 in
- let (dim', sum_m) = empty n p in
- for i = 0 to n - 1 do
- for j = 0 to p - 1 do
- sum_m.(i).(j) <- C.add m1.(i).(j) m2.(i).(j)
- done;
- done;
- (dim',sum_m)
- else
- raise ImproperDimensions
-
-
- (* Multiplies two matrices. If the matrices have dimensions m x n and p x q, n
- * and p must be equal, and the resulting matrix will have dimension n x q *)
- let mult (matrix1: matrix) (matrix2: matrix) : matrix =
- let ((m,n), _), ((p,q), _) = matrix1, matrix2 in
- if n = p then
- let (dim, result) = empty m q in
- for i = 0 to m - 1 do
- for j = 0 to q - 1 do
- let (_,row), (_,column) = get_row matrix1 (i + 1),
- get_column matrix2 (j + 1) in
- result.(i).(j) <- dot row column
- done;
- done;
- (dim,result)
- else
- raise ImproperDimensions
-
- (*************** Helper Functions for Row Reduce ***************)
-
- (*
- (* returns the index of the first non-zero elt in an array*)
- let zero (arr: elt array) : int option =
- let index = ref 1 in
- let empty (i: int option) (e: elt) : int option =
- match i, C.compare e C.zero with
- | None, Equal -> (index := !index + 1; None)
- | None, _ -> Some (!index)
- | _, _ -> i in
- Array.fold_left empty None arr
-
- (* returns the the location of the nth non-zero
- * element in the matrix. Scans column wise. So the nth non-zero element is
- * the FIRST non-zero element in the nth non-zero column *)
- let nth_nz_location (m: matrix) (_: int): (int*int) option =
- let ((n,p), _) = m in
- let rec check_col (to_skip: int) (j: int) =
- if j <= p then
- let (_,col) = get_column m j in
- match zero col with
- | None -> check_col to_skip (j + 1)
- | Some i ->
- if to_skip = 0 then
- Some (i,j)
- else (* we want a later column *)
- check_col (to_skip - 1) (j + 1)
- else None in
- check_col (n - 1) 1
-
- (* returns the the location of the first
- * non-zero and non-one elt. Scans column wise, from
- * left to right. Basically, it ignores columns
- * that are all zero or that *)
- let fst_nz_no_loc (m: matrix): (int*int) option =
- let ((_, p), _) = m in
- let rec check_col (j: int) =
- if j <= p then
- let (_,col) = get_column m j in
- match zero col with
- | None -> check_col (j + 1)
- | Some i ->
- match C.compare col.(i-1) C.one with
- | Equal -> check_col (j + 1)
- | _ -> Some (i,j)
- else None in
- check_col 1
- *)
-
- (* Compares two elements in an elt array and returns the greater and its
- * index. Is a helper function for find_max_col_index *)
- let compare_helper (e1: elt) (e2: elt) (ind1: int) (ind2: int) : (elt*int) =
- match C.compare e1 e2 with
- | Equal -> (e2, ind2)
- | Greater -> (e1, ind1)
- | Less -> (e2, ind2)
-
- (* Finds the element with the greatest absolute value in a column. Is not
- * 0-indexed. If two elements are both the maximum value, returns the one with
- * the lowest index. Returns None if this element is zero (if column is all 0)
- *)
- let find_max_col_index (array1: elt array) (start_index: int) : int option =
- let rec find_index (max_index: int) (curr_max: elt) (curr_index: int)
- (arr: elt array) =
- if curr_index = Array.length arr then
- (if curr_max = C.zero then None
- else Some (max_index+1)) (* Arrays are 0-indexed but matrices aren't *)
- else
- (match C.compare arr.(curr_index) C.zero with
- | Equal -> find_index max_index curr_max (curr_index+1) arr
- | Greater ->
- (let (el, index) = compare_helper (arr.(curr_index))
- curr_max curr_index max_index in
- find_index index el (curr_index+1) arr)
- | Less ->
- (let abs_curr_elt = C.subtract C.zero arr.(curr_index) in
- let (el, index) = compare_helper abs_curr_elt curr_max curr_index
- max_index in
- find_index index el (curr_index+1) arr))
- in
- find_index 0 C.zero (start_index -1) array1
-
- (* Basic row operations *)
- (* Scales a row by sc *)
- let scale_row (m: matrix) (num: int) (sc: elt) : unit =
- let (_, row) = get_row m num in
- let new_row = Array.map (C.multiply sc) row in
- set_row m num new_row
-
- (* Swaps two rows of a matrix *)
- let swap_row (m: matrix) (r1: int) (r2: int) : unit =
- let (len1, row1) = get_row m r1 in
- let (len2, row2) = get_row m r2 in
- let _ = assert (len1 = len2) in
- let _ = set_row m r1 row2 in
- let _ = set_row m r2 row1 in
- ()
-
- (* Subtracts a multiple of r2 from r1 *)
- let sub_mult (m: matrix) (r1: int) (r2: int) (sc: elt) : unit =
- let (len1, row1) = get_row m r1 in
- let (len2, row2) = get_row m r2 in
- let _ = assert (len1 = len2) in
- for i = 0 to len1 - 1 do (* Arrays are 0-indexed *)
- row1.(i) <- C.subtract row1.(i) (C.multiply sc row2.(i))
- done;
- set_row m r1 row1
-
- (*************** End Helper Functions for Row Reduce ***************)
-
- (* Returns the row reduced form of a matrix. Is not done in place, but creates
- * a new matrix *)
- let row_reduce (mat: matrix) : matrix =
- let[@tailcall] rec row_reduce_h (n_row: int) (n_col: int) (mat2: matrix) : unit =
- let ((num_row, _), _) = mat2 in
- if (n_col = num_row + 1) then ()
- else
- let (_,col) = get_column mat2 n_col in
- match find_max_col_index col n_row with
- | None (* Column all 0s *) -> row_reduce_h n_row (n_col+1) mat2
- | Some index ->
- begin
- swap_row mat2 index n_row;
- let pivot = get_elt mat2 (n_row, n_col) in
- scale_row mat2 (n_row) (C.divide C.one pivot);
- for i = 1 to num_row do
- if i <> n_row then sub_mult mat2 i n_row (get_elt mat2 (i,n_col))
- done;
- row_reduce_h (n_row+1) (n_col+1) mat2
- end
- in
- (* Copies the matrix *)
- let ((n,p),m) = mat in
- let (dim,mat_cp) = empty n p in
- for i = 0 to n - 1 do
- for j = 0 to p - 1 do
- mat_cp.(i).(j) <- m.(i).(j)
- done;
- done;
- let _ = row_reduce_h 1 1 (dim,mat_cp) in (dim,mat_cp)
-
- (*************** End Main Functions ***************)
-
- (*************** Optional module functions ***************)
-
- (* calculates the trace of a matrix *)
- let trace (((n,p),m): matrix) : elt =
- let rec build (elt: elt) (i: int) =
- if i > -1 then
- build (C.add m.(i).(i) elt) (i - 1)
- else
- elt in
- if n = p then build C.zero (n - 1)
- else raise ImproperDimensions
-
- (* calculates the transpose of a matrix and retuns a new one *)
- let transpose (((n,p),m): matrix) =
- let (dim,m') = empty p n in
- for i = 0 to n - 1 do
- for j = 0 to p - 1 do
- m'.(j).(i) <- m.(i).(j)
- done;
- done;
- assert(dim = (p,n));
- ((p,n),m')
-
- (* Returns the inverse of a matrix. Uses a pretty simple algorithm *)
- let inverse (mat: matrix) : matrix =
- let ((n, p), _) = mat in
- if n = p then
- (* create augmented matrix *)
- let augmented = empty n (2*n) in
- for i = 1 to n do
- let (dim,col) = get_column mat i in
- let arr = Array.make n C.zero in
- begin
- assert(dim = n);
- arr.(i-1) <- C.one;
- set_column augmented i col;
- set_column augmented (n + i) arr
- end
- done;
- let augmented' = row_reduce augmented in
- (* create the inverted matrix and fill in with appropriate values *)
- let inverse = empty n n in
- for i = 1 to n do
- let (dim, col) = get_column augmented' (n + i) in
- let _ = assert(dim = n) in
- let _ = set_column inverse i col in
- ()
- done;
- inverse
- else
- raise NonSquare
-
- (***************** HELPER FUNCTIONS FOR DETERMINANT *****************)
- (* creates an identity matrix of size n*)
- let create_identity (n:int) : matrix =
- let (dim,m) = empty n n in
- for i = 0 to n - 1 do
- m.(i).(i) <- C.one
- done;
- (dim,m)
-
- (* Finds the index of the maximum value of an array *)
- let find_max_index (arr: elt array) (start_index : int) : int =
- let rec find_index (max_index: int) (curr_index: int) =
- if curr_index = Array.length arr then max_index+1
- else
- match C.compare arr.(curr_index) arr.(max_index) with
- | Equal | Less -> find_index max_index (curr_index + 1)
- | Greater -> find_index curr_index (curr_index + 1) in
- find_index (start_index - 1) start_index
-
- (* Creates the pivoting matrix for A. Returns swqps. Adapted from
- * http://rosettacode.org/wiki/LU_decomposition#Common_Lisp *)
- let pivotize (((n,p),m): matrix) : matrix * int =
- if n = p then
- let swaps = ref 0 in
- let pivot_mat = create_identity n in
- for j = 1 to n do
- let (_,col) = get_column ((n,p),m) j in
- let max_index = find_max_index col j in
- if max_index <> j then
- (swaps := !swaps + 1; swap_row pivot_mat max_index j)
- else ()
- done;
- (pivot_mat,!swaps)
- else raise ImproperDimensions
-
- (* decomposes a matrix into a lower triangualar, upper triangualar
- * and a pivot matrix. It returns (L,U,P). Adapted from
- * http://rosettacode.org/wiki/LU_decomposition#Common_Lisp *)
- let lu_decomposition (((n,p),m): matrix) : (matrix*matrix*matrix)*int =
- if n = p then
- let mat = ((n,p),m) in
- let lower, upper, (pivot,s) = empty n n, empty n n, pivotize mat in
- let (_ ,l),(_ ,u), _ = lower,upper,pivot in
- let ((_, _),mat') = mult pivot mat in
- for j = 0 to n - 1 do
- l.(j).(j) <- C.one;
- for i = 0 to j do
- let sum = ref C.zero in
- for k = 0 to i - 1 do
- sum := C.add (!sum) (C.multiply u.(k).(j) l.(i).(k))
- done;
- u.(i).(j) <- C.subtract mat'.(i).(j) (!sum)
- done;
- for i = j to n - 1 do
- let sum = ref C.zero in
- for k = 0 to j - 1 do
- sum := C.add (!sum) (C.multiply u.(k).(j) l.(i).(k))
- done;
- let sub = C.subtract mat'.(i).(j) (!sum) in
- l.(i).(j) <- C.divide sub u.(j).(j)
- done;
- done;
- (lower,upper,pivot),s
- else raise ImproperDimensions
-
- (* Computes the determinant of a matrix *)
- let determinant (m: matrix) : elt =
- try
- let ((n,p), _) = m in
- if n = p then
- let rec triangualar_det (a,mat) curr_index acc =
- if curr_index < n then
- let acc' = C.multiply mat.(curr_index).(curr_index) acc in
- triangualar_det (a,mat) (curr_index + 1) acc'
- else acc in
- let ((dim1,l),(dim2,u), _),s = lu_decomposition m in
- let det1, det2 = triangualar_det (dim1,l) 0 C.one,
- triangualar_det (dim2,u) 0 C.one in
- if s mod 2 = 0 then C.multiply det1 det2
- else C.subtract C.zero (C.multiply det1 det2)
- else raise ImproperDimensions
- with
- | _ -> C.zero
-
-
- (*************** Optional module functions ***************)
-
-
-end
diff --git a/shapes/matrix/MatrixI.ml b/shapes/matrix/MatrixI.ml
deleted file mode 100755
index fbc4e21..0000000
--- a/shapes/matrix/MatrixI.ml
+++ /dev/null
@@ -1,105 +0,0 @@
-exception NonSquare
-exception ImproperDimensions
-
-module type MATRIX =
-sig
-
- (******** TYPES ********)
- type elt
-
- type matrix
-
- (* empty matrix of nxp dimensions *)
- val empty : int -> int -> matrix
-
- (* Takes a list of lists and converts that to a matrix *)
- val from_list : (elt list list) -> matrix
-
- val from_array: elt array array -> matrix
-
- (******** OPERATIONS ON ONE MATRIX ********)
- (* Takes in a matrix and returns its dimensions. ie, nxp *)
- val get_dimensions : matrix -> (int * int)
-
- (* get's the row of a matrix: Not zero-indexed. *)
- val get_row : matrix -> int -> (int * elt array)
-
- (* similar to get_row *)
- val get_column: matrix -> int -> (int * elt array)
-
- (* sets the row of a matrix in place! Not zero-index *)
- val set_row: matrix -> int -> elt array -> unit
-
- (* similar to set_row, but for a column *)
- val set_column: matrix -> int -> elt array -> unit
-
- (* gets the element at the specified index. *)
- val get_elt: matrix -> (int * int) -> elt
-
- (* sets the element at the specified index *)
- val set_elt: matrix -> (int * int) -> elt -> unit
-
- (* Scales every element in the matrix by another elt *)
- val scale : matrix -> elt -> matrix
-
-
- (******** MORE ADVANCED SINGLE MATRIX OPERATIONS ********)
- (* Returns the row reduced form of a matrix *)
- val row_reduce: matrix -> matrix
- (* We will implement the algorithm found in the link above *)
-
- (* Returns the inverse of a matrix *)
- val inverse: matrix -> matrix
-
- (*Transposes a matrix. If the input has dimensions m x n, the output will
- * have dimensions n x m *)
- val transpose: matrix -> matrix
-
- (* Returns the trace of the matrix *)
- val trace: matrix -> elt
-
- (******** OPERATIONS ON TWO MATRICES ********)
- (* Adds two matrices. They must have the same dimensions *)
- val add : matrix -> matrix -> matrix
-
- (* Multiplies two matrices. If the matrices have dimensions m x n and p x q, n
- * and p must be equal, and the resulting matrix will have dimension m x q *)
- val mult: matrix -> matrix -> matrix
-
- (**** Other Library Functions ***)
- (* Function to make over our matrices *)
- val map : (elt -> elt) -> matrix -> matrix
-
- (*val iter : (elt -> unit) -> matrix -> unit*)
-
- (* Returns the LUP decomposition of a matrix *)
- val lu_decomposition : matrix -> (matrix * matrix * matrix) * int
-
- (* Returns the determinant of the matrix *)
- val determinant: matrix -> elt
-
- (************** Other Library Functions *************)
- val iter : (elt -> unit) -> matrix -> unit
-
- val iteri : (int -> int -> elt -> unit) -> matrix -> unit
-
- (* folds over each row using base case u and function f *)
- val reduce: ('a -> elt -> 'a) -> 'a -> matrix -> 'a
-
- val fold_row: f:(elt array -> 'b) -> matrix -> 'b list
-
- (********** Specific for Simplex Algorithm ***********)
- (** All of the following functions will raise ImproperDimensions
- * Exception if the matrix is not the right size for the operation
- **)
-
- (* Scales a row *)
- val scale_row: matrix -> int -> elt -> unit
-
- (* Swaps two rows *)
- val swap_row: matrix -> int -> int -> unit
-
- (* Subtracts a multiple of one row (the 2nd int) from another (the 1st int) *)
- val sub_mult: matrix -> int -> int -> elt -> unit
-
-end
diff --git a/shapes/matrix/Order.ml b/shapes/matrix/Order.ml
deleted file mode 100755
index 5f2aa22..0000000
--- a/shapes/matrix/Order.ml
+++ /dev/null
@@ -1,2 +0,0 @@
-(* Defines a general ordering type *)
-type order = Equal | Less | Greater
diff --git a/shapes/matrix/dune b/shapes/matrix/dune
deleted file mode 100755
index 1c0cab6..0000000
--- a/shapes/matrix/dune
+++ /dev/null
@@ -1,3 +0,0 @@
-(library
- (name matrix)
-)
diff --git a/shapes/tools/dune b/shapes/tools/dune
deleted file mode 100755
index a2c3fdb..0000000
--- a/shapes/tools/dune
+++ /dev/null
@@ -1,6 +0,0 @@
-(library
- (name tools)
- (libraries
- gg
- )
- )
diff --git a/shapes/tools/utils.ml b/shapes/tools/utils.ml
deleted file mode 100755
index b8a473f..0000000
--- a/shapes/tools/utils.ml
+++ /dev/null
@@ -1,63 +0,0 @@
-open Gg.V2
-
-let norm_angle vect =
- mod_float
- ((angle vect) +. Gg.Float.two_pi)
- Gg.Float.two_pi
-
-
-let intersection
- : (Gg.v2 * Gg.v2) -> (Gg.v2 * Gg.v2) -> Gg.v2 option
- = fun (p0, p1) (p2, p3) ->
- let i = p1 - p0
- and j = p3 - p2 in
-
- let d = (x i *. y j) -. (y i *. x j) in
- if Float.( (abs d) <= 0.01 ) then
- None
- else
- let m = ((x i) *. (y p0)
- -. (x i) *. (y p2)
- -. (y i) *. (x p0)
- +. (y i) *. (x p2)) /. d in
- Some (p2 + m * j)
- (*
- let k = ((x j) *. (y p0)
- -. (x j) *. (y p2)
- -. (y j) *. (x p0)
- +. (y j) *. (x p2)) /. d in
- Some (p0 + k * i)
- *)
-
-
-let center
- : Gg.v2 -> Gg.v2 -> Gg.v2 -> Gg.v2 option
- = fun p0 p1 p2 ->
- (* deltas *)
- let d1 = p1 - p0
- and d2 = p2 - p1 in
-
- (* perpendiculars *)
- let d1p = ortho d1
- and d2p = ortho d2 in
-
- (* Chord midpoints *)
- let m1 = half (p0 + p1)
- and m2 = half (p1 + p2) in
-
- (* midpoint offsets *)
- let m1n = m1 + d1p
- and m2n = m2 + d2p in
-
- intersection (m1, m1n) (m2, m2n)
-
-let rotate
- : Gg.v2 -> float -> Gg.v2
- = fun p0 theta ->
- let r = x (to_polar p0) in
- of_polar (v r theta)
-
-let equal_point
- : float -> Gg.v2 -> Gg.v2 -> bool
- = fun eps p0 p1 ->
- Gg.V2.equal_f (fun v0 v1 -> (Float.abs (v1 -. v0)) <= eps ) p0 p1
diff --git a/shapes/tools/utils.mli b/shapes/tools/utils.mli
deleted file mode 100755
index 4e12906..0000000
--- a/shapes/tools/utils.mli
+++ /dev/null
@@ -1,21 +0,0 @@
-(** Return a normalize angle *)
-val norm_angle
- : Gg.v2 -> float
-
-(** return the interesction for two segments *)
-val intersection
- : (Gg.v2 * Gg.v2) -> (Gg.v2 * Gg.v2) -> Gg.v2 option
-
-(** Return the center of the cercle for three points
- None if the point cannot be evaluated
-*)
-val center
- : Gg.v2 -> Gg.v2 -> Gg.v2 -> Gg.v2 option
-
-(** Rotate the vector by the given angle *)
-val rotate
- : Gg.v2 -> float -> Gg.v2
-
-(** Test equality between two points *)
-val equal_point
- : float -> Gg.v2 -> Gg.v2 -> bool