15 files changed, 1221 insertions, 0 deletions

diff --git a/script.it/shapes/bezier.ml b/script.it/shapes/bezier.ml
new file mode 100755
index 0000000..f5f288c
--- /dev/null
+++ b/script.it/shapes/bezier.ml
@@ -0,0 +1,228 @@
+(**
+
+   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/script.it/shapes/bezier.mli b/script.it/shapes/bezier.mli
new file mode 100755
index 0000000..2f5bbcf
--- /dev/null
+++ b/script.it/shapes/bezier.mli
@@ -0,0 +1,40 @@
+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/script.it/shapes/bspline.ml b/script.it/shapes/bspline.ml
new file mode 100755
index 0000000..bb60227
--- /dev/null
+++ b/script.it/shapes/bspline.ml
@@ -0,0 +1,149 @@
+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/script.it/shapes/bspline.mli b/script.it/shapes/bspline.mli
new file mode 100755
index 0000000..a36aa22
--- /dev/null
+++ b/script.it/shapes/bspline.mli
@@ -0,0 +1,24 @@
+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/script.it/shapes/dd_splines.pdf b/script.it/shapes/dd_splines.pdf
new file mode 100755
index 0000000..2618162
--- /dev/null
+++ b/script.it/shapes/dd_splines.pdf
diff --git a/script.it/shapes/dune b/script.it/shapes/dune
new file mode 100755
index 0000000..d03a217
--- /dev/null
+++ b/script.it/shapes/dune
@@ -0,0 +1,7 @@
+(library
+ (name shapes)
+ (libraries 
+   tools
+   matrix
+   )
+ )
diff --git a/script.it/shapes/matrix/EltsI.ml b/script.it/shapes/matrix/EltsI.ml
new file mode 100755
index 0000000..fcfdb50
--- /dev/null
+++ b/script.it/shapes/matrix/EltsI.ml
@@ -0,0 +1,28 @@
+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/script.it/shapes/matrix/Helpers.ml b/script.it/shapes/matrix/Helpers.ml
new file mode 100755
index 0000000..6980052
--- /dev/null
+++ b/script.it/shapes/matrix/Helpers.ml
@@ -0,0 +1,16 @@
+(* 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/script.it/shapes/matrix/Matrix.ml b/script.it/shapes/matrix/Matrix.ml
new file mode 100755
index 0000000..7f1d54b
--- /dev/null
+++ b/script.it/shapes/matrix/Matrix.ml
@@ -0,0 +1,529 @@
+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/script.it/shapes/matrix/MatrixI.ml b/script.it/shapes/matrix/MatrixI.ml
new file mode 100755
index 0000000..fbc4e21
--- /dev/null
+++ b/script.it/shapes/matrix/MatrixI.ml
@@ -0,0 +1,105 @@
+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/script.it/shapes/matrix/Order.ml b/script.it/shapes/matrix/Order.ml
new file mode 100755
index 0000000..5f2aa22
--- /dev/null
+++ b/script.it/shapes/matrix/Order.ml
@@ -0,0 +1,2 @@
+(* Defines a general ordering type *)
+type order = Equal | Less | Greater
diff --git a/script.it/shapes/matrix/dune b/script.it/shapes/matrix/dune
new file mode 100755
index 0000000..1c0cab6
--- /dev/null
+++ b/script.it/shapes/matrix/dune
@@ -0,0 +1,3 @@
+(library
+ (name matrix)
+)
diff --git a/script.it/shapes/tools/dune b/script.it/shapes/tools/dune
new file mode 100755
index 0000000..a2c3fdb
--- /dev/null
+++ b/script.it/shapes/tools/dune
@@ -0,0 +1,6 @@
+(library
+ (name tools)
+ (libraries 
+   gg
+   )
+  )
diff --git a/script.it/shapes/tools/utils.ml b/script.it/shapes/tools/utils.ml
new file mode 100755
index 0000000..b8a473f
--- /dev/null
+++ b/script.it/shapes/tools/utils.ml
@@ -0,0 +1,63 @@
+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/script.it/shapes/tools/utils.mli b/script.it/shapes/tools/utils.mli
new file mode 100755
index 0000000..4e12906
--- /dev/null
+++ b/script.it/shapes/tools/utils.mli
@@ -0,0 +1,21 @@
+(** 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