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(**************************************************************************)
(* *)
(* Ocamlgraph: a generic graph library for OCaml *)
(* Copyright (C) 2004-2010 *)
(* Sylvain Conchon, Jean-Christophe Filliatre and Julien Signoles *)
(* *)
(* This software is free software; you can redistribute it and/or *)
(* modify it under the terms of the GNU Library General Public *)
(* License version 2.1, with the special exception on linking *)
(* described in file LICENSE. *)
(* *)
(* This software is distributed in the hope that it will be useful, *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *)
(* *)
(**************************************************************************)
(*** Operateurs Complex ***)
let ( ~-& ) (x, y) = (-.x, -.y)
let ( ~& ) (x, y) = (x, -.y)
let ( +& ) (x1, y1) (x2, y2) =
(x1 +. x2, y1 +. y2)
let ( -& ) (x1, y1) (x2, y2) =
(x1 +. x2, y1 +. y2)
let ( *& ) (x1, y1) (x2, y2) =
(x1*.x2 -. y1*.y2, x1*.y2 +. y1*.x2)
let ( /& ) (x1, y1) (x2, y2) =
let n2 = x2*.x2 +. y2*.y2 in
((x1*.x2 +. y1*.y2)/.n2, (-.x1*.y2 +. y1*.x2)/.n2)
let ( *.& ) f (x, y) =
(f*.x, f*.y)
let norm_sqr (x, y) =
x*.x +. y*.y
let norm (x, y) =
sqrt(x*.x +. y*.y)
let normalize (x, y) =
let n = sqrt(x*.x +. y*.y) in
(x/.n, y/.n)
let expi t =
(cos t, sin t)
(*** Fonctions Hyperboliques ***)
let th t =
let ept = exp t
and emt = exp (-.t) in
(ept -. emt)/.(ept +. emt)
let ath x =
0.5*.log((1.0 +. x)/.(1.0 -. x))
let pi = 3.14159265358979323846
let pi_over_2 = pi/.2.0
let pi_over_4 = pi/.4.0
let one = (1.0, 0.0)
let translate a z =
(a +& z)/&(one +& (~&a) *& z)
let gamma a u t =
let utht = th t *.& u in
(a +& utht) /& (one +& (~&a) *& utht)
let delta a u t =
let atht = th t *.& a
and utht = th t *.& u in
normalize ((u +& atht) /& (one +& (~&a) *& utht))
(* solving a Cramer system *)
let cramer a1 a2 b1 b2 c1 c2 =
let cdet = a1*.b2 -. a2*.b1
and xdet = c1*.b2 -. c2*.b1
and ydet = a1*.c2 -. a2*.c1 in
(xdet/.cdet, ydet/.cdet) ;;
let drag_origin (x0, y0) (x1, y1) (x2, y2) =
let (x1, y1) = translate (-.x0, -.y0) (x1, y1) in
let x3 = x1*.x2 -. y1*.y2 in
let y3 = x1*.y2 +. y1*.x2 in
cramer (1.0 -. x3) (-.y3) (-.y3) (1.0 +. x3) (x2 -. x1) (y2 -. y1)
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