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geometry.ml
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geometry.ml
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(* -*- mode: Tuareg;-*- *)
(* Filename: barycenter.ml *)
(* Authors: lgm *)
(* Creation: Tue Jan 16 12:40:15 2007 *)
(* Copyright: Biosimilarity LLC 2004 - 2006. All rights reserved. *)
(* See LICENSE.BIOSIM in the license directory. *)
(* Description: *)
(* -------------------------------------------------------------------- *)
open Json_type
module Geometry =
struct
type dimnames =
X
| Y
| Z
| Yaw
| Pitch
| Roll
module DimHash
=
struct
type t = dimnames
let equal = (==)
let hash = Hashtbl.hash
end
module DimTable = Hashtbl.Make( DimHash )
type point =
{x:float; y:float; z:float; yaw:float; pitch:float; roll:float}
type platonic =
Tetrahedron
| Cube
| Octahedron
| Dodecahedron
| Icosohedron
type solid =
ConvexPolyhedra of platonic * point * float
| Sphere of point * float
type complex =
Extremum of point list
| Solid of solid
| Complex of complex list
exception CaseNotCoveredException
let unitx () =
{x=1.0;y=0.0;z=0.0;yaw=0.0;pitch=0.0;roll=0.0}
let unity () =
{x=0.0;y=1.0;z=0.0;yaw=0.0;pitch=0.0;roll=0.0}
let unitz () =
{x=0.0;y=0.0;z=1.0;yaw=0.0;pitch=0.0;roll=0.0}
let unityaw () =
{x=0.0;y=0.0;z=0.0;yaw=1.0;pitch=0.0;roll=0.0}
let unitpitch () =
{x=0.0;y=0.0;z=0.0;yaw=0.0;pitch=1.0;roll=0.0}
let unitroll () =
{x=0.0;y=0.0;z=0.0;yaw=0.0;pitch=0.0;roll=1.0}
let origin () =
{x=0.0;y=0.0;z=0.0;yaw=0.0;pitch=0.0;roll=0.0}
let _dimensionUnitTableInitialized = ref false
let _dtut = ref (DimTable.create 6)
let dimensionUnitTable =
if (!_dimensionUnitTableInitialized)
then !_dtut
else
begin
(DimTable.add !_dtut X (unitx ()));
(DimTable.add !_dtut Y (unity ()));
(DimTable.add !_dtut Z (unitz ()));
(DimTable.add !_dtut Yaw (unityaw ()));
(DimTable.add !_dtut Pitch (unitpitch ()));
(DimTable.add !_dtut Roll (unitroll ()));
!_dtut
end
let smult p s =
{x=p.x*.s;
y=p.y*.s;
z=p.z*.s;
yaw=p.yaw*.s;
pitch=p.pitch*.s;
roll=p.roll*.s}
let dot p1 p2 =
((p1.x*.p2.x)
+.(p1.y*.p2.y)
+.(p1.z*.p2.z)
+.(p1.yaw*.p2.yaw)
+.(p1.pitch*.p2.pitch)
+.(p1.roll*.p2.roll))
let norm p =
(sqrt (dot p p))
let vplus p1 p2 =
{x=p1.x+.p2.x;
y=p1.y+.p2.y;
z=p1.z+.p2.y;
yaw=p1.yaw+.p2.yaw;
pitch=p1.pitch+.p2.pitch;
roll=p1.roll+.p2.roll}
let vminus p1 p2 =
(vplus p1 (smult p2 (-1.0)))
let rec scale cplx sf =
(match cplx with
Extremum( pts ) ->
Extremum( (List.map (fun pt -> (smult pt sf)) pts) )
| Solid s ->
(match s with
ConvexPolyhedra (kind,center,edgeLength) ->
(Solid (ConvexPolyhedra (kind,center,(edgeLength *. sf))))
| Sphere (center,radius) ->
(Solid (Sphere (center,(radius *. sf)))))
| Complex( cplxs ) ->
match cplxs with
[] -> cplx
| top :: restCplxs ->
Complex( (List.map (fun plx -> (scale plx sf)) cplxs) ))
let rec translate cplx delta =
(match cplx with
Extremum( pts ) ->
Extremum( (List.map (fun pt -> (vplus pt delta)) pts) )
| Solid s ->
(match s with
ConvexPolyhedra (kind,center,edgeLength) ->
(Solid (ConvexPolyhedra (kind,(vplus center delta),edgeLength)))
| Sphere (center,radius) ->
(Solid (Sphere ((vplus center delta),radius))))
| Complex( cplxs ) ->
match cplxs with
[] -> cplx
| top :: restCplxs ->
Complex( (List.map (fun plx -> (translate plx delta)) cplxs) ))
let top cplx =
(match cplx with
Extremum( _ ) -> cplx
| Solid( _ ) -> cplx
| Complex( cplxs ) ->
match cplxs with
[] -> cplx
| top :: _ -> top)
let rec barycenter ensemble =
match ensemble with
Extremum( pts ) ->
let n = float_of_int (List.length pts) in
let (x,y,z,yaw,pitch,roll) =
(List.fold_left
(fun (u,v,w,way,hctip,llor) {x=x;y=y;z=z;yaw=yaw;pitch=pitch;roll=roll} ->
(u+.x, v+.y, w+.z, way+.yaw, hctip+.pitch, llor+.roll))
(0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
pts) in
{x=x/.n; y=y/.n; z=z/.n; yaw=yaw/.n; pitch=pitch/.n; roll=roll/.n}
| Solid s ->
(match s with
ConvexPolyhedra (kind,center,edgeLength) -> center
| Sphere (center,radius) -> center)
| Complex( cplxs ) ->
let centers =
(List.map
(fun center -> (barycenter center))
cplxs) in
(barycenter (Extremum( centers )))
let rec completeComplex cplx ctor =
match cplx with
Extremum( pts ) ->
(match pts with
[] -> raise CaseNotCoveredException
| p1 :: [] ->
(* ------------------------------------------------------------ *)
(* This case merely calculates the pt unit length from p1 in *)
(* the ctor direction. *)
(* ------------------------------------------------------------ *)
(vplus (DimTable.find dimensionUnitTable ctor) p1)
| p1 :: p2 :: [] ->
(* ------------------------------------------------------------ *)
(* The calculation for this case is as follows. Let *)
(* l = ||p2-p1||. We seek the point pt such that ||pt-p2|| = l; *)
(* ||pt-p1|| = l; pt lines on the line perpendicular to p2-p1 *)
(* in the ctor direction. *)
(* ------------------------------------------------------------ *)
let c = (DimTable.find dimensionUnitTable ctor) in
let d = (vminus p2 p1) in (* vector from p1 to p2 *)
let l = (norm d) in (* length of d *)
let t = ((dot (vminus c d) d) /. (dot d d)) in
(* scale factor along d where the *)
(* perpendicular to d in ctor *)
(* direction intersects d *)
let s = (l /. (norm (vminus c (smult d t)))) in
(* normalizing scale factor *)
(vplus
(smult (vminus c (smult d t)) s)
(smult d t))
| p1 :: p2 :: p3 :: [] ->
(* ------------------------------------------------------------ *)
(* The calculation for this case is as follows. Let *)
(* l = average(||p2-p1||,||p3-p2||,||p1-p3||). We seek the *)
(* point pt such that ||pt-pi|| = l, i=1,2,3; *)
(* pt lines on the line normal to the plane described by p1,p2, *)
(* p3 in the ctor direction. *)
(* ------------------------------------------------------------ *)
let c = (DimTable.find dimensionUnitTable ctor) in
let d = (vminus p3 p2) in
let e = (vminus p3 p1) in
let a1 = (dot c d) in
let b1 = (dot d d) in
let c1 = (dot e d) in
let a2 = (dot c e) in
let b2 = c1 in
let c2 = (dot e e) in
let u = (((b1*.a2) +. (b2*.a1))/.((b1*.c2)+.(b2*.c1))) in
let t = ((a1 -. (u*.c1))/.b1) in
let l = (((norm d) +. (norm e)) /. (2.0)) in
let r = (vplus (smult d t) (smult e u)) in
let v = (vminus c r) in
let w = (l /. (norm v)) in
(vplus (smult v w) r)
| ptlist ->
(* ------------------------------------------------------------ *)
(* i have realized that par's will hit this case. The way to *)
(* handle this is to calculate the barycenter of the points, *)
(* then drop a line from that point to the ctor *)
(* ------------------------------------------------------------ *)
let pc = (barycenter (Extremum( ptlist ))) in
(vplus (DimTable.find dimensionUnitTable ctor) pc))
| Solid s ->
(match s with
ConvexPolyhedra (kind,center,edgeLength) ->
(completeComplex (Extremum( [center] )) ctor)
| Sphere (center,radius) ->
(completeComplex (Extremum( [center] )) ctor))
| Complex( cplxs ) ->
let centers =
(List.map
(fun center -> (barycenter center))
cplxs) in
(completeComplex (Extremum( centers )) ctor)
let rec stringOfComplex cplx indentation =
match cplx with
Extremum( pts ) ->
(indentation
^ "Simplex"
^ "("
^ (List.fold_left
(fun acc pt ->
acc
^ "\n"
^ (indentation ^ " ")
^ (stringOfPoint pt))
""
pts)
^ "\n"
^ indentation
^ ")")
| Solid s ->
(indentation
^ "Solid"
^ "("
^ (match s with
ConvexPolyhedra (kind,center,edgeLength) ->
(match kind with
Tetrahedron -> "Tetrahedron"
| Cube -> "Cube"
| Octahedron -> "Octahedron"
| Dodecahedron -> "Dodecahedron"
| Icosohedron -> "Icosohedron")
^ "("
^ (stringOfPoint center)
^ ","
^ (string_of_float edgeLength)
^ ")"
| Sphere (center,radius) ->
"Sphere"
^ "("
^ (stringOfPoint center)
^ ","
^ (string_of_float radius)
^ ")")
^ ")"
^ "\n")
| Complex( cplxs ) ->
(indentation
^ "Complex"
^ "("
^ (List.fold_left
(fun acc cplx ->
acc
^ "\n"
^ (stringOfComplex cplx (indentation ^ " ")))
""
cplxs)
^ "\n"
^ indentation
^ ")")
and stringOfPoint pt =
("("
^ (string_of_float pt.x)
^ ","
^ (string_of_float pt.y)
^ ","
^ (string_of_float pt.z)
^ ","
^ (string_of_float pt.yaw)
^ ","
^ (string_of_float pt.pitch)
^ ","
^ (string_of_float pt.roll)
^ ")")
let jsonOfPt pt =
Object [ "x", Float pt.x;
"y", Float pt.y;
"z", Float pt.z;
"yaw", Float pt.yaw;
"pitch", Float pt.pitch;
"roll", Float pt.roll ]
let jsonOfSolid s =
(Object
(match s with
ConvexPolyhedra (kind,center,edgeLength) ->
(match kind with
Tetrahedron ->
["Kind", String "Tetrahedron";
"Center", (jsonOfPt center);
"Edge", Float edgeLength]
| Cube ->
["Kind", String "Cube";
"Center", (jsonOfPt center);
"Edge", Float edgeLength]
| Octahedron ->
["Kind", String "Octahedron";
"Center", (jsonOfPt center);
"Edge", Float edgeLength]
| Dodecahedron ->
["Kind", String "Dodecahedron";
"Center", (jsonOfPt center);
"Edge", Float edgeLength]
| Icosohedron ->
["Kind", String "Icosohedron";
"Center", (jsonOfPt center);
"Edge", Float edgeLength])
| Sphere (center,radius) ->
["Kind", String "Sphere";
"Center", (jsonOfPt center);
"Radius", Float radius]))
let jsonOfComplex cplx fn =
let rec jsonOfCplx cplx =
(match cplx with
Extremum( pts ) ->
Object
[ "Simplex", Array (List.map jsonOfPt pts) ]
| Solid s -> Object ["Solid", (jsonOfSolid s)]
| Complex( cplxs ) ->
let jplxs =
(List.map
(fun ccplx -> (jsonOfCplx ccplx))
cplxs) in
Object [ "Complex", Array (jplxs :> Json_type.json_type list) ]) in
let rslt = Json_io.save_json fn (jsonOfCplx cplx) in
rslt
end