{- |

Module : $Header$

Description : definition of the datatype describing

the abstract FreeCAD terms and and a few tools describing simple

mathematical operations on those building-blocks (3d vectors,

rotation matrices, rotation quaternions)

Copyright : (c) Robert Savu and Uni Bremen 2011

License : GPLv2 or higher, see LICENSE.txt

Maintainer : Robert.Savu@dfki.de

Stability : experimental

Portability : portable

Declaration of the abstract datatypes of FreeCAD terms

-}

--

--data structures for FreeCAD documents and objects

--

module FreeCAD.As

where

import qualified Data.Set as Set

data Vector3 = Vector3 { x::Double, y::Double, z::Double } deriving (Show, Eq, Ord)

--a vector in cartesian coordinates

data Matrix33 = Matrix33 { a11::Double ,a12::Double ,a13::Double

,a21::Double ,a22::Double ,a23::Double

,a31::Double ,a32::Double ,a33::Double

} deriving (Show, Eq, Ord) --used as a rotation matrix

data Vector4 = Vector4 { q0::Double, q1::Double, q2::Double, q3::Double}

deriving (Show, Eq, Ord)

-- quaternion rotational representation

data Placement = Placement { position::Vector3, orientation::Vector4 }

deriving (Show, Eq, Ord)

{-

-- | the placement is determined by 2 vectors:

-- the first one points to the 'center' of the objet in the space

-- the second one determines the orientation of the object in the given space

data Edgelist = []

| 1:Edgelist

| 0:Edgelist

-}

--reference from compound objects to 'building-blocks'

--objects made through strings or containment of the other

--objects

data BaseObject = Box Double Double Double -- Height, Width, Length

| Cylinder Double Double Double -- Angle, Height, Radius

| Sphere Double Double Double Double --Angle1,Angle2,Angle3,Radius

| Cone Double Double Double Double --Angle,Radius1,Radius2,Height

| Torus Double Double Double Double Double

--Angle1, Angle2, Angle3, Radius1, Radius2

| Line Double -- length

| Circle Double Double Double --StartAngle, EndAngle, Radius

| Rectangle Double Double --Height, Length

deriving (Show, Eq, Ord)

--TODO: Plane, Vertex, etc..

data Object = BaseObject BaseObject

| Cut ExtendedObject ExtendedObject

| Common ExtendedObject ExtendedObject

| Fusion ExtendedObject ExtendedObject

| Section ExtendedObject ExtendedObject

--section of an object (intersection with a plane

| Extrusion ExtendedObject Double --TODO

-- | Fillet, (Base::String, Edges::Edgelist, Radius::Double)),

--not enough data in the xml

-- | Chamfer, (Base::String, Edges::Edgelist, Amount::Double)),

--not enough data in the xml

-- | Mirror, (Base::String, Position2::Vector))

--mirroring of an object

deriving (Show, Eq, Ord)

data ExtendedObject = Placed PlacedObject | Ref String deriving (Show, Eq, Ord)

data PlacedObject = PlacedObject {p::Placement, o::Object} deriving (Show, Eq, Ord)

data NamedObject = NamedObject { name::String

, object:: PlacedObject}

| EmptyObject --for objects that are WIP

deriving (Show, Eq, Ord)

-- the first parameter is the name of the object as it is stored in the

-- FreeCAD document. the second parameter determines the placement of the object

-- (a pair of vectors) the third parameter contains the type of the object and

--a list of doubles (numbers) describing the characteristics

--of the object (e.g. dimensions, angles, etc)

type Document = [NamedObject]

-- | Datatype for FreeCAD Signatures

-- Signatures are just sets of named objects

data Sign = Sign { objects :: Set.Set NamedObject } deriving (Eq, Ord, Show)

distance3:: Vector3 -> Vector3 -> Double

distance3 (Vector3 ax ay az) (Vector3 bx by bz) = sqrt (x1*x1 + x2*x2 + x3*x3)

where

x1 = ax - bx

x2 = ay - by

x3 = az - bz

subtract3:: Vector3 -> Vector3 -> Vector3

subtract3 a b = Vector3 ex ey ez

where

ex = (x a) - (x b)

ey = (y a) - (y b)

ez = (z a) - (z b)

norm3:: Vector3 -> Double

norm3 a = distance3 a (Vector3 0 0 0)

scalarprod3:: Double -> Vector3 ->Vector3

scalarprod3 a (Vector3 bx by bz) = Vector3 abx aby abz

where

abx = a*bx

aby = a*by

abz = a*bz

median3:: [Vector3] -> Vector3

median3 a = scalarprod3 (fromIntegral (length a)) (v3Sum a)

v3Sum:: [Vector3] -> Vector3

v3Sum [a,b] = Vector3 xc yc zc

where

xc = (x a)*(x b)

yc = (y a)*(y b)

zc = (z a)*(z b)

v3Sum (a:b:as) = v3Sum (c:as)

where

xc = (x a)*(x b)

yc = (y a)*(y b)

zc = (z a)*(z b)

c = Vector3 xc yc zc

v3DotProd:: Vector3 -> Vector3 -> Double

v3DotProd v1 v2 = (x v1)*(x v2) + (y v1)*(y v2) + (z v1)*(z v2)

v4DotProd:: Vector4 -> Vector4 -> Double

v4DotProd v1 v2 = (q0 v1)*(q0 v2)+(q1 v1)*(q1 v2)+(q2 v1)*(q2 v2)+

(q3 v1)*(q3 v2)

v3VecProd:: Vector3 -> Vector3 -> Vector3

v3VecProd v1 v2 = Vector3 m n p

where

m = (y v1)*(z v2) - (z v1)*(y v2)

n = (z v1)*(x v2) - (x v1)*(z v2)

p = (x v1)*(y v2) - (y v1)*(x v2)

quatProd:: Vector4 -> Vector4 -> Vector4

quatProd v1 v2 = Vector4 m n p q

where

m = (q3 v2)*(q0 v1)+(q2 v2)*(q1 v1)-(q1 v2)*(q2 v1)+(q0 v2)*(q3 v1)

n = -(q2 v2)*(q0 v1)+(q3 v2)*(q1 v1)+(q0 v2)*(q2 v1)+(q1 v2)*(q3 v1)

p = (q1 v2)*(q0 v1)-(q0 v2)*(q1 v1)+(q3 v2)*(q2 v1)+(q2 v2)*(q3 v1)

q = -(q0 v2)*(q0 v1)-(q1 v2)*(q1 v1)-(q2 v2)*(q2 v1)+(q3 v2)*(q3 v1)

-- from quaternion to rotation matrix

quat2matrix:: Vector4 -> Matrix33

quat2matrix q = Matrix33 m11 m12 m13 m21 m22 m23 m31 m32 m33

where

m11 = (1 - 2*p2**2 - 2*p3**2)

m12 = (2*(p1*p2 - p3*p4))

m13 = (2*(p1*p3 + p2*p4))

m21 = (2*(p1*p2 + p3*p4))

m22 = (1 - 2*p1**2 - 2*p3**2)

m23 = (2*(p2*p3 - p1*p4))

m31 = (2*(p1*p3 - p2*p4))

m32 = (2*(p1*p4 + p2*p3))

m33 = (1 - 2*p1**2 - 2*p2**2)

p1 = q0 q

p2 = q1 q

p3 = q2 q

p4 = q3 q

rotate:: Matrix33 -> Vector3 -> Vector3

rotate a v = Vector3 xx yy zz

where

xx = (a11 a)*(x v) + (a12 a)*(y v) + (a13 a)*(z v)

yy = (a21 a)*(x v) + (a22 a)*(y v) + (a23 a)*(z v)

zz = (a31 a)*(x v) + (a32 a)*(y v) + (a33 a)*(z v)