cga/Graphics/HalfEdge.hs

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{-# OPTIONS_HADDOCK ignore-exports #-}
-- |This module provides methods to build a cyclic half-edge data structure
-- from an already parsed obj mesh file. As such, it depends on details
-- of the parsed data structures.
--
-- In particular, 'indirectHeFaces', 'indirectHeVerts' and 'indirectToDirect'
-- assume specific structure of some input lists. Check their respective
-- documentation.
--
-- As the data structure has a lot of cross-references and the knots are
-- not really known at compile-time, we have to use helper data structures
-- such as arrays, lists or vectors under the hood and tie the knots through
-- index lookups.
--
-- For an explanation of the abstract concept of the half-edge data structure,
-- check <http://www.flipcode.com/archives/The_Half-Edge_Data_Structure.shtml>
module Graphics.HalfEdge (
HeVert(..)
, HeFace(..)
, HeEdge(..)
, buildHeEdge
, buildHeEdgeFromStr
) where
import Algebra.Vector
import Control.Monad.ST
import Data.Array.Unboxed
import Data.Array.ST
import qualified Data.ByteString.Char8 as B
import Data.Functor
import Parser.Meshparser
import Safe
-- |The vertex data structure for the half-edge.
data HeVert a = HeVert {
vcoord :: a -- the coordinates of the vertex
, emedge :: HeEdge a -- one of the half-edges emanating from the vertex
}
-- |The face data structure for the half-edge.
data HeFace a = HeFace {
bordedge :: HeEdge a -- one of the half-edges bordering the face
}
-- |The actual half-edge data structure.
data HeEdge a = HeEdge {
startvert :: HeVert a -- start-vertex of the half-edge
, oppedge :: Maybe (HeEdge a) -- oppositely oriented adjacent half-edge
, edgeface :: HeFace a -- face the half-edge borders
, nextedge :: HeEdge a -- next half-edge around the face
}
-- This is a helper data structure of half-edge edges
-- for tying the knots in 'indirectToDirect'.
data IndirectHeEdge = IndirectHeEdge {
edgeindex :: Int -- edge index
, svindex :: Int -- index of start-vertice
, nvindex :: Int -- index of next-vertice
, indexf :: Int -- index of face
, offsetedge :: Int -- offset to get the next edge
}
-- This is a helper data structure of half-edge vertices
-- for tying the knots in 'indirectToDirect'.
data IndirectHeVert = IndirectHeVert {
emedgeindex :: Int -- emanating edge index (starts at 1)
, edgelist :: [Int] -- index of edge that points to this vertice
}
-- This is a helper data structure of half-edge faces
-- for tying the knots in 'indirectToDirect'.
data IndirectHeFace =
IndirectHeFace (Int, [Int]) -- (faceIndex, [verticeindex])
-- |Construct the indirect data structure for half-edge faces.
-- This function assumes that the input faces are parsed exactly like so:
--
-- @
-- f 1 3 4 5
-- f 4 6 1 3
-- @
--
-- becomes
--
-- > [[1,3,4,5],[4,6,1,3]]
indirectHeFaces :: [[Int]] -- ^ list of faces with their respective
-- list of vertice-indices
-> [IndirectHeFace]
indirectHeFaces = fmap IndirectHeFace . zip [0..]
-- |Construct the indirect data structure for half-edge edges.
indirectHeEdges :: [IndirectHeFace] -> [IndirectHeEdge]
indirectHeEdges = concat . fmap indirectHeEdge
where
indirectHeEdge :: IndirectHeFace -> [IndirectHeEdge]
indirectHeEdge (IndirectHeFace (_, [])) = []
indirectHeEdge p@(IndirectHeFace (_, pv@(v:_))) = go p 0
where
go (IndirectHeFace (_, [])) _
= []
-- connect last to first element
go (IndirectHeFace (fi, [vlast])) ei
= [IndirectHeEdge ei vlast v fi (negate $ length pv - 1)]
-- regular non-last element
go (IndirectHeFace (fi, vfirst:vnext:vrest)) ei
= (:) (IndirectHeEdge ei vfirst vnext fi 1)
(go (IndirectHeFace (fi, vnext:vrest)) (ei + 1))
-- |Construct the indirect data structure for half-edge vertices.
-- It is assumed that the list of points is indexed in order of their
-- appearance in the obj mesh file.
indirectHeVerts :: [a] -- ^ list of points
-> [IndirectHeEdge] -- ^ list of indirect edges
-> Array Int IndirectHeVert -- ^ output list, starts at index 1
indirectHeVerts pts hes'
= runSTArray $ do
arr <- newArray (1, length pts) (IndirectHeVert 0 [])
:: ST s (STArray s Int IndirectHeVert)
-- build the array
let go [] _ = return ()
go (IndirectHeEdge _ _ nv _ offset:hes) i
= do
(IndirectHeVert _ xs) <- readArray arr nv
writeArray arr nv (IndirectHeVert (i + offset) (i:xs))
go hes (i + 1)
go hes' 0
return arr
-- |Tie the knots!
-- It is assumed that the list of points is indexed in order of their
-- appearance in the obj mesh file.
-- TODO: make this function safe.
indirectToDirect :: [a] -- ^ list of points
-> [IndirectHeEdge]
-> [IndirectHeFace]
-> Array Int IndirectHeVert -- ^ assumed to start at index 1
-> HeEdge a
indirectToDirect pts pe@(e:_) fs vertarr
= thisEdge e
where
thisEdge (IndirectHeEdge ei sv _ fi off)
= HeEdge (thisVert (vertarr ! sv) sv)
(getOppEdge sv fi)
(thisFace (fs !! fi))
(thisEdge . (!!) pe $ (ei + off))
thisFace (IndirectHeFace (_, vi:_))
= HeFace (thisEdge (pe !! vi))
thisVert (IndirectHeVert eedg _) coordi
= HeVert (pts !! (coordi - 1))
(thisEdge (pe !! (eedg - 1)))
getOppEdge sv fi
= (\x -> thisEdge (pe !! x))
<$>
(headMay
. filter (\x -> (/=) fi . indexf $ (pe !! x))
. edgelist
$ (vertarr ! sv))
-- |Build the half-edge data structure from a list of points
-- and from a list of faces.
-- The points are assumed to have been parsed in order of their appearance
-- in the .obj mesh file, so that the indices match.
-- The faces are assumed to have been parsed in order of their appearance
-- in the .obj mesh file as follows:
--
-- @
-- f 1 3 4 5
-- f 4 6 1 3
-- @
--
-- becomes
--
-- > [[1,3,4,5],[4,6,1,3]]
buildHeEdge :: [a] -> [[Int]] -> Maybe (HeEdge a)
buildHeEdge [] _ = Nothing
buildHeEdge _ [] = Nothing
buildHeEdge pts fs
= let faces' = indirectHeFaces fs
edges' = indirectHeEdges faces'
verts' = indirectHeVerts pts edges'
in Just $ indirectToDirect pts edges' faces' verts'
-- |Build the HeEdge data structure from the .obj mesh file contents.
buildHeEdgeFromStr :: B.ByteString -- ^ contents of an .obj mesh file
-> Maybe (HeEdge PT)
buildHeEdgeFromStr bmesh =
let pts = meshVertices bmesh
fs = meshFaces bmesh
in buildHeEdge pts fs