cga/Graphics/HalfEdge.hs

241 lines
8.2 KiB
Haskell

{-# 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.
--
-- 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 lists and maps 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.Applicative
import Control.Monad
import qualified Data.ByteString.Char8 as B
import qualified Data.IntMap.Lazy as Map
import Data.Maybe
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
} | NoVert
-- |The face data structure for the half-edge.
data HeFace a = HeFace {
bordedge :: HeEdge a -- one of the half-edges bordering the face
} | NoFace
-- |The actual half-edge data structure.
data HeEdge a = HeEdge {
startvert :: HeVert a -- start-vertex of the half-edge
, oppedge :: HeEdge a -- oppositely oriented adjacent half-edge
, edgeface :: HeFace a -- face the half-edge borders
, nextedge :: HeEdge a -- next half-edge around the face
} | NoEdge
-- 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 :: [IndirectHeEdge] -- ^ list of indirect edges
-> Map.IntMap IndirectHeVert -- ^ output map, starts at index 1
indirectHeVerts hes' = go hes' Map.empty 0
where
go [] map' _ = map'
go (IndirectHeEdge _ _ nv _ offset:hes) map' i
= go hes
(Map.alter updateMap nv map')
(i + 1)
where
updateMap (Just (IndirectHeVert _ xs))
= Just (IndirectHeVert (i + offset) (i:xs))
updateMap Nothing
= Just (IndirectHeVert (i + offset) [i])
-- |Tie the knots!
-- It is assumed that the list of points is indexed in order of their
-- appearance in the obj mesh file.
--
-- pseudo-code:
--
-- @
-- indirectToDirect :: [a] -- parsed vertices, e.g. 2d points (Double, Double)
-- -> [IndirectHeEdge]
-- -> [IndirectHeFace]
-- -> [IndirectHeVert]
-- -> HeEdge a
-- indirectToDirect points edges faces vertices
-- = thisEdge (head edges)
-- where
-- thisEdge edge
-- = HeEdge (thisVert (vertices !! svindex edge) $ svindex edge)
-- (thisOppEdge (svindex edge) $ indexf edge)
-- (thisFace $ faces !! indexf edge)
-- (thisEdge $ edges !! (edgeindex edge + offsetedge edge))
-- thisFace face = HeFace $ thisEdge (edges !! (head . snd $ face))
-- thisVert vertice coordindex
-- = HeVert (points !! (coordindex - 1))
-- (thisEdge $ points !! (emedgeindex vertice - 1))
-- thisOppEdge startverticeindex faceindex
-- = case headMay
-- . filter ((/=) faceindex . indexf)
-- . fmap (edges !!)
-- . edgelist -- getter
-- $ vertices !! startverticeindex
-- of Just x -> thisEdge x
-- Nothing -> NoEdge
-- @
indirectToDirect :: [a] -- ^ list of points
-> [IndirectHeEdge]
-> [IndirectHeFace]
-> Map.IntMap IndirectHeVert -- ^ assumed to start at index 1
-> HeEdge a
indirectToDirect pts pe@(e:_) fs vertmap
= thisEdge e
where
thisEdge (IndirectHeEdge ei sv _ fi off)
= case (fs `atMay` fi, pe `atMay` (ei + off), Map.lookup sv vertmap) of
(Just face,
Just edge,
Just vert) -> HeEdge (thisVert vert sv)
(getOppEdge sv fi)
(thisFace face)
(thisEdge edge)
_ -> NoEdge
thisFace (IndirectHeFace (_, vi:_))
= case pe `atMay` vi of
Just edge -> HeFace (thisEdge edge)
Nothing -> NoFace
thisFace (IndirectHeFace _) = NoFace
thisVert (IndirectHeVert eedg _) coordi
= case (pts `atMay` (coordi - 1), pe `atMay` (eedg - 1)) of
(Just vert, Just edge) -> HeVert vert $ thisEdge edge
_ -> NoVert
getOppEdge sv fi
= case join
$ headMay
. filter ((/=) fi . indexf)
. catMaybes
. fmap (pe `atMay`)
. edgelist
<$> Map.lookup sv vertmap
of Just x -> thisEdge x
Nothing -> NoEdge
indirectToDirect _ _ _ _ = NoEdge
-- |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 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
-> HeEdge PT
buildHeEdgeFromStr bmesh =
let pts = meshVertices bmesh
faces' = indirectHeFaces . meshFaces $ bmesh
edges = indirectHeEdges faces'
verts = indirectHeVerts edges
in indirectToDirect pts edges faces' verts