From 8f66d83ed8b1a67eedf9fa47e1b609459b39d7ea Mon Sep 17 00:00:00 2001 From: Siddharth Bhat Date: Fri, 18 Aug 2023 09:37:17 -0700 Subject: [PATCH 1/2] wip: temp movement of files --- SciLean/Modules/DDG/SurfaceMesh.lean | 532 + data/bunny.off | 1504 ++ data/sphere_s3.off | 30724 +++++++++++++++++++++++++ examples/SurfaceMeshTests.lean | 46 + lakefile.lean | 4 + 5 files changed, 32810 insertions(+) create mode 100644 SciLean/Modules/DDG/SurfaceMesh.lean create mode 100644 data/bunny.off create mode 100644 data/sphere_s3.off create mode 100644 examples/SurfaceMeshTests.lean diff --git a/SciLean/Modules/DDG/SurfaceMesh.lean b/SciLean/Modules/DDG/SurfaceMesh.lean new file mode 100644 index 00000000..953f86da --- /dev/null +++ b/SciLean/Modules/DDG/SurfaceMesh.lean @@ -0,0 +1,532 @@ +/- +Copyright (c) 2023 Siddharth Bhat. All rights reserved. +Released under Apache 2.0 license as described in the file LICENSE. +Authors: Siddharth Bhat + +Surface Mesh based on discrete differential geometry. +https://github.com/GeometryCollective/geometry-processing-js/blob/c7ea47ae808979a5361e3fcd61bf921a194bf897/core/mesh.js#L3-L213 +-/ + +import SciLean.Core +import Lean.Data.HashMap + +open Lean Data + +-- abbrev V3 : Type := ℝ^{3} +-- 3D vector. +structure V3 where + x : Float + y : Float + z : Float + + +def V3.map (f: Float → Float) (v3 : V3) : V3 where + x := f v3.x + y := f v3.y + z := f v3.z + +/- index of vertices --/ +abbrev Index (_name : Name) := Nat +abbrev Index.invalid : Index α := 424242 +abbrev Index.ofNat {name : Name} (n : Nat) : Index name := n + +structure Vertex where + index : Index `Vertex := .invalid + halfedge : Index `Halfedge := .invalid +deriving Inhabited + +/-- Half edge data structure -/ +structure Halfedge where + index : Index `Halfedge := .invalid + next : Index `Halfedge := .invalid + prev : Index `Halfedge := .invalid + edge : Index `Edge := .invalid + twin : Option (Index `Halfedge) := .none + vertex : Index `Vertex := .invalid + face : Index `Face := .invalid + corner : Option (Index `Corner) := .none + onBoundary : Bool := false +deriving Inhabited + +structure Face where + index : Index `Face := .invalid + halfedge : Index `Halfedge := .invalid +deriving Inhabited + +structure Corner where + index : Index `Corner := .invalid + halfedge : Index `Halfedge := .invalid +deriving Inhabited + +structure Edge where + index : Index `Edge := .invalid + halfedge : Index `Halfedge := .invalid +deriving Inhabited + +structure Boundary where + face : (Index `Face) + -- gens : Array (Index `Halfedge) := #[] +deriving Inhabited + +/- + * @property {module:Core.Vertex[]} vertices The vertices contained in this mesh. + * @property {module:Core.Edge[]} edges The edges contained in this mesh. + * @property {module:Core.Face[]} faces The faces contained in this mesh. + * @property {module:Core.Corner[]} corners The corners contained in this mesh. + * @property {module:Core.Halfedge[]} halfedges The halfedges contained in this mesh. + * @property {module:Core.Face[]} boundaries The boundary loops contained in this mesh. + * @property {Array.} generators An array of halfedge arrays, i.e., + -/ +structure SurfaceMesh where + positions : Array V3 := {} + vertices : Array Vertex := {} + edges : Array Edge := {} + faces : Array Face := {} + corners : Array Corner := {} + halfedges : Array Halfedge := {} + boundaries : Array Boundary := {} + +instance : Inhabited SurfaceMesh where default := {} + + +/- +Computes the euler characteristic of this mesh. +-/ +def SurfaceMesh.eulerCharacteristic (s: SurfaceMesh) : Int := + (s.vertices.size : Int) - (s.edges.size : Int) + (s.faces.size : Int) + +-- # Monad to build surface meshes. +inductive MeshBuilderError +| nonManifoldEdge (i j : Index ``Vertex) +| parseError (err : String) +deriving Inhabited + +def MeshBuilderError.toString : MeshBuilderError → String +| nonManifoldEdge i j => s!"non-manifold edge {i} → {j}" +| parseError err => err + +instance : ToString MeshBuilderError where + toString := MeshBuilderError.toString + +abbrev MeshBuilderM (α : Type) := EStateM MeshBuilderError SurfaceMesh α + +-- ### Vertex accessors +def MeshBuilderM.newVertex : MeshBuilderM (Index ``Vertex) := + fun s => + let ix := s.vertices.size + let data : Vertex := {} + let data := { data with index := ix } + EStateM.Result.ok ix { s with vertices := s.vertices.push data } + +def MeshBuilderM.modifyVertex (ix : Index ``Vertex) + (fn : Vertex → Vertex) : MeshBuilderM Vertex := + fun s => + assert! (ix < s.vertices.size) + let out := fn s.vertices[ix]! + EStateM.Result.ok out { s with vertices := s.vertices.set! ix out } + +/- +def MeshBuilderM.getVertex (ix : Index ``Vertex) : MeshBuilderM Vertex := + MeshBuilderM.modifyVertex ix id + +def MeshBuilderM.setVertex (ix : Index ``Vertex) (v : Vertex) : MeshBuilderM Vertex := + MeshBuilderM.modifyVertex ix (fun _ => v) +-/ +-- ### Edge accessors +def MeshBuilderM.newEdge : MeshBuilderM (Index ``Edge) := + fun s => + let ix := s.edges.size + let data : Edge := {} + let data : Edge := { data with index := ix } + EStateM.Result.ok ix { s with edges := s.edges.push data } + +def MeshBuilderM.modifyEdge (ix : Index ``Edge) + (fn : Edge → Edge) : MeshBuilderM Edge := + fun s => + let out := fn s.edges[ix]! + EStateM.Result.ok out { s with edges := s.edges.set! ix out } + +def MeshBuilderM.modifyEdge_ (ix : Index ``Edge) + (fn : Edge → Edge) : MeshBuilderM Unit := do + let _ ← MeshBuilderM.modifyEdge ix fn + +def MeshBuilderM.getEdge (ix : Index ``Edge) : MeshBuilderM Edge := + MeshBuilderM.modifyEdge ix id + +def MeshBuilderM.setEdge (ix : Index ``Edge) (v : Edge) : MeshBuilderM Edge := + MeshBuilderM.modifyEdge ix (fun _ => v) + +-- ### Halfedge accessors +def MeshBuilderM.newHalfedge : MeshBuilderM (Index ``Halfedge) := + fun s => + let ix := s.halfedges.size + let data : Halfedge := { (default : Halfedge) with index := ix } + EStateM.Result.ok ix { s with halfedges := s.halfedges.push data } + +def MeshBuilderM.modifyHalfedge (ix : Index ``Halfedge) + (fn : Halfedge → Halfedge) : MeshBuilderM Halfedge := + fun s => + let out := fn s.halfedges[ix]! + EStateM.Result.ok out { s with halfedges := s.halfedges.set! ix out } + +def MeshBuilderM.modifyHalfedge_ (ix : Index ``Halfedge) + (fn : Halfedge → Halfedge) : MeshBuilderM Unit := do + let _ ← MeshBuilderM.modifyHalfedge ix fn + +def MeshBuilderM.getHalfedge (ix : Index ``Halfedge) : MeshBuilderM Halfedge := + MeshBuilderM.modifyHalfedge ix id + +def MeshBuilderM.setHalfedge (ix : Index ``Halfedge) (v : Halfedge) : MeshBuilderM Halfedge := + MeshBuilderM.modifyHalfedge ix (fun _ => v) + +def MeshBuilderM.modifyBoundaries (f : Array Boundary → Array Boundary) : MeshBuilderM Unit := + modify (fun s => { s with boundaries := f s.boundaries }) + +-- ### Face accessors +-- TODO: return the face +def MeshBuilderM.newFace : MeshBuilderM (Index ``Face) := + fun s => + let ix := s.faces.size + let data : Face := {} + let data := { data with index := ix } + EStateM.Result.ok ix { s with faces := s.faces.push data } + +-- TODO: modify anything with the typeclass [IsPointerTo ``Face]. +def MeshBuilderM.modifyFace (ix : Index ``Face) + (fn : Face → Face) : MeshBuilderM Face := + fun s => + let out := fn s.faces[ix]! + EStateM.Result.ok out { s with faces := s.faces.set! ix out } + +def MeshBuilderM.modifyFace_ (ix : Index ``Face) + (fn : Face → Face) : MeshBuilderM Unit := do + let _ ← MeshBuilderM.modifyFace ix fn + +def MeshBuilderM.getFace (ix : Index ``Face) : MeshBuilderM Face := + MeshBuilderM.modifyFace ix id + +def MeshBuilderM.setFace (ix : Index ``Face) (v : Face) : MeshBuilderM Face := + MeshBuilderM.modifyFace ix (fun _ => v) + +-- ### Corner accessors +def MeshBuilderM.newCorner : MeshBuilderM (Index ``Corner) := + fun s => + let ix := s.corners.size + let data : Corner := {} + let data := { data with index := ix } + EStateM.Result.ok ix { s with corners := s.corners.push data } + +-- TODO: modify anything with the typeclass [IsPointerTo ``Corner]. +def MeshBuilderM.modifyCorner (ix : Index ``Corner) + (fn : Corner → Corner) : MeshBuilderM Corner := + fun s => + let out := fn s.corners[ix]! + EStateM.Result.ok out { s with corners := s.corners.set! ix out } + +def MeshBuilderM.modifyCorner_ (ix : Index ``Corner) + (fn : Corner → Corner) : MeshBuilderM Unit := do + let _ ← MeshBuilderM.modifyCorner ix fn + +def MeshBuilderM.getCorner (ix : Index ``Corner) : MeshBuilderM Corner := + MeshBuilderM.modifyCorner ix id + +def MeshBuilderM.setCorner (ix : Index ``Corner) (v : Corner) : MeshBuilderM Corner := + MeshBuilderM.modifyCorner ix (fun _ => v) + + + + +/- +* Constructs this mesh. +* @method module:Core.Mesh#build +* @param {Object} polygonSoup A polygon soup mesh containing vertex positions and indices. +* @param {module:LinearAlgebra.Vector[]} polygonSoup.v The vertex positions of the polygon soup mesh. +* @param {number[]} polygonSoup.f The indices of the polygon soup mesh. +* @returns {boolean} True if this mesh is constructed successfully and false if not +* (when this mesh contains any one or a combination of the following - non-manifold vertices, +* non-manifold edges, isolated vertices, isolated faces). + +indices: indexes of triangles, where a triangle is a contingous sequence of 3 indexes, of the vertices + of the triangle. +-/ + +partial def MeshBuilderM.makeBoundary + (start : Halfedge) + (boundaryCycle : Array (Index ``Halfedge)) + (he : Halfedge) : MeshBuilderM Unit := do + let bhIx ← newHalfedge + let boundaryCycle := boundaryCycle.push bhIx + + -- create new face + let fIx ← newFace + -- TODO: check if this notion of boundary is correct? + modifyBoundaries fun boundaries => boundaries.push { face := fIx : Boundary } + + + -- grab the next halfedge along the boundary that does not have a twin halfedge + let mut nextHe := he + while nextHe.twin.isSome do { + nextHe ← getHalfedge (← getHalfedge nextHe.twin.get!).next + } + + + -- Set the current halfedge's attributes + modifyHalfedge_ bhIx (fun h => { h with vertex := nextHe.index }) + modifyHalfedge_ bhIx (fun h => { h with edge := nextHe.edge }) + modifyHalfedge_ bhIx (fun h => { h with onBoundary := true }) + + -- point the new halfedge and face to each other + modifyHalfedge_ bhIx (fun h => { h with face := fIx }) + modifyFace_ fIx (fun f => { f with halfedge := bhIx }) + + -- point the new halfedge and he to each other + modifyHalfedge_ bhIx (fun h => { h with twin := he.index }) + modifyHalfedge_ bhIx (fun h => { h with twin := he.index }) + -- TODO: allow the `modifyHalfedge_` to take a typeclass called `IsHalfedgeIndex`. + modifyHalfedge_ he.index (fun h => { h with twin := he.index }) + + -- continue walk + let he := nextHe; + if he.index == start.index + then return + else makeBoundary start boundaryCycle he + + +partial def MeshBuilderM.assertNoIsolatedVertices : MeshBuilderM Unit := return () +partial def MeshBuilderM.assertNoIsolatedFaces : MeshBuilderM Unit := return () +partial def MeshBuilderM.assertNoNonManifoldVertices : MeshBuilderM Unit := return () + +partial def MeshBuilderM.build_ + (positions : Array V3) (indices : Array (Index ``Vertex)) : MeshBuilderM Unit := do { + let mut existingHalfedges : + HashMap (Index `Vertex × Index `Vertex) (Index `Halfedge) := {}; + let mut edgeCount : + HashMap (Index `Vertex × Index `Vertex) Nat := {}; + modify (fun s => { s with positions := positions }); -- store positions in the SurfaceMesh + + -- pre-allocate all vertices for random access via faces. + for _ in List.range positions.size do { + let _ ← newVertex; + } + assert! (indices.size % 3 == 0); + for i in List.range (indices.size / 3) do { + let I := i * 3; + let f ← newFace; + -- create a halfedge for each edge of the newly created face + for _ in List.range 3 do { + let _ ← newHalfedge; -- make the new half edges + } + for J in List.range 3 do { + -- current halfedge goes from vertex i to vertex j + let K : Nat := (J + 1) % 3; + let i := I + J; + let j := I + K; + -- set the current halfedge's attributes + let _ ← modifyHalfedge_ i (fun he => { he with next := j }); + let _ ← modifyHalfedge_ i (fun he => { he with prev := I + (J + 3 - 1) % 3 }); + let _ ← modifyHalfedge_ i (fun he => { he with onBoundary := false }); + -- hasTwinHalfedge.set(h, false); + + -- point the new halfedge and vertex i to each other + assert! (i < indices.size); + let _ ← modifyHalfedge i (fun he => { he with vertex := indices[i]! }); + let _ ← modifyVertex indices[i]! (fun v => { v with halfedge := i }); + + -- point the new halfedge and face to each other + let _ ← modifyHalfedge i (fun he => { he with face := f }); + let _ ← modifyFace f (fun f => { f with halfedge := i }); + + -- swap if (i > j) to maintain invariant that (i <= j) + let edgeKey := + let vi := indices[i]!; + let vj := indices[j]! + if vi <= vj then (vi, vj) else (vj, vi); + dbg_trace s!"adding edge {edgeKey}..." + assert! edgeKey.fst <= edgeKey.snd + let hIx := I + J; -- TODO: cleanup + let oldEdgeCount := edgeCount.findD edgeKey 0; + match existingHalfedges.find? edgeKey with + | .some twin' => { + dbg_trace s!"edge {edgeKey} exists with twin {twin'}" + -- if a halfedge between vertex i and j has been + -- created in the past, then it is the twin halfedge + -- of the current halfedge + let _ ← modifyHalfedge_ hIx (fun h => { h with twin := twin' }); + let _ ← modifyHalfedge_ twin' (fun twin => { twin with twin := hIx }); + let twinEdge ← getHalfedge twin'; + let _ ← modifyHalfedge_ hIx (fun h => { h with edge := twinEdge.edge }); + edgeCount := edgeCount.insert edgeKey (oldEdgeCount + 1); + } + | .none => { + let e ← newEdge; + dbg_trace s!"edge {edgeKey} does not exist. Made edge {e}" + let _ ← modifyEdge e (fun e => { e with halfedge := hIx }); + let _ ← modifyHalfedge_ hIx (fun h => { h with edge := e }); + edgeCount := edgeCount.insert edgeKey 1; + }; + -- record the newly created edge and halfedge from vertex i to j + existingHalfedges := existingHalfedges.insert edgeKey hIx; + + if edgeCount.findD edgeKey 0 > 2 then { + throw <| MeshBuilderError.nonManifoldEdge i j; + } + } + } + dbg_trace "creating imaginary halfedges"; -- TODO: move traces into a separate file. + -- create and insert boundary halfedges and "imaginary" faces for boundary cycles + -- also create and insert corners. + -- Note that every vertex corresponds to the halfedge from that vertex to + -- the next one in the triangle. + for i in List.range indices.size do { + dbg_trace s!"getting halfedge {i}" + let h ← getHalfedge i; + -- If a halfedge has no twin halfedge, create a new face and + -- link it the corresponding boundary cycle + -- TODO: move this function into the function. + if h.twin.isNone then { + MeshBuilderM.makeBoundary h #[] h + } + -- point the newly created corner and its halfedge to each other + -- TODO: think about the maths here. + if ! (← getHalfedge i).onBoundary then { + let cIx ← newCorner; + dbg_trace "new corner"; + let _ ← modifyCorner cIx (fun c => { c with halfedge := h.index }); + let _ ← modifyHalfedge h.index (fun h => { h with corner := cIx }); + } + let _ ← assertNoIsolatedVertices; + let _ ← assertNoIsolatedFaces; + let _ ← assertNoNonManifoldVertices; + } +} +def MeshBuilderM.run (mb : MeshBuilderM Unit) : Except MeshBuilderError SurfaceMesh := + let emptySurfaceMesh : SurfaceMesh := {} + match EStateM.run mb emptySurfaceMesh with + | .ok () surfaceMesh => .ok surfaceMesh + | .error err _ => .error err + + +def SurfaceMesh.build (positions: Array V3) (indices: Array (Index ``Vertex)) : + Except MeshBuilderError SurfaceMesh := + (MeshBuilderM.build_ positions indices).run + +def SurfaceMesh.build' (positions: Array V3) (indices: Array (Index ``Vertex)) : + Option SurfaceMesh := + (build positions indices).toOption + +def SurfaceMesh.build! (positions: Array V3) (indices: Array (Index ``Vertex)) : + SurfaceMesh := (build' positions indices).get! + +/- +-- TODO: figure out code organization for widgets. +@[widget_module] +def Mesh : Component SurfaceMesh where + javascript := include_str "../build" / "js" / "mesh.js" +-/ + +/- Random mesh generation -/ + +/-- Generate a random floating point number in [0, 1] -/ +def randFloat01 [G : RandomGen γ] (gen : γ) : Float × γ := Id.run do + let (val, gen) := G.next gen + let (lo, hi) := G.range gen + return ((Float.ofNat <| val - lo) / (Float.ofNat <| hi - lo), gen) + +/-- Create a random vertex with coordinates sampled from uniform [0, 1] -/ +def randVertex01 [RandomGen γ] (gen : γ) : V3 × γ := Id.run do + let (val1, gen) := randFloat01 gen + let (val2, gen) := randFloat01 gen + let (val3, gen) := randFloat01 gen + return ({ x := val1, y := val2, z := val3 }, gen) + + +/-- Create `nvertices` random vertices with coordinates sampled from [-scale/2, scale/2] -/ +def randVertices [RandomGen γ] + (gen : γ) (nvertices : Nat) (scale : Float := 10) : (Array V3) × γ := Id.run do + let mut out : Array V3 := #[] + let mut gen := gen + for _ in List.range nvertices do + let (vertex, gen') := randVertex01 gen; gen := gen' + let vertex : V3 := vertex.map (fun coord => (coord - 0.5) * scale) + out := out.push vertex + return (out, gen) + + +/-- Create a random triangle face with three random vertices with indexes `[0..nvertices)` -/ +def randTriFace [RandomGen γ] (gen : γ) (nvertices : Nat) : (Array Nat) × γ := Id.run do + let (v1, gen) := randNat gen 0 (nvertices-1); + let (v2, gen) := randNat gen 0 (nvertices-1); + let (v3, gen) := randNat gen 0 (nvertices-1); + return (#[v1, v2, v3], gen) + +/-- Create a random mesh with `nfaces` random faces. Each face is generated by `randTriFace` -/ +def randTriFaces [RandomGen γ] (gen : γ) (nvertices : Nat) (nfaces : Nat) : (Array Nat) × γ := Id.run do + let mut out : Array Nat := #[] + let mut gen := gen + for _ in List.range nfaces do + let (face, gen') := randTriFace gen nvertices; gen := gen' + out := out.append face + return (out, gen) + +/-- Create a random mesh with `nvertices` vertices and `nfaces` faces -/ +def SurfaceMesh.rand [RandomGen γ] (gen : γ) (nvertices : Nat) (nfaces : Nat) : + (Except MeshBuilderError SurfaceMesh) × γ := Id.run do + let (vs, gen) := randVertices gen nvertices + let (fs, gen) := randTriFaces gen nvertices nfaces + return (SurfaceMesh.build vs fs, gen) + + +/-- Coerce a list of reals into a vector. Throws a ParseError if length of list is not 3 -/ +def V3.ofList : List Float → MeshBuilderM V3 +| [x, y, z] => pure { x := x, y := y, z := z } +| xs => throw <| MeshBuilderError.parseError s!"unable to convert list to vertex '{xs}'" + +def V3.ofArray : Array Float → MeshBuilderM V3 := + V3.ofList ∘ Array.toList + +/-- Load the mesh data from a .OFF format string -/ +def SurfaceMesh.fromOFFString (lines : Array String) : MeshBuilderM Unit := do + let mut vertices : Array V3 := #[] + let mut faces : Array Nat := #[] + let mut i := 0 + if lines[i]!.trim != "OFF" + then throw <| MeshBuilderError.parseError s!"expected 'OFF' on line {i+1}. but found '{lines[i]!}' which is not .OFF" + i := i + 1 + + let [n_vertices, n_faces, _n_edges] := lines[i]!.trim.splitOn " " + | throw <| MeshBuilderError.parseError s!"expected number of vertices, faces, edges information on line {i+1}, but found '{lines[i]!}'" + i := i + 1 + + let .some n_vertices := n_vertices.toNat? + | throw <| MeshBuilderError.parseError s! "unable to parse num vertices {n_vertices}" + + let .some n_faces := n_faces.toNat? + | throw <| MeshBuilderError.parseError s! "unable to parse num faces {n_faces}" + + for _ in List.range n_vertices do + let coords_raw := lines[i]!.trim.splitOn " " + let mut v : Array Float := #[] + for coord in coords_raw do + let .ok coord := Lean.Json.Parser.num |>.run coord + | throw <| MeshBuilderError.parseError s!"unable to parse vertex coordinate {coord} on line {i+1}" + v := v.push coord.toFloat + vertices := vertices.push (← V3.ofArray v) + i := i + 1 + + for _ in List.range n_faces do + let face_indexes_raw := lines[i]!.trim.splitOn " " + let mut f : Array Nat := #[] + for ix in face_indexes_raw.drop 1 do + let .some ix := ix.toNat? + | throw <| MeshBuilderError.parseError s!"unable to parse face index {ix} on line {i+1}" + f := f.push ix + faces := faces.append f + i := i + 1 + MeshBuilderM.build_ vertices faces + +def SurfaceMesh.fromOFFFile (p : System.FilePath) : IO SurfaceMesh := do + let out : Except MeshBuilderError SurfaceMesh := + (SurfaceMesh.fromOFFString (← IO.FS.lines p)).run + match out with + | .ok out => return out + | .error err => throw <| .userError err.toString diff --git a/data/bunny.off b/data/bunny.off new file mode 100644 index 00000000..fd48298b --- /dev/null +++ b/data/bunny.off @@ -0,0 +1,1504 @@ +OFF +502 1000 0 +-91.9244 -22.1071 148.532 +-4.60061 -47.358 45.4858 +-42.8484 -5.62622 163.042 +-71.6792 -1.88642 156.035 +-21.991 -53.3567 45.6468 +8.63638 -45.3538 43.4033 +-50.9593 -44.114 44.8077 +-60.1358 -41.4667 46.5695 +-0.660407 -54.2028 51.854 +-44.2577 -40.0079 48.0064 +33.348 -31.2043 48.2996 +-43.0682 -16.1079 128.272 +-40.0136 -39.6499 53.5226 +-1.83925 -54.3832 58.0615 +-28.5259 2.9786 123.45 +10.9935 -34.2413 123.287 +-32.8686 1.9463 174.164 +-78.2609 -46.0529 143.478 +3.76681 -56.8138 62.0817 +-37.6498 -41.9943 64.4778 +-87.1111 1.74734 121.229 +18.0676 -39.3655 109.816 +-9.97993 -55.9118 61.502 +-2.57472 -56.7602 65.4523 +9.36285 -54.132 62.9993 +-21.3382 21.3463 182.357 +-14.8568 -54.0211 66.6781 +-80.0937 -53.4367 127.986 +-27.9502 -38.1966 66.532 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6400 2481 10081 +3 10210 10081 11 diff --git a/examples/SurfaceMeshTests.lean b/examples/SurfaceMeshTests.lean new file mode 100644 index 00000000..8f9ff105 --- /dev/null +++ b/examples/SurfaceMeshTests.lean @@ -0,0 +1,46 @@ +import SciLean.Modules.DDG.SurfaceMesh + +def testTetrahedron : IO Bool := do + let base0 : V3 := V3.mk 0 0 0 + let base1 : V3 := V3.mk 2 0 0 + let base2 : V3 := V3.mk 1 1 0 + let apex : V3 := V3.mk 0 0 1 + let indices : Array (Index ``Vertex) := #[] + let indices := indices.append #[0, 1, 2] -- base + let indices := indices.append #[0, 1, 3] -- (0, 1) to apex tri + let indices := indices.append #[0, 2, 3] -- ditto + let indices := indices.append #[1, 2, 3] -- ditto + let mesh ← match SurfaceMesh.build #[base0, base1, base2, apex] indices with + | .error err => IO.println s!"ERROR: {err}"; return false + | .ok mesh => pure mesh + IO.println s!"tetrahedron #vertices: {mesh.vertices.size}" + IO.println s!"tetrahedron #edges: {mesh.edges.size}" + IO.println s!"tetrahedron #faces: {mesh.faces.size}" + assert! mesh.eulerCharacteristic == 2 + return true + +def testSphere : IO Bool := do + let sphereData ← SurfaceMesh.fromOFFFile "data/sphere_s3.off" -- load mesh + IO.println s!"sphere #vertices: {sphereData.vertices.size}" + IO.println s!"sphere #edges: {sphereData.edges.size}" + IO.println s!"sphere #faces: {sphereData.faces.size}" + assert! sphereData.eulerCharacteristic == 2 -- homeomorphic to a sphere. + return True + +def testBunny : IO Bool := do + let bunnyData ← SurfaceMesh.fromOFFFile "data/bunny.off" -- load mesh + IO.println s!"bunny #vertices: {bunnyData.vertices.size}" + IO.println s!"bunny #edges: {bunnyData.edges.size}" + IO.println s!"bunny #faces: {bunnyData.faces.size}" + assert! bunnyData.eulerCharacteristic == 2 -- homeomorphic to a sphere. + return True + +def main := do + let ret ← testTetrahedron + assert! ret + + let ret ← testSphere + assert! ret + + let ret ← testBunny + assert! ret diff --git a/lakefile.lean b/lakefile.lean index 7cc22482..38f48099 100644 --- a/lakefile.lean +++ b/lakefile.lean @@ -32,6 +32,10 @@ lean_exe ForLoopTest { root := `tests.sum_speed_test } +lean_exe SurfaceMeshTests { + root := `examples.SurfaceMeshTests +} + meta if get_config? doc = some "dev" then -- do not download and build doc-gen4 by default require «doc-gen4» from git "https://github.com/leanprover/doc-gen4" @ "master" From 442f40e19cb6c4c2120c712b6505b9f2745022fa Mon Sep 17 00:00:00 2001 From: Siddharth Bhat Date: Fri, 18 Aug 2023 13:24:17 -0700 Subject: [PATCH 2/2] make tests pass --- SciLean/Data/DataArray/VecN.lean | 80 +++++++++++++++------------- SciLean/Modules/DDG/SurfaceMesh.lean | 49 ++++++----------- SciLean/Modules/DDG/Trace.lean | 15 ++++++ examples/SurfaceMeshTests.lean | 8 +-- 4 files changed, 79 insertions(+), 73 deletions(-) create mode 100644 SciLean/Modules/DDG/Trace.lean diff --git a/SciLean/Data/DataArray/VecN.lean b/SciLean/Data/DataArray/VecN.lean index ac37fbc6..cba9f995 100644 --- a/SciLean/Data/DataArray/VecN.lean +++ b/SciLean/Data/DataArray/VecN.lean @@ -2,11 +2,11 @@ import SciLean.Data.DataArray.DataArray namespace SciLean -structure Vec2 (α : Type) where +structure Vec2 (α : Type) where (x y : α) -namespace Vec2 +namespace Vec2 def get (v : Vec2 α) (i : Idx 2) : α := if i.1 = 0 then @@ -19,7 +19,7 @@ namespace Vec2 ⟨vi, v.y⟩ else ⟨v.x, vi⟩ - + def intro (f : Idx 2 → α) : Vec2 α := ⟨f 0, f 1⟩ instance : GetElem (Vec2 α) (Idx 2) α (λ _ _ => True) where @@ -38,16 +38,16 @@ namespace Vec2 getElem_introElem := sorry_proof instance [ba : PlainDataType α] : PlainDataType (Vec2 α) where - btype := + btype := match ba.btype with - | .inl bitType => + | .inl bitType => if h : 2 * bitType.bits ≤ 8 then .inl { bits := 2 * bitType.bits h_size := h fromByte := fun b => let ones : UInt8 := 255 - let mask := (ones - (ones <<< bitType.bits)) -- 00000111 + let mask := (ones - (ones <<< bitType.bits)) -- 00000111 { x := bitType.fromByte (b &&& mask) y := bitType.fromByte ((b >>> bitType.bits) &&& mask) @@ -62,7 +62,7 @@ namespace Vec2 .inr { bytes := 2 h_size := sorry_proof - fromByteArray := fun b i _ => + fromByteArray := fun b i _ => { x := bitType.fromByte (b.uget i sorry_proof) y := bitType.fromByte (b.uget (i+1) sorry_proof) @@ -76,19 +76,19 @@ namespace Vec2 fromByteArray_toByteArray := sorry_proof fromByteArray_toByteArray_other := sorry_proof } - | .inr byteType => + | .inr byteType => .inr { bytes := 2 * byteType.bytes h_size := sorry_proof fromByteArray := fun b i _ => { - x := byteType.fromByteArray b i sorry_proof + x := byteType.fromByteArray b i sorry_proof y := byteType.fromByteArray b (i + byteType.bytes) sorry_proof } toByteArray := fun b i _ v => Id.run do let mut b := b - b := byteType.toByteArray b i sorry_proof v.x - b := byteType.toByteArray b (i + byteType.bytes) sorry_proof v.y + b := byteType.toByteArray b i sorry_proof v.x + b := byteType.toByteArray b (i + byteType.bytes) sorry_proof v.y b toByteArray_size := sorry_proof fromByteArray_toByteArray := sorry_proof @@ -99,11 +99,20 @@ namespace Vec2 end Vec2 -structure Vec3 (α : Type) where +structure Vec3 (α : Type) where (x y z : α) -namespace Vec3 +namespace Vec3 + def ofArray [Inhabited α] (xs : Array α) : Vec3 α where + x := xs.get! 0 + y := xs.get! 1 + z := xs.get! 2 + + def map (f : α → β) (v : Vec3 α) : Vec3 β where + x := f v.x + y := f v.y + z := f v.z def get (v : Vec3 α) (i : Idx 3) : α := if i.1 = 0 then @@ -120,7 +129,7 @@ namespace Vec3 ⟨v.x, vi, v.z⟩ else ⟨v.x, v.y, vi⟩ - + def intro (f : Idx 3 → α) : Vec3 α := ⟨f 0, f 1, f 2⟩ instance : GetElem (Vec3 α) (Idx 3) α (λ _ _ => True) where @@ -139,16 +148,16 @@ namespace Vec3 getElem_introElem := sorry_proof instance [ba : PlainDataType α] : PlainDataType (Vec3 α) where - btype := + btype := match ba.btype with - | .inl bitType => + | .inl bitType => if h : 3 * bitType.bits ≤ 8 then .inl { bits := 3 * bitType.bits h_size := h fromByte := fun b => let ones : UInt8 := 255 - let mask := (ones - (ones <<< bitType.bits)) -- 00000111 + let mask := (ones - (ones <<< bitType.bits)) -- 00000111 { x := bitType.fromByte (b &&& mask) y := bitType.fromByte ((b >>> bitType.bits) &&& mask) @@ -165,7 +174,7 @@ namespace Vec3 .inr { bytes := 3 h_size := sorry_proof - fromByteArray := fun b i _ => + fromByteArray := fun b i _ => { x := bitType.fromByte (b.uget i sorry_proof) y := bitType.fromByte (b.uget (i+1) sorry_proof) @@ -181,21 +190,21 @@ namespace Vec3 fromByteArray_toByteArray := sorry_proof fromByteArray_toByteArray_other := sorry_proof } - | .inr byteType => + | .inr byteType => .inr { bytes := 3 * byteType.bytes h_size := sorry_proof fromByteArray := fun b i _ => { - x := byteType.fromByteArray b i sorry_proof + x := byteType.fromByteArray b i sorry_proof y := byteType.fromByteArray b (i + byteType.bytes) sorry_proof z := byteType.fromByteArray b (i + 2 * byteType.bytes) sorry_proof } toByteArray := fun b i _ v => Id.run do let mut b := b - b := byteType.toByteArray b i sorry_proof v.x - b := byteType.toByteArray b (i + byteType.bytes) sorry_proof v.y - b := byteType.toByteArray b (i + 2 * byteType.bytes) sorry_proof v.z + b := byteType.toByteArray b i sorry_proof v.x + b := byteType.toByteArray b (i + byteType.bytes) sorry_proof v.y + b := byteType.toByteArray b (i + 2 * byteType.bytes) sorry_proof v.z b toByteArray_size := sorry_proof fromByteArray_toByteArray := sorry_proof @@ -205,10 +214,10 @@ namespace Vec3 end Vec3 -structure Vec4 (α : Type) where +structure Vec4 (α : Type) where (x y z w : α) -namespace Vec4 +namespace Vec4 def get (v : Vec4 α) (i : Idx 4) : α := if i = 0 then @@ -229,7 +238,7 @@ namespace Vec4 ⟨v.x, v.y, vi, v.w⟩ else ⟨v.x, v.y, v.z, vi⟩ - + def intro (f : Idx 4 → α) : Vec4 α := ⟨f 0, f 1, f 2, f 3⟩ instance : GetElem (Vec4 α) (Idx 4) α (λ _ _ => True) where @@ -248,16 +257,16 @@ namespace Vec4 getElem_introElem := sorry_proof instance [ba : PlainDataType α] : PlainDataType (Vec4 α) where - btype := + btype := match ba.btype with - | .inl bitType => + | .inl bitType => if h : 4 * bitType.bits ≤ 8 then .inl { bits := 4 * bitType.bits h_size := h fromByte := fun b => let ones : UInt8 := 255 - let mask := (ones - (ones <<< bitType.bits)) -- 00000111 + let mask := (ones - (ones <<< bitType.bits)) -- 00000111 { x := bitType.fromByte (b &&& mask) y := bitType.fromByte ((b >>> bitType.bits) &&& mask) @@ -276,7 +285,7 @@ namespace Vec4 .inr { bytes := 4 h_size := sorry_proof - fromByteArray := fun b i _ => + fromByteArray := fun b i _ => { x := bitType.fromByte (b.uget i sorry_proof) y := bitType.fromByte (b.uget (i+1) sorry_proof) @@ -294,26 +303,25 @@ namespace Vec4 fromByteArray_toByteArray := sorry_proof fromByteArray_toByteArray_other := sorry_proof } - | .inr byteType => + | .inr byteType => .inr { bytes := 3 * byteType.bytes h_size := sorry_proof fromByteArray := fun b i _ => { - x := byteType.fromByteArray b i sorry_proof + x := byteType.fromByteArray b i sorry_proof y := byteType.fromByteArray b (i + byteType.bytes) sorry_proof z := byteType.fromByteArray b (i + 2 * byteType.bytes) sorry_proof w := byteType.fromByteArray b (i + 3 * byteType.bytes) sorry_proof } toByteArray := fun b i _ v => Id.run do let mut b := b - b := byteType.toByteArray b i sorry_proof v.x - b := byteType.toByteArray b (i + byteType.bytes) sorry_proof v.y - b := byteType.toByteArray b (i + 2 * byteType.bytes) sorry_proof v.z + b := byteType.toByteArray b i sorry_proof v.x + b := byteType.toByteArray b (i + byteType.bytes) sorry_proof v.y + b := byteType.toByteArray b (i + 2 * byteType.bytes) sorry_proof v.z b := byteType.toByteArray b (i + 3 * byteType.bytes) sorry_proof v.w b toByteArray_size := sorry_proof fromByteArray_toByteArray := sorry_proof fromByteArray_toByteArray_other := sorry_proof } - diff --git a/SciLean/Modules/DDG/SurfaceMesh.lean b/SciLean/Modules/DDG/SurfaceMesh.lean index 953f86da..058e3075 100644 --- a/SciLean/Modules/DDG/SurfaceMesh.lean +++ b/SciLean/Modules/DDG/SurfaceMesh.lean @@ -8,22 +8,11 @@ https://github.com/GeometryCollective/geometry-processing-js/blob/c7ea47ae808979 -/ import SciLean.Core +import SciLean.Data.DataArray.VecN import Lean.Data.HashMap open Lean Data --- abbrev V3 : Type := ℝ^{3} --- 3D vector. -structure V3 where - x : Float - y : Float - z : Float - - -def V3.map (f: Float → Float) (v3 : V3) : V3 where - x := f v3.x - y := f v3.y - z := f v3.z /- index of vertices --/ abbrev Index (_name : Name) := Nat @@ -78,7 +67,7 @@ deriving Inhabited * @property {Array.} generators An array of halfedge arrays, i.e., -/ structure SurfaceMesh where - positions : Array V3 := {} + positions : Array (SciLean.Vec3 Float) := {} vertices : Array Vertex := {} edges : Array Edge := {} faces : Array Face := {} @@ -297,7 +286,7 @@ partial def MeshBuilderM.assertNoIsolatedFaces : MeshBuilderM Unit := return () partial def MeshBuilderM.assertNoNonManifoldVertices : MeshBuilderM Unit := return () partial def MeshBuilderM.build_ - (positions : Array V3) (indices : Array (Index ``Vertex)) : MeshBuilderM Unit := do { + (positions : Array (SciLean.Vec3 Float)) (indices : Array (Index ``Vertex)) : MeshBuilderM Unit := do { let mut existingHalfedges : HashMap (Index `Vertex × Index `Vertex) (Index `Halfedge) := {}; let mut edgeCount : @@ -337,17 +326,15 @@ partial def MeshBuilderM.build_ let _ ← modifyFace f (fun f => { f with halfedge := i }); -- swap if (i > j) to maintain invariant that (i <= j) - let edgeKey := + let edgeKey := let vi := indices[i]!; let vj := indices[j]! if vi <= vj then (vi, vj) else (vj, vi); - dbg_trace s!"adding edge {edgeKey}..." assert! edgeKey.fst <= edgeKey.snd let hIx := I + J; -- TODO: cleanup let oldEdgeCount := edgeCount.findD edgeKey 0; match existingHalfedges.find? edgeKey with | .some twin' => { - dbg_trace s!"edge {edgeKey} exists with twin {twin'}" -- if a halfedge between vertex i and j has been -- created in the past, then it is the twin halfedge -- of the current halfedge @@ -359,26 +346,23 @@ partial def MeshBuilderM.build_ } | .none => { let e ← newEdge; - dbg_trace s!"edge {edgeKey} does not exist. Made edge {e}" let _ ← modifyEdge e (fun e => { e with halfedge := hIx }); let _ ← modifyHalfedge_ hIx (fun h => { h with edge := e }); edgeCount := edgeCount.insert edgeKey 1; }; -- record the newly created edge and halfedge from vertex i to j existingHalfedges := existingHalfedges.insert edgeKey hIx; - + if edgeCount.findD edgeKey 0 > 2 then { throw <| MeshBuilderError.nonManifoldEdge i j; } } } - dbg_trace "creating imaginary halfedges"; -- TODO: move traces into a separate file. -- create and insert boundary halfedges and "imaginary" faces for boundary cycles -- also create and insert corners. -- Note that every vertex corresponds to the halfedge from that vertex to -- the next one in the triangle. for i in List.range indices.size do { - dbg_trace s!"getting halfedge {i}" let h ← getHalfedge i; -- If a halfedge has no twin halfedge, create a new face and -- link it the corresponding boundary cycle @@ -390,7 +374,6 @@ partial def MeshBuilderM.build_ -- TODO: think about the maths here. if ! (← getHalfedge i).onBoundary then { let cIx ← newCorner; - dbg_trace "new corner"; let _ ← modifyCorner cIx (fun c => { c with halfedge := h.index }); let _ ← modifyHalfedge h.index (fun h => { h with corner := cIx }); } @@ -406,15 +389,15 @@ def MeshBuilderM.run (mb : MeshBuilderM Unit) : Except MeshBuilderError SurfaceM | .error err _ => .error err -def SurfaceMesh.build (positions: Array V3) (indices: Array (Index ``Vertex)) : +def SurfaceMesh.build (positions: Array (SciLean.Vec3 Float)) (indices: Array (Index ``Vertex)) : Except MeshBuilderError SurfaceMesh := (MeshBuilderM.build_ positions indices).run -def SurfaceMesh.build' (positions: Array V3) (indices: Array (Index ``Vertex)) : +def SurfaceMesh.build' (positions: Array (SciLean.Vec3 Float)) (indices: Array (Index ``Vertex)) : Option SurfaceMesh := (build positions indices).toOption -def SurfaceMesh.build! (positions: Array V3) (indices: Array (Index ``Vertex)) : +def SurfaceMesh.build! (positions: Array (SciLean.Vec3 Float)) (indices: Array (Index ``Vertex)) : SurfaceMesh := (build' positions indices).get! /- @@ -433,7 +416,7 @@ def randFloat01 [G : RandomGen γ] (gen : γ) : Float × γ := Id.run do return ((Float.ofNat <| val - lo) / (Float.ofNat <| hi - lo), gen) /-- Create a random vertex with coordinates sampled from uniform [0, 1] -/ -def randVertex01 [RandomGen γ] (gen : γ) : V3 × γ := Id.run do +def randVertex01 [RandomGen γ] (gen : γ) : SciLean.Vec3 Float × γ := Id.run do let (val1, gen) := randFloat01 gen let (val2, gen) := randFloat01 gen let (val3, gen) := randFloat01 gen @@ -442,12 +425,12 @@ def randVertex01 [RandomGen γ] (gen : γ) : V3 × γ := Id.run do /-- Create `nvertices` random vertices with coordinates sampled from [-scale/2, scale/2] -/ def randVertices [RandomGen γ] - (gen : γ) (nvertices : Nat) (scale : Float := 10) : (Array V3) × γ := Id.run do - let mut out : Array V3 := #[] + (gen : γ) (nvertices : Nat) (scale : Float := 10) : (Array (SciLean.Vec3 Float)) × γ := Id.run do + let mut out : Array (SciLean.Vec3 Float) := #[] let mut gen := gen for _ in List.range nvertices do let (vertex, gen') := randVertex01 gen; gen := gen' - let vertex : V3 := vertex.map (fun coord => (coord - 0.5) * scale) + let vertex : (SciLean.Vec3 Float) := vertex.map (fun coord => (coord - 0.5) * scale) out := out.push vertex return (out, gen) @@ -477,16 +460,16 @@ def SurfaceMesh.rand [RandomGen γ] (gen : γ) (nvertices : Nat) (nfaces : Nat) /-- Coerce a list of reals into a vector. Throws a ParseError if length of list is not 3 -/ -def V3.ofList : List Float → MeshBuilderM V3 +def V3.ofList : List Float → MeshBuilderM (SciLean.Vec3 Float) | [x, y, z] => pure { x := x, y := y, z := z } | xs => throw <| MeshBuilderError.parseError s!"unable to convert list to vertex '{xs}'" -def V3.ofArray : Array Float → MeshBuilderM V3 := - V3.ofList ∘ Array.toList +def V3.ofArray (xs : Array Float) : MeshBuilderM (SciLean.Vec3 Float) := + return (SciLean.Vec3.ofArray xs) /-- Load the mesh data from a .OFF format string -/ def SurfaceMesh.fromOFFString (lines : Array String) : MeshBuilderM Unit := do - let mut vertices : Array V3 := #[] + let mut vertices : Array (SciLean.Vec3 Float) := #[] let mut faces : Array Nat := #[] let mut i := 0 if lines[i]!.trim != "OFF" diff --git a/SciLean/Modules/DDG/Trace.lean b/SciLean/Modules/DDG/Trace.lean new file mode 100644 index 00000000..ab7efbd9 --- /dev/null +++ b/SciLean/Modules/DDG/Trace.lean @@ -0,0 +1,15 @@ +/- +Copyright (c) 2023 Siddharth Bhat. All rights reserved. +Released under Apache 2.0 license as described in the file LICENSE. +Authors: Siddharth Bhat + +Trace classes for DDG module. + +For more information on writing your own `Sampleable` and `Testable` +instances, see `Testing.SlimCheck.Testable`. +-/ + +import Lean +open Lean + +initialize registerTraceClass `SciLean.Modules.DDG.SurfaceMesh diff --git a/examples/SurfaceMeshTests.lean b/examples/SurfaceMeshTests.lean index 8f9ff105..33820e55 100644 --- a/examples/SurfaceMeshTests.lean +++ b/examples/SurfaceMeshTests.lean @@ -1,10 +1,10 @@ import SciLean.Modules.DDG.SurfaceMesh def testTetrahedron : IO Bool := do - let base0 : V3 := V3.mk 0 0 0 - let base1 : V3 := V3.mk 2 0 0 - let base2 : V3 := V3.mk 1 1 0 - let apex : V3 := V3.mk 0 0 1 + let base0 : SciLean.Vec3 Float := SciLean.Vec3.mk 0 0 0 + let base1 : SciLean.Vec3 Float := SciLean.Vec3.mk 2 0 0 + let base2 : SciLean.Vec3 Float := SciLean.Vec3.mk 1 1 0 + let apex : SciLean.Vec3 Float := SciLean.Vec3.mk 0 0 1 let indices : Array (Index ``Vertex) := #[] let indices := indices.append #[0, 1, 2] -- base let indices := indices.append #[0, 1, 3] -- (0, 1) to apex tri