geometry3Sharp

Open-Source (Boost-license) C# library for geometric computing.

geometry3Sharp only uses C# language features available in .NET 3.5, so it works with the Mono C# runtime used in Unity 5.x (NOTE: you must configure Unity for this to work, see note at bottom of this file).

Currently there is a small amount of unsafe code, however this code is only used in the OBJ reader and a few fast-buffer-copy routines, which can be deleted if you need a safe version (eg for Unity web player).

Some portions of the code are ported from the WildMagic5 C++ library, developed by David Eberly at Geometric Tools. WildMagic5 is distributed under the Boost license as well, available here. Any errors in code marked as ported from WildMagic5 are most certainly ours!

Questions? Contact Ryan Schmidt @rms80 / gradientspace

Core

• DVector: indexed list with vector-style interface, but internally stored as separate blocks of memory

  • appending is amortized O(1), never a full buffer copy like normal list

• RefCountVector: track index reference counts, maintain list of free indices

• VectorArray2/VectorArray3: wrapper around regular array providing N-element access

  • eg operator[] gets/sets Vector3d for VectorArray3d, internally is double[3*count]

• HBitArray: hierarchical BitArray, efficient iteration over large-but-sparse bitsets

• Units: enums, conversions, string representations

• gParallel: multi-threading utilities, including parallel ForEach that works w/ .Net 3.5

• gSerialization: binary serialization of core types (vectors, frames, polygons, DMesh3)

• CommandArgumentSet: string-based argument representation/parsing, useful for command line args, etc

Math

• reasonably complete set of vector-math objects, implemented as structs

  • Vector2/3, Matrix2/3, Quaternion, Segment2/3, Line2/3, Ray3, Triangle2/3, AxisAlignedBox2/3, (oriented) Box2/3
  • Index2/3/4
  • Interval1d, and Interval1i which is IEnumerable
  • double & float versions of vector/line/ray/segment/box types (and int types for vectors)
  • implicit float->double conversion operators between types, explicit double->float operators
  • transparent Unity interop (see below)

• Frame3f: position+orientation representation

  • accessors for transformed x/y/z axes
  • frame transformations
  • free and constrained axis alignment
  • projection to/from frame for points, directions, other frames,
  • minimum-rotation frame-to-frame alignment
  • ray-plane intersection
  • Frames are awesome and you should use them instead of matrices!!

• TransformSequence: stack of affine transformations

• IndexUtil: utility functions for working with tuples/lists of indices (cycling, filtering, etc)

• BoundsUtil: construct bboxes from different data sources, containment tests

• Integrate1d: Romberg integration, Gaussian quadrature with legendre polynomials, trapezoid rule

• Interval1d: 1D interval class/intersection/etc

Solvers

• basic arbitrary-size DenseMatrix, DiagonalMatrix, SymmetricSparseMatrix
• SparseSymmetricCG conjugate-gradient matrix solver
• SingularValueDecomposition SVD for arbitrary matrices

Color

• Colorf: float rgba color, with many standard colors pre-defined
• Colorb: byte rgba color
• ColorHSV: Hue-Saturation-Value color, convert to/from RGB

Distance Queries

• 2D:
  • point/curve: DistPoint2Circle2
  • point/area: DistPoint2Box2
  • linear/linear: DistLine2Line2, DistLine2Segment2, DistSegment2Segment2
• 3D
  • point/area: DistPoint3Triangle3
  • point/curve: DistPoint3Circle3
  • point/volume: DistPoint3Cylinder3 (signed)
  • linear/linear: DistLine3Ray3, DistLine3Segment3, DistRay3Segment3, DistRay3Ray3
  • linear/area: DistLine3Triangle3, DistSegment3Triangle3
  • area/area: DistTriangle3Triangle3

Intersection Queries

• 2D:
  • linear/linear: IntrLine2Line2, IntrSegment2Segment2
  • linear/area: IntrLine2Triangle2, IntrSegment2Triangle2
  • area/area: IntrTriangle2Triangle2
• 3D:
  • linear/area: IntrRay3Triangle3
  • linear/volume: IntrLine3Box3, IntrSegment3Box3, IntrRay3Box3, IntrLine3AxisAlignedBox3, IntrRay3AxisAlignedBox3
  • area/area: IntrTriangle3Triangle3
  • ray-sphere and ray-cylinder

Meshes

• SimpleMesh: standard indexed mesh class

  • dense index space, backed by DVector buffers

• DMesh3: dynamic mesh class

  • reference-counted sparse index space
  • has edge topology, neighbour queries, etc
  • data stored as DVector buffers of POD-types
  • positions are doubles, normals/colors/uv floats (and optional)
  • add/remove vertices
  • manifold-preserving Split/Flip/Collapse operators

• DSubmesh3: sub-region of a DMesh3

  • creates a new DMesh3 that is a subset of triangles of input DMesh3
  • keeps track of index map relationships, region border information

• Remesher: edge split/flip/collapse + vtx smooth remeshing

  • entire mesh can be constrained to lie on an IProjectionTarget (eg for reprojection onto initial surface)
  • use MeshConstraints to preserve features
  • individual edge split/flip/collapse restrictions
  • vertices can be pinned to fixed positions
  • vertices can be constrained to an IProjectionTarget - eg 3D polylines, smooth curves, surfaces, etc
  • MeshConstraintUtil constructs common constraint situations

• RegionRemesher: applies Remesher to sub-region of a DMesh3, via DSubmesh3

  • boundary of sub-region automatically preserved
  • BackPropropagate() function integrates submesh back into input mesh

• Mesh manipulation/query utilities

  • MeshEditor: low-level mesh editing operations
    • operations check that they can be applied and most will back themselves out if operation fails
    • RemoveTriangles, AddTriangleFan, Stitch Loops, AppendMesh
    • ReinsertSubmesh can re-insert modified submesh via DSubmesh3
    • RemoveAllBowtieVertices removes neighbourhoods around bowtie vertices
  • MeshVertexSelection: create/manipulate set of vertices. grow by one-rings, tris-to-verts, etc
  • MeshFaceSelection: similiar. LocalOptimize() 'cleans up' irregular selection boundaries.
  • MeshConnectedComponents: find connected components, with configurable seed and filter functions
  • MeshTransforms: mesh Translate/Rotate/Scale, map to/from Frame3, convert Y/Z up, Left/Right-handedness
  • MeshMeasurements: mesh volume, center of mass, inertia tensor, centroid, bounds under arbitrary transforms
  • MeshNormals: estimate vertex normals
  • MeshWeights: vertex one-ring operations based on different weighting schemes
    • OneRingCentroid, CotanCentroid, VoronoiArea, MeanValueCentroid,
  • MeshBoundaryLoops: find set of closed boundary edge loops in DMesh3, output as EdgeLoop objects
  • will find smallest loops in cases where boundary has "bowtie" vertices
  • FaceGroupUtil: utility functions for manipulating mesh face/triangle groups
  • MeshUtil: utility functions for mesh operations

• MeshDecomposition: breaks large mesh up into smaller submeshes of maximum size, eg for use in rendering or parallel computation

  • produces Component objects that can track associations
  • client provides IMeshComponentManager implementation that implements desired submesh functionality
  • currently only supports decomposition via a linear axis sorting

• various mesh generators in /mesh_generators

  • most mesh generators support generating shared or not-shared vertices along sharp edges, UV seams, etc
  • some support generating sections of shape (eg wedge-shaped portion of cylinder)
  • TrivialBox3Generator
  • OpenCylinderGenerator, CappedCylinderGenerator, ConeGenerator (support start/end angles)
  • TrivialDiscGenerator, PuncturedDiscGenerator, TrivialRectGenerator, RoundRectGenerator
  • VerticalGeneralizedCylinderGenerator
  • TubeGenerator: polygon swept along polyline
  • Curve3Axis3RevolveGenerator: 3D polyline revolved around 3D axis
  • Curve3Curve3RevolveGenerator: 3D polyline revolved around 3D polyline (!)

Mesh Operations

• LaplacianMeshDeformer: basic laplacian mesh deformation, currently only symmetrized uniform weights, conjugate-gradient solve
• MeshExtrusion: duplicate existing boundary edge loop, offset to new position, stitch together with original
• MeshIterativeSmooth: standard iterative vertex-laplacian smoothing with uniform, cotan, mean-value weights
• SimpleHoleFiller: topological filling of an open boundary edge loop. No attempt to preserve shape whatsoever!
• MeshICP: basic iterative-closest-point alignment to target surface
• MeshLoopSmooth: smooth embedded EdgeLoop of mesh

Spatial Data Structures

• DMeshAABBTree: triangle mesh axis-aligned bounding box tree
  • bottom-up construction using mesh topology to accelerate leaf node layer
  • generic traversal interface
  • Queries for NearestTriangle, FindNearestHitTriangle (raycast), (more to come)

2D Curves

• Circle2d, Arc2d, Ellipse2d, EllipseArc2d, PolyLine2d
• Polygon2d: closed polyline with signed area, point-in-polygon test, polygon/polygon intersection, polygon-in-polygon, simplification
• NURBSCurve2: open nonuniform, closed and periodic uniform NURBS splines, derivatives up to 3rd order, curvature, total arc length and arc-length sampling. Uses BSplineBasis internally, which works in any dimension
• All curves implement common IParametricCurve2d interface, as does Segment2d.
• ParametricCurveSequence2: open or closed sequential set of connected parametric curves
• CurveSampler2: parameter-space or arc-length sampling of IParametricCurve2d. AutoSample function transparently handles multi-segment sequential curves. Reasonably good knot-interval sampling of NURBS curves, does the right things with sharp knots.
• PlanarComplex2: assembly of open and closed IParametricCurve2d curves, as well as point-samplings. Chaining of curves into sequences. Extraction of clean closed loops with interior holes, determined by polygon containment.
• GeneralPolygon2d: outer polygon with interior polygonal holes, with configurable outer/inner clockwise-ness
• PlanarSolid2d: parametric variant of GeneralPolygon2D

3D Curves

• DCurve3: 3D polyline
• CurveUtil: queries like Ray/curve intersection based on curve thickness, nearest index, etc
• InPlaceIterativeCurveSmooth, SculptMoveDeformation, ArcLengthSoftTranslation: simple DCurve3 deformers
• CurveResampler: edge split/collapses resampling of a 3D polyline
• Circle3d
• SampledArcLengthParam: arc-length parameterization discrete-sampled 3D curve

3D Solids

• Cylinder3d

I/O

• format-agnostic StandardMeshReader and StandardMeshWriter
  • can register additional format handlers beyond supported defaults
  • constructs mesh via generic interface, SimpleMeshBuilder and DMesh3Builder provided
• readers & writers configurable via ReadOptions and WriteOptions
• OBJReader/Writer - supports vertex colors extension, read/write face groups, UVs, OBJ .mtl files
  • stores texture map paths but you have to load images yourself
  • currently cannot produce meshes with multiple UVs per vertex (not supported in DMesh3), vertices will be duplicated along UV seams
• STLReader/Writer: STL format, basic vertex welding to reconstruct topology
• OFFReader/Writer: OFF file format
• gSerialization: binary Store/Restore functions for many g3 types / data structures

Misc

• 2D implicit blobs
• 2D Marching Quads

Unity Interop

geometry3Sharp supports transparent conversion with Unity types. To enable this, define G3_USING_UNITY in your Unity project, by adding this string to the Scripting Define Symbols box in the Player Settings.

Once enabled, code like this will work transparently:

Vector3 unityVec;
Vector3f g3Vec;
unityVec = g3vec;
g3vec = unityVec;

float->double types will work transparently, while double->float will require an explicit cast:

Vector3d g3vecd;
g3vecd = gameObject.transform.position;
gameObject.transform.position = (Vector3)g3vecd;

This will work for Vector2, Vector3, Quaterion, Ray, Color, and Bounds (w/ AxisAlignedBox3f) Note that these conversions will not work for equations, so to add a Vector3f and a Vector3, you will need to explicitly cast one to the other.