geometry3Sharp Documentation

Use the following classes for 2D geometric computations:

• ConvexHull2: Computes a 2D convex hull using either doubles or 64-bit integers.
• Arrangement2d: Computes a 2D line-segment arrangement by finding split points at intersections.
• GraphSplitter2D: Bisects an existing DGraph with infinite lines (a simpler alternative to Arrangement2d).
• GraphCells2D: Extracts enclosed regions ("cells") from a DGraph2 as boundary loops.

3D Curves

• DCurve3: A 3D polyline.
• CurveUtil: Provides queries such as Ray/curve intersection (based on thickness) and finding the nearest index.
• CurveResampler: Performs edge split/collapse resampling of a 3D polyline.
• DGraph3: A dynamic arbitrary-topology 3D graph (nodes and edges).
• DGraph3Util: Utilities for DGraph3, including ExtractCurves and DisconnectJunctions.
• Deformers: Includes InPlaceIterativeCurveSmooth, SculptMoveDeformation, and ArcLengthSoftTranslation for DCurve3 manipulation.

3D Solids

• Cylinder3d.
• DenseGridTrilinearImplicit: A trilinear interpolant of a 3D grid.
• CachingDenseGridTrilinearImplicit: A variant of DenseGridTrilinearImplicit that uses lazy evaluation of grid values based on an implicit function.

The Frame3f class represents a position and orientation. It is recommended to use Frame3f instead of matrices for representing transformations.

Capabilities:

• Accessors for transformed x, y, and z axes.
• Frame transformations.
• Free and constrained axis alignment.
• Projection to/from frames for points and directions.
• Minimum-rotation frame-to-frame alignment.
• Ray-plane intersection.

geometry3Sharp provides two primary mesh representations depending on your needs:

• SimpleMesh: A standard indexed mesh class. It uses a dense index space and is backed by DVector buffers. Use this for static geometry where topology doesn't change.
• DMesh3: A dynamic mesh class designed for active editing. It features a reference-counted sparse index space and includes full edge topology, allowing for neighbor queries. Data is stored in DVector buffers of POD-types (positions are double, while normals, colors, and UVs are float). It supports adding/removing vertices and triangles, manifold-preserving operators (Split, Flip, Collapse, PokeTriangle), and edge-welding via MergeEdges.

You can perform edge split/flip/collapse and vertex smoothing using the following classes:

• Remesher: Performs standard remeshing. You can constrain the mesh to an IProjectionTarget (like a surface or curve) and use MeshConstraints to pin vertices or restrict edge operations.
• RemesherPro: A high-performance extension of Remesher. It includes:
  • FastestRemesh(): Uses an active-set queue for faster convergence.
  • SharpEdgeReprojectionRemesh(): Aligns triangle face normals to a projection target to preserve sharp edges.
  • FastSplitIteration(): Quickly increases vertex resolution by splitting edges.
• RegionRemesher: Applies remeshing to a specific sub-region of a DMesh3 (via DSubmesh3) while automatically preserving the sub-region's boundary. Use BackPropropagate() to integrate the modified submesh back into the original mesh.

geometry3Sharp is compatible with Unity. To enable transparent interop between g3 and Unity vector types, set the G3_USING_UNITY Scripting Define in your Unity project.

While the library is written for C# 4.5, it will still work with the .NET 3.5 Unity runtime, though some features may be missing.

The library provides several I/O options for mesh data:

• StandardMeshReader / StandardMeshWriter: Format-agnostic interfaces that allow registering additional format handlers. Use SimpleMeshBuilder or DMesh3Builder to construct meshes via these interfaces. Configuration is handled via ReadOptions and WriteOptions.
• OBJReader/Writer: Supports vertex colors, face groups, and UVs. Note that it stores texture map paths but does not load images. It cannot produce meshes with multiple UVs per vertex; vertices will be duplicated along UV seams.
• STLReader/Writer: Supports the STL format with basic vertex welding to reconstruct topology.
• OFFReader/Writer: Supports the OFF file format.
• gSerialization: Provides binary Store/Restore functions for many g3 types and data structures.
• SVGWriter: Writes 2D geometric elements in SVG format.

Depending on your requirements for shape preservation and topology, use one of the following hole-filling algorithms:

• SimpleHoleFiller: Performs topological filling of an open boundary edge loop. It does not attempt to preserve the original shape.
• SmoothedHoleFill: Fills holes with approximate boundary tangent continuity.
• MinimalHoleFill: Constructs a 'minimal' fill that is often developable, which is effective for recovering sharp edges.
• PlanarHoleFiller: Maps planar holes to 2D to fill them; handles nested holes (e.g., from a plane cut through a torus).

To enable transparent conversion between geometry3Sharp types and Unity types, you must define the G3_USING_UNITY symbol in your Unity project.

Setup Steps:

1. Open Player Settings in Unity.
2. Locate the Scripting Define Symbols box.
3. Add G3_USING_UNITY to the list.

Usage Details:

• Supported Types: Vector2, Vector3, Quaternion, Ray, Color, and Bounds (with AxisAlignedBox3f).
• Type Conversions:
  • float $\leftrightarrow$ double conversions are transparent for Vector3 (e.g., Vector3 $\leftrightarrow$ Vector3f).
  • Converting double to float (e.g., Vector3d $\to$ Vector3) requires an explicit cast.
• Limitations: Conversions do not work for equations; you must explicitly cast one side to the other when adding a Vector3f to a Vector3.