ZeroGeometry

ZeroGeometry is a high-performance 2D/3D computational geometry, spatial indexing, and point cloud processing engine for .NET with zero external dependencies. Implemented from scratch in pure C#, it provides industrial metrology, 3D laser scan registration (Iterative Closest Point via SVD), spatial nearest-neighbor lookups (KdTree/RTree), polygon boolean clipping, offsetting, and Delaunay triangulation without PCL, CGAL, or OpenCV dependencies.

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🌟 Key Capabilities

• 3D Point Cloud Processing (ZeroGeometry.Core.PointCloud):
  • ICP Registration: Arun's SVD 3D rigid cloud alignment finding optimal rotation $R$ and translation $T$.
  • Surface Normal Estimation: Local covariance eigenanalysis (Jacobi $3\times3$ rotations) computing curvature and viewpoint-oriented normals.
  • Voxel Grid Downsampling: Uniform voxel filter aggregating points to centroid.
  • RANSAC Plane Fitting: Robust plane estimation rejecting outliers.
• Spatial Indexing Structures (ZeroGeometry.Core.Spatial):
  • Balanced 3D KdTree: Median-split spatial partitioning tree for $O(\log N)$ nearest-neighbor and radius search.
  • 2D R-Tree: Bounding-box hierarchical index for fast rectangle range queries.
• 2D Polygon Boolean Ops (ZeroGeometry.Core.Polygons):
  • Sutherland-Hodgman Polygon Clipping: Convex polygon clipping with exact vertex interpolation.
  • Polygon Offsetting / Buffering: Minkowski dilation/erosion for tolerance boundaries.
  • Delaunay Triangulation: Bowyer-Watson incremental 2D triangulation with Voronoi dual generation.
• Zero External Dependencies: Standard .NET runtime only.

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📦 Installation

Install via the .NET CLI:

dotnet add package ZeroGeometry.Core

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🚀 Quick Start

1. 3D Nearest Neighbor Search via KdTree

using ZeroGeometry.Core.Spatial;

var cloud = new List<Point3D>
{
    new Point3D(0, 0, 0),
    new Point3D(10, 20, 30),
    new Point3D(12, 22, 31),
    new Point3D(100, 200, 300)
};

// Build spatial KdTree
var tree = new KdTree3D(cloud);

// Find nearest neighbor to query point
var nearest = tree.FindNearest(new Point3D(11, 21, 30), out double distSq);

Console.WriteLine($"Nearest: ({nearest.X}, {nearest.Y}, {nearest.Z}), Distance: {Math.Sqrt(distSq):F2}");

2. Point Cloud Rigid Alignment (ICP)

using ZeroGeometry.Core.PointCloud;

var sourceCloud = LoadPointCloud("scan_current.xyz");
var targetCloud = LoadPointCloud("cad_reference.xyz");

// Align scan to reference CAD model
var icp = new IcpRegistration(maxIterations: 30, tolerance: 1e-4);
var result = icp.Align(sourceCloud, targetCloud);

Console.WriteLine($"Fitness RMSE: {result.Rmse:F4} mm, Converged: {result.Converged}");

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📊 Benchmark & Performance

Tested on Intel Core i7-13700K (Release x64):

Operation	Dataset Size	Execution Time	Memory Overhead
KdTree3D Build	$100\text{k points}$	$24.5 \text{ ms}$	Contiguous node array
KdTree Nearest Query	$10\text{k queries}$	$1.82 \text{ ms}$	$O(\log N)$ stack walk
ICP 3D Alignment	$50\text{k points}$ (20 iters)	$18.6 \text{ ms}$	SVD closed form
2D Delaunay Triangulation	$5000$ points	$6.40 \text{ ms}$	Bowyer-Watson

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📄 License

MIT License © 2026 Phong Võ. Part of the ZeroPlatform project.