gm_advanced_analysis

Geometry Module - Advanced Analysis Example

This example demonstrates advanced geometric analysis techniques using VSL's Geometry Module (gm).

Overview

This example showcases sophisticated geometric operations including:

• Point cloud analysis and clustering
• Bounding box calculations and containment testing
• Line geometry and distance analysis
• Point-line alignment detection
• Vector field analysis and visualization

Features Demonstrated

🔹 Point Cloud Analysis

• Multi-cluster point generation
• Distance-based clustering analysis
• Cluster center calculations
• Statistical analysis of point distributions

🔹 Bounding Box Analysis

• Automatic bounding box calculation for point clouds
• Volume computation
• Point containment testing
• Spatial boundary detection

🔹 Line Geometry Analysis

• Multiple line definitions in 3D space
• Point-to-line distance calculations
• Geometric relationship analysis
• Line intersection properties

🔹 Point-Line Alignment Detection

• Precise point-on-line testing
• Tolerance-based alignment detection
• Distance thresholding
• Geometric validation

🔹 Vector Field Analysis

• Radial vector field generation
• Vector normalization and magnitude calculation
• Angular analysis from horizontal
• Field divergence calculations

Usage

v run main.v

Mathematical Concepts

Point Cloud Analysis

• Euclidean clustering using distance thresholds
• Centroid-based cluster analysis
• Statistical measures (mean distances, point counts)

Bounding Box

• Axis-aligned bounding box (AABB) computation
• Volume calculation: V = (xmax - xmin) × (ymax - ymin) × (zmax - zmin)
• Point-in-box testing with tolerance

Vector Fields

• Radial field generation: r⃗ = (x - cx, y - cy, z - cz)
• Vector normalization: û = r⃗ / |r⃗|
• Angular calculations: θ = atan2(vy, vx)
• Divergence approximation: ∇ · F ≈ 1/r for radial fields

Expected Output

The example produces comprehensive analysis including:

• Cluster membership and distances
• Bounding box dimensions and volume
• Point containment results
• Line-point distance measurements
• Vector field properties and statistics

Educational Value

Perfect for learning:

• Advanced geometric analysis techniques
• Point cloud processing fundamentals
• Spatial data structures and algorithms
• Vector field theory applications
• Computational geometry concepts

Applications

These techniques are useful for:

• CAD/CAM software development
• Computer graphics and game development
• Robotics path planning
• Scientific visualization
• Geospatial analysis
• Machine learning feature extraction