computational-geometrylisted

# Computational Geometry for AEC This skill encapsulates the full breadth of computational geometry knowledge required for architecture, engineering, and construction workflows. It covers fundamental primitives, advanced surface mathematics, mesh processing, tessellation strategies, point cloud pipelines, and the precise tolerance management that separates prototype-grade geometry from fabrication-ready output. --- ## 1. Geometry Type Hierarchy Every computational design system is built on a layered hierarchy of geometric types. Understanding the properties, capabilities, and conversion paths of each type is essential for selecting the right representation at every stage of a project. ### 1.1 Points, Vectors, Planes, Frames **Point (Point3d)** - Definition: A dimensionless location in 3D Euclidean space defined by (x, y, z) coordinates. - Properties: No length, area, or volume. Carries only positional information. - AEC use cases: Survey control points, grid intersections, insertion points for components, structural node locations, sensor positions. - Conversion: A point can seed any higher-order geometry. Points become curve control points, mesh vertices, or centroid markers. **Vector (Vector3d)** - Definition: A direction and magnitude in 3D space, defined by (x, y, z) components. Unlike a point, a vector has no fixed position. - Properties: Magnitude (length), direction (unit vector). Supports dot product, cross product, angle computation, projection. - AEC use case