Native Spatial Circle and Ordered Arc Construction from Three Points in AutoLISP without UCS Modification

This technical article describes 3C and 3A, two standalone AutoLISP utilities for constructing native circular CAD geometry from three spatial points without modifying the current user coordinate system (UCS). The shared algorithm translates the input points, normalizes the geometry by the longest triangle edge, and evaluates a vector circumcenter formula. The article derives the mathematical construction, explains the UCS–WCS–OCS coordinate transformation pipeline, and describes how native CIRCLE and ARC entities are created and validated through entity readback. For ordered arcs, modular angular differences are used to select the sweep passing through the intermediate point, including arcs exceeding 180 degrees. Numerical validation combines coordinate-resolution, triangle-shape, radial, planar, and angular consistency checks. A worked example of inclined circular geometry produces a center at (1, 3, 4) and a radius of 6. Previously recorded AutoCAD 2022 Core Console test results are summarized, including 154 assertions for circle integration, 273 assertions per arc regression run under two UCS configurations, and 36 assertions for a separate arc command test suite. These results were not independently rerun during preparation of the article. BricsCAD compatibility, complete graphical interface behavior, and performance with real-world surveying measurements remain outside the verified test scope. The contribution is a practical engineering integration of established computational geometry with native CAD entity construction, rather than a claim of inventing new mathematical principles. Author: Dzmitry Tsiapkin Keywords: AutoLISP, AutoCAD, 3D Circle, 3D Arc, Computational Geometry, Surveying, WCS, UCS, OCS.