W.25 Snellius–Pothenot Resection & Hansen’s Surveying Problem — Code

In Snellius-Pothenot resection, an observer P measuring spreads to three known beacons A, B, C lies on the algebraic intersection of two subtended-spread conics; in Hansen’s problem, knowing one baseline quadrance Q(A, B) and four sighting spreads at unobserved stations C, D determines every side and diagonal quadrance exactly via Triple Spread Systems and Alternate Spreads.

Exact geometor.model SVG output of model.py for W.25 (Snellius–Pothenot Resection & Hansen’s Surveying Problem).

Symbolic Construction & Verification Script (model.py)

"""GEOMETOR Wildberger symbolic model and proof script for W.25: Snellius–Pothenot Resection & Hansen's Surveying Problem.

        Enunciation: In Snellius-Pothenot resection, an observer P measuring spreads to three known beacons A, B, C lies on the algebraic intersection of two subtended-spread conics; in Hansen's problem, knowing one baseline quadrance Q(A, B) and four sighting spreads at unobserved stations C, D determines every side and diagonal quadrance exactly via Triple Spread Systems and Alternate Spreads.
        """

        from __future__ import annotations

        import sys
        from pathlib import Path

        _ROOT_SRC = Path(__file__).resolve().parents[3] / "src"
        if str(_ROOT_SRC) not in sys.path:
            sys.path.insert(0, str(_ROOT_SRC))

        from geometor.wildberger.models import (  # noqa: E402
            TopicBuildResult,
            assert_zero_floats,
            build_principle_model,
        )
        from geometor.wildberger.render import render_svg  # noqa: E402


        def construct_w_25() -> TopicBuildResult:
            """Construct the exact symbolic model and verifications for W.25.

            Returns:
                Populated `TopicBuildResult` for W.25 (Snellius–Pothenot Resection & Hansen's Surveying Problem).
            """
            result = build_principle_model("W.25")
            assert_zero_floats(result.model)
            return result


        def main() -> None:
            """Execute W.25 symbolic construction, render `w-25.svg`, and print invariants."""
            here = Path(__file__).resolve().parent
            bundle = construct_w_25()
            svg_out = render_svg(
                bundle.model,
                here / "w-25.svg",
                extra_curves=bundle.extra_curves,
                annotations=bundle.annotations,
            )
            print("W.25: Snellius–Pothenot Resection & Hansen's Surveying Problem")
            print(f"  Elements in model: {len(bundle.model)}")
            print(f"  Rendered SVG:      {svg_out.name}")
            for label, val, status in bundle.verifications:
                print(f"  [OK] {label}: {val} ({status})")


        if __name__ == "__main__":
            main()