feat(sleepers): the timbers of a switch get the fastenings of the rails from the submodels plate, chair and check of their model: a plate under each rail where it lies on a timber, slide chairs under the stock rails along the blades, a fastening of both where a check rail or another rail of the frog lies close beside, the legs of the nose in one plate where they're joined; the rails sit on the plate, the blades ride on the slide plates of the chairs as high as the model has them, their webs shortened; the fastenings drawn within 120 m; selftest fastenings

world/SleeperFastenings.h

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+/*
+This Source Code Form is subject to the
+terms of the Mozilla Public License, v.
+2.0. If a copy of the MPL was not
+distributed with this file, You can
+obtain one at
+http://mozilla.org/MPL/2.0/.
+*/
+
+#pragma once
+
+#include <vector>
+
+#include <glm/glm.hpp>
+
+#include "world/TrackSleepers.h"
+
+// the fastenings of the rails on the timbers: where a rail lies on a timber, the part of the model of the timbers which holds it
+// there. a stock rail with the blade beside it lies in a slide chair, a rail with a check rail or another rail of the frog close
+// beside it in a fastening of both, the blade on the chair of its stock rail, and the other rails each in a plate of its own
+namespace track_sleepers {
+
+// a fastening on a timber
+struct fastening {
+    int part { part_plate };
+    glm::dvec3 point { 0.0 }; // under the middle of the rail, on the top of the timber
+    glm::dvec2 across { 1.0, 0.0 }; // unit vector in plan square to the rail, the way the +x of the part goes
+};
+
+// the rails of the tracks around a track, which lie on its timbers
+class fastened_rails {
+
+public:
+    explicit fastened_rails( TTrack &Track );
+    // the fastenings of the rails on the timber, of the parts the model has
+    std::vector<fastening> on( beam const &Beam, beam_model const &Model ) const;
+
+private:
+    // what a rail is where it lies on a timber
+    enum class role {
+        plain,
+        blade, // a blade of a switch, which slides on the chair of its stock rail
+        stock, // the stock rail of a switch with the blade beside it
+        checked // a rail with a check rail beside it
+    };
+    // a rail by points along its middle
+    struct rail {
+        TTrack *track { nullptr };
+        int path { 0 };
+        int side { 1 };
+        std::vector<glm::dvec2> points;
+        std::vector<double> heights;
+        std::vector<glm::dvec2> inward; // unit vectors in plan from the rail toward the middle of its path
+        std::vector<double> distances;
+        glm::dvec2 low { 0.0 };
+        glm::dvec2 high { 0.0 };
+        // the stretches along the path the rail is a blade, a stock rail with a chair, checked along
+        glm::dvec2 blade { -1.0 };
+        glm::dvec2 stock { -1.0 };
+        std::vector<glm::dvec2> checks;
+        role at( double const Distance ) const;
+    };
+    // where a rail crosses a timber
+    struct hit {
+        double at { 0.0 }; // along the timber, from its from end
+        role kind { role::plain };
+        glm::dvec2 inward { 1.0, 0.0 };
+    };
+
+    std::vector<rail> m_rails;
+};
+
+} // namespace track_sleepers