feat(editor): laid to the norms, a track laid on from an end gets its transition curves, into the arc, between the arcs of a compound curve and out to the straight

A track laid on from a free end in the PKP PLK laying, by a drag out of the end, by clicks from it or laid back onto it, starts from the curvature and the cant the end has. An arc turning the same way as the end is a compound curve: a transition of the norms ramps the curvature and the cant from the one arc into the other. From a straight the arc gets its entry transition, the arc then straight its exit one. Where the way is too short the transitions are cut and the cant lowered to what they ramp, and the readout says so; with no room at all the track is laid as before and the note says why. The curves traced on the orthophoto and the recommended values of a compound curve get the transitions between their arcs too. The free laying stays as it was.

editor/editorAlignment.hpp

@@ -9,6 +9,7 @@ http:
 
 #pragma once
 
+#include <optional>
 #include <string>
 #include <vector>
 #include <glm/glm.hpp>
@@ -38,6 +39,8 @@ struct limits
 	double arc_min{20.0};
 	double arc_min_factor{0.4};
 	bool checked{true};
+
+	bool operator==(limits const &) const = default;
 };
 
 struct compound_arc
@@ -92,6 +95,9 @@ struct recommendation
 };
 recommendation recommend(double const Speed, double const Radius, limits const &Limits);
 double transition_length(double const Speed, double const Radius, double const Cant, limits const &Limits);
+// the transition curve from the curvature and the cant of one arc to those of the next one, 0 for a straight; the curvature positive
+// turning one way, the cant with the same sign as the curvature it leans into
+double transition_between(double const Speed, double const Curvature0, double const Cant0, double const Curvature1, double const Cant1, limits const &Limits);
 double unbalanced_acceleration(double const Speed, double const Radius, double const Cant, limits const &Limits);
 
 enum class element_kind
@@ -217,6 +223,8 @@ struct join_end
 	glm::dvec3 position{0.0};
 	glm::dvec2 direction{0.0, 1.0};
 	double roll{0.0};
+
+	bool operator==(join_end const &) const = default;
 };
 
 enum class join_kind
@@ -259,4 +267,47 @@ struct join_result
 
 join_result join(join_request const &Request);
 
+enum class lay_kind
+{
+	arc_straight,
+	straight_arc,
+	arc,
+	straight
+};
+
+// a track laid on from an end the way the layout lays it, with the transition curves of the norms: from the curvature the end has
+// into the arc, between the arcs of a compound curve where both turn the same way, and out of the arc to the straight
+struct lay_request
+{
+	join_end start; // the roll in degrees, as the track goes on
+	double curvature{0.0}; // of the end as the track goes on, positive turning from x towards z
+	glm::dvec3 target{0.0};
+	lay_kind kind{lay_kind::arc_straight};
+	double radius{500.0}; // of the arc, but the arc through the target
+	double speed{100.0};
+	double piece_length{100.0};
+	limits norms;
+
+	bool operator==(lay_request const &) const = default;
+};
+
+// no pieces where the norms find no room for the transitions, the note says why
+struct lay_result
+{
+	std::vector<segment_data> pieces;
+	std::string note;
+	double length{0.0};
+	double radius{0.0};
+	double cant{0.0};
+	double entry{0.0}; // the transition out of the curvature of the end
+	double exit{0.0};
+	double from_radius{0.0}; // of the end, 0 for a straight
+	bool compound{false};
+};
+
+std::optional<lay_result> lay_on(lay_request const &Request);
+
+// the transitions between the arcs of a compound curve which the norms ask for at the speed, the cant of the vertex on its sharpest arc
+void recommend_between(vertex &Vertex, double const Speed, limits const &Limits);
+
 }