feat: Implement synthetic edges city↔airport (Task 10)

- Add TransferTime constants (AirportToCity, CityToStation, StationToStation)
- Update Edge struct with Synthetic field
- Enhance addSyntheticEdgesForNode to use constants and mark synthetic edges
- Update BuildGraphFromStations to set Synthetic field
- Mark synthetic edges in GeoJSON output as dashed lines
- Write TestSyntheticAirportCityEdges and TestRouteWithSyntheticAirportCityEdges tests

cmd/api/handlers.go

@@ -40,7 +40,9 @@ type routeSearchResponse struct {
 
 // routeGeoJSONResponse represents the response for route GeoJSON.
 type routeGeoJSONResponse struct {
-	Type string `json:"type"`
+	Type               string              `json:"type"`
+	Features           []map[string]interface{} `json:"features"`
+	SyntheticEdgeStyle map[string]string `json:"synthetic_edge_style,omitempty"`
 }
 
 // CityAutocomplete handles GET /v1/cities?query=.
@@ -100,9 +102,69 @@ func RouteGeoJSON(hc *HandlerContext, w http.ResponseWriter, r *http.Request) {
 		http.Error(w, "invalid route ID", http.StatusBadRequest)
 		return
 	}
-	// In a full implementation, would convert route to GeoJSON
-	// For now, return a simple JSON response
-	resp := routeGeoJSONResponse{Type: "FeatureCollection"}
+
+	// Generate GeoJSON from the graph's edges, distinguishing synthetic vs real
+	// Synthetic edges (e.g., city↔airport transfers) are marked with dashed lines
+	// Real edges (actual scheduled trips) are solid lines
+	features := make([]map[string]interface{}, 0)
+
+	for _, edge := range hc.Router.Edges() {
+		// Determine line style based on edge type
+		strokeColor := "#1976d2" // default blue for train
+		strokeDasharray := ""    // solid for real edges
+
+		if edge.Synthetic {
+			strokeDasharray = "5, 5" // dashed line for synthetic edges
+		}
+
+		// Color by transport type
+		switch edge.TransportType {
+		case routing.TransportTypePlane:
+			strokeColor = "#ff9800" // orange for plane
+		case routing.TransportTypeBus:
+			strokeColor = "#cddc39" // lime for bus
+		case routing.TransportTypeTrain:
+			strokeColor = "#1976d2" // blue for train (default)
+		}
+
+		// Create LineString geometry
+		// Use edge endpoints as coordinate placeholders
+		fromCoord := []float64{0, 0} // placeholder
+		toCoord := []float64{0, 0}   // placeholder
+
+		// In a full implementation, would use actual node coordinates from PostGIS
+		// For now, use fixed placeholder coordinates
+		geoJsonLine := map[string]interface{}{
+			"type": "LineString",
+			"coordinates": []interface{}{
+				fromCoord, toCoord,
+			},
+			"properties": map[string]interface{}{
+				"transport":             edge.Transport,
+				"transport_type":        string(edge.TransportType),
+				"kind": "real",
+				"synthetic":             edge.Synthetic,
+				"duration":              edge.Duration,
+				"cost":                  edge.Cost,
+				"is_transfer":           edge.IsTransfer,
+				"stroke_color":          strokeColor,
+				"stroke_width":          2,
+				"stroke_dasharray":      strokeDasharray,
+			},
+		}
+
+		features = append(features, map[string]interface{}{
+			"type":        "Feature",
+			"geometry":    geoJsonLine,
+			"properties":  map[string]interface{}{},
+		})
+	}
+
+	resp := routeGeoJSONResponse{
+		Type:               "FeatureCollection",
+		Features:          features,
+		SyntheticEdgeStyle: map[string]string{"stroke_dasharray": "5, 5", "stroke_color": "#ff9800"},
+	}
 	w.Header().Set("Content-Type", "application/json")
 	json.NewEncoder(w).Encode(resp)
 }