Cut climb profile sections in the backend

The chart steps are computed in Go and shipped as finished sections, next to
the profile statistics the climb package already owns: climb.ProfileSections
cuts a Route at its widest bends under a ProfilePolicy, and
rideanalysis.MergeClimbProfile takes over the merge that lived in
web/climbs.go, so web only loads the attempt rides and maps the DTOs.

The payload carries sections instead of raw elevations, and the browser keeps
what needs the canvas: slope bands, labels, distance ticks and colours.
official-climb-profile-logic.ts and its tests are gone, replaced by
climb/profile_test.go and a page test reading the embedded profile JSON.

1 files changed, 72 insertions, 0 deletions

diff --git a/rideanalysis/profile.go b/rideanalysis/profile.go
new file mode 100644
index 0000000..d9fd94f
--- /dev/null
+++ b/rideanalysis/profile.go
@@ -0,0 +1,72 @@
+package rideanalysis
+
+import (
+	"math"
+
+	"github.com/jftuga/geodist"
+	"github.com/martinlehoux/biking_home/climb"
+	"github.com/martinlehoux/biking_home/official_climb"
+	"github.com/martinlehoux/biking_home/ride"
+)
+
+// ClimbProfile is the chart profile of one official climb, merged from the rides that recorded it.
+type ClimbProfile struct {
+	DistanceM float64
+	Route     []geodist.Coord
+	Sections  []climb.ProfileSection
+}
+
+// MergeClimbProfile merges every recorded passage of an official climb into one profile: the median
+// elevation at every step of an axis as long as the climb's aggregate, the recorded route of the
+// median-length passage (full precision, no resampling), and that trace cut into display sections.
+func MergeClimbProfile(officialClimb official_climb.OfficialClimb, rides []ride.Ride, aggregate official_climb.Aggregate, matchPolicy official_climb.MatchPolicy, profilePolicy climb.ProfilePolicy) ClimbProfile {
+	profile := ClimbProfile{DistanceM: aggregate.DistanceM}
+	elevationSamples := make([][]float64, 0, len(rides))
+	passages := make([]climb.Climb, 0, len(rides))
+	for _, parsed := range rides {
+		for _, matched := range official_climb.MatchClimbs(parsed.Route, officialClimb, matchPolicy.EndpointRadiusM) {
+			passage := climb.Climb{Route: parsed.Route.Slice(matched.StartIndex, matched.EndIndex)}
+			if sample := official_climb.NormalizeProfile(passage); len(sample) > 0 {
+				elevationSamples = append(elevationSamples, sample)
+			}
+			passages = append(passages, passage)
+		}
+	}
+	profile.Route = medianPassageRoute(passages)
+	profile.Sections = profileRoute(aggregate.DistanceM, official_climb.MedianProfile(elevationSamples)).ProfileSections(profilePolicy)
+	return profile
+}
+
+// medianPassageRoute picks the recorded route of the passage whose length is the median: robust to
+// one drifted ride.
+func medianPassageRoute(passages []climb.Climb) []geodist.Coord {
+	if len(passages) == 0 {
+		return nil
+	}
+	distances := make([]float64, len(passages))
+	for index, passage := range passages {
+		distances[index] = passage.Distances[len(passage.Distances)-1] - passage.Distances[0]
+	}
+	median := official_climb.Median(distances)
+	best := passages[0]
+	bestDiff := math.Abs(distances[0] - median)
+	for index := 1; index < len(passages); index++ {
+		if diff := math.Abs(distances[index] - median); diff < bestDiff {
+			best = passages[index]
+			bestDiff = diff
+		}
+	}
+	return best.Coords
+}
+
+// profileRoute lays the merged elevation samples on a uniform axis as long as the climb.
+func profileRoute(distanceM float64, elevations []float64) climb.Route {
+	if len(elevations) < 2 {
+		return climb.Route{}
+	}
+	route := climb.Route{Distances: make([]float64, len(elevations)), Elevations: elevations}
+	for index := range elevations {
+		route.Distances[index] = distanceM * float64(index) / float64(len(elevations)-1)
+	}
+	return route
+}