pkg/calc: fix Deltas wrap on rectangular maps + add signed ShortestDelta

The pre-existing `Deltas` helper used the height to wrap the x-axis,
which silently produced wrong values on any rectangular galaxy
(`w != h`). Square galaxies — the only configuration the engine
ships today — masked the bug, so it stayed in tree.

`Deltas` is now a thin wrapper around the new `ShortestDelta(a, b,
size)`, which returns the signed per-axis shortest delta on a 1-D
circle (range `(-size/2, size/2]`). The signed flavour is what the
Phase 19 ship-group renderer needs to draw an IncomingGroup
trajectory across the torus seam; `Deltas` continues to return the
pair of absolute deltas for distance computation.

Adds `pkg/calc/map_test.go` with table-driven coverage for both
helpers, including a regression that exercises the rectangular
case the bug was hiding behind, and the half-circumference
tie-break.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

pkg/calc/map.go

@@ -2,19 +2,38 @@ package calc
 
 import "math"
 
-// shortest distance between points on torus map
+// ShortDistance returns the shortest Euclidean distance between two
+// points on a torus of size w×h.
 func ShortDistance(w, h uint32, x1, y1, x2, y2 float64) float64 {
 	return math.Hypot(Deltas(w, h, x1, y1, x2, y2))
 }
 
+// Deltas returns the per-axis absolute distance between two points on
+// a torus of size w×h. Each axis wraps independently: the x-axis
+// against width w, the y-axis against height h. The returned values
+// are always non-negative; combine via math.Hypot for the Euclidean
+// torus distance, or use [ShortestDelta] when the signed direction
+// matters (for example when drawing a wrap-aware line).
 func Deltas(w, h uint32, x1, y1, x2, y2 float64) (float64, float64) {
-	dx := math.Abs(x2 - x1)
-	dy := math.Abs(y2 - y1)
-	if dx > float64(w/2) {
-		dx = float64(h) - dx
+	return math.Abs(ShortestDelta(x1, x2, w)), math.Abs(ShortestDelta(y1, y2, h))
 }
-	if dy > float64(h/2) {
-		dy = float64(h) - dy
+
+// ShortestDelta returns the signed delta (b - a) on a 1-D circle of
+// circumference size, picking whichever direction has the shorter
+// absolute distance. The result lies in (-size/2, size/2]: at exactly
+// half the circumference the function returns +size/2 so the tie-case
+// is deterministic regardless of input order.
+func ShortestDelta(a, b float64, size uint32) float64 {
+	if size == 0 {
+		return b - a
 	}
-	return dx, dy
+	s := float64(size)
+	d := math.Mod(b-a, s)
+	half := s / 2
+	if d > half {
+		d -= s
+	} else if d <= -half {
+		d += s
+	}
+	return d
 }

pkg/calc/map_test.go

@@ -0,0 +1,57 @@
+package calc_test
+
+import (
+	"math"
+	"testing"
+
+	"galaxy/calc"
+)
+
+func TestShortestDelta(t *testing.T) {
+	cases := []struct {
+		name string
+		a, b float64
+		size uint32
+		want float64
+	}{
+		{"identity", 5, 5, 100, 0},
+		{"forward small", 10, 30, 100, 20},
+		{"backward small", 30, 10, 100, -20},
+		{"wraps right edge", 95, 5, 100, 10},
+		{"wraps left edge", 5, 95, 100, -10},
+		{"exact half wraps positive", 0, 50, 100, 50},
+		{"slight beyond half goes negative", 0, 51, 100, -49},
+		{"size zero is degenerate identity", 5, 30, 0, 25},
+	}
+	for _, tc := range cases {
+		t.Run(tc.name, func(t *testing.T) {
+			got := calc.ShortestDelta(tc.a, tc.b, tc.size)
+			if got != tc.want {
+				t.Fatalf("ShortestDelta(%v, %v, %d) = %v, want %v",
+					tc.a, tc.b, tc.size, got, tc.want)
+			}
+		})
+	}
+}
+
+// TestDeltasRectangularGalaxy guards against the pre-Phase-19 bug
+// where the x-axis wrap used the height instead of the width on
+// rectangular maps.
+func TestDeltasRectangularGalaxy(t *testing.T) {
+	w, h := uint32(100), uint32(50)
+	dx, dy := calc.Deltas(w, h, 95, 10, 5, 15)
+	if dx != 10 {
+		t.Errorf("dx = %v, want 10 (wrap distance on width 100)", dx)
+	}
+	if dy != 5 {
+		t.Errorf("dy = %v, want 5 (no wrap on height 50)", dy)
+	}
+}
+
+func TestShortDistanceTorus(t *testing.T) {
+	got := calc.ShortDistance(100, 100, 95, 95, 5, 5)
+	want := math.Hypot(10, 10)
+	if math.Abs(got-want) > 1e-9 {
+		t.Fatalf("ShortDistance through wrap = %v, want %v", got, want)
+	}
+}