feat(photos): добавить пресеты кривой и починить переключение фото

- PCHIP для предпросмотра и серверного рендера
- пресеты всех каналов в профиле, импорт и экспорт
- мерж настроек auth без потери разделов
- сохранение вкладки и правок текущего фото при переключении

backend/internal/photos/edit.go

@@ -317,8 +317,9 @@ func clampInt(v, min, max int) int {
 }
 
 // curveLUT builds a 256-entry lookup table from the control points of a
-// curve. The first and last points extend to the edges of the range, and the
-// values in between are interpolated linearly.
+// curve. The first and last points extend to the edges of the range as flat
+// shelves, and the values in between are interpolated with a monotone cubic
+// Hermite spline (PCHIP, Fritsch–Carlson).
 func curveLUT(points []CurvePoint) [256]uint8 {
 	var lut [256]uint8
 	pts := normalizeCurve(points)
@@ -328,16 +329,71 @@ func curveLUT(points []CurvePoint) [256]uint8 {
 		}
 		return lut
 	}
+	tangents := curveTangents(pts)
 	for i := 0; i < 256; i++ {
 		x := float64(i) / 255
-		lut[i] = uint8(math.Round(clamp01(curveEval(pts, x)) * 255))
+		lut[i] = uint8(math.Round(clamp01(curveEvalWithTangents(pts, tangents, x)) * 255))
 	}
 	return lut
 }
 
-// curveEval evaluates the curve at x using linear interpolation between the
-// surrounding control points.
+// curveTangents returns the PCHIP slopes at the control points. Interior
+// tangents are weighted harmonic means of the neighbouring slopes; endpoint
+// tangents use the one-sided three-point formula with the Fritsch–Carlson
+// shape-preserving clamp.
+func curveTangents(points []CurvePoint) []float64 {
+	n := len(points)
+	if n < 2 {
+		return nil
+	}
+	h := make([]float64, n-1)
+	delta := make([]float64, n-1)
+	for i := 0; i < n-1; i++ {
+		h[i] = points[i+1].X - points[i].X
+		delta[i] = (points[i+1].Y - points[i].Y) / h[i]
+	}
+	m := make([]float64, n)
+	if n == 2 {
+		m[0] = delta[0]
+		m[1] = delta[0]
+		return m
+	}
+	m[0] = endpointTangent(h[0], h[1], delta[0], delta[1])
+	m[n-1] = endpointTangent(h[n-2], h[n-3], delta[n-2], delta[n-3])
+	for i := 1; i < n-1; i++ {
+		if delta[i-1]*delta[i] <= 0 {
+			m[i] = 0
+			continue
+		}
+		w1 := 2*h[i] + h[i-1]
+		w2 := h[i] + 2*h[i-1]
+		m[i] = (w1 + w2) / (w1/delta[i-1] + w2/delta[i])
+	}
+	return m
+}
+
+// endpointTangent is the one-sided endpoint slope of the PCHIP spline.
+func endpointTangent(h0, h1, d0, d1 float64) float64 {
+	m := ((2*h0+h1)*d0 - h0*d1) / (h0 + h1)
+	if m*d0 <= 0 {
+		return 0
+	}
+	if d0*d1 < 0 && math.Abs(m) > math.Abs(3*d0) {
+		return 3 * d0
+	}
+	return m
+}
+
+// curveEval evaluates the curve at x with a monotone cubic Hermite spline.
+// Outside the first and last points the value is constant.
 func curveEval(points []CurvePoint, x float64) float64 {
+	if len(points) < 2 {
+		return x
+	}
+	return curveEvalWithTangents(points, curveTangents(points), x)
+}
+
+func curveEvalWithTangents(points []CurvePoint, tangents []float64, x float64) float64 {
 	if x <= points[0].X {
 		return points[0].Y
 	}
@@ -345,19 +401,23 @@ func curveEval(points []CurvePoint, x float64) float64 {
 	if x >= last.X {
 		return last.Y
 	}
-	for i := 1; i < len(points); i++ {
-		if x > points[i].X {
-			continue
-		}
-		x0, y0 := points[i-1].X, points[i-1].Y
-		x1, y1 := points[i].X, points[i].Y
-		if x1-x0 < 1e-9 {
-			return y1
-		}
-		t := (x - x0) / (x1 - x0)
-		return y0 + t*(y1-y0)
+	i := 1
+	for i < len(points)-1 && x > points[i].X {
+		i++
 	}
-	return last.Y
+	p0, p1 := points[i-1], points[i]
+	h := p1.X - p0.X
+	if h < 1e-9 {
+		return p1.Y
+	}
+	t := (x - p0.X) / h
+	t2 := t * t
+	t3 := t2 * t
+	h00 := 2*t3 - 3*t2 + 1
+	h10 := t3 - 2*t2 + t
+	h01 := -2*t3 + 3*t2
+	h11 := t3 - t2
+	return h00*p0.Y + h10*h*tangents[i-1] + h01*p1.Y + h11*h*tangents[i]
 }
 
 // lightAdjuster holds the precomputed factors of the light adjustments. The