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app/utils/gradeSystems.ts

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+/**
+ * German Grading System Utilities
+ * German grades: 1 (best) to 6 (worst)
+ */
+
+export type GradeSystem = "percentage" | "german" | "us-letter";
+
+export interface GradeSystemConfig {
+  type: GradeSystem;
+  displayName: string;
+  description: string;
+}
+
+export const GRADE_SYSTEMS: Record<GradeSystem, GradeSystemConfig> = {
+  percentage: {
+    type: "percentage",
+    displayName: "Percentage (0-100%)",
+    description: "Standard percentage-based grading",
+  },
+  german: {
+    type: "german",
+    displayName: "German (1-6)",
+    description: "1 = sehr gut (very good), 6 = ungenügend (insufficient)",
+  },
+  "us-letter": {
+    type: "us-letter",
+    displayName: "US Letter (A-F)",
+    description: "A = 90-100%, F = below 60%",
+  },
+};
+
+/**
+ * Convert percentage (0-100) to German grade (1-6)
+ * German grading scale:
+ * 1 (sehr gut / very good): 92-100%
+ * 2 (gut / good): 81-91%
+ * 3 (befriedigend / satisfactory): 67-80%
+ * 4 (ausreichend / sufficient): 50-66%
+ * 5 (mangelhaft / deficient): 30-49%
+ * 6 (ungenügend / insufficient): 0-29%
+ */
+export function percentageToGermanGrade(percentage: number): number {
+  if (percentage >= 92) return 1.0;
+  if (percentage >= 81) return 2.0;
+  if (percentage >= 67) return 3.0;
+  if (percentage >= 50) return 4.0;
+  if (percentage >= 30) return 5.0;
+  return 6.0;
+}
+
+/**
+ * Convert percentage to German grade with decimal precision
+ * Uses linear interpolation within each grade range
+ */
+export function percentageToGermanGradeDetailed(percentage: number): number {
+  if (percentage >= 92) {
+    // 1.0 - 1.5 range (92-100%)
+    const position = (100 - percentage) / (100 - 92);
+    return 1.0 + position * 0.5;
+  } else if (percentage >= 81) {
+    // 1.5 - 2.5 range (81-91%)
+    const position = (92 - percentage) / (92 - 81);
+    return 1.5 + position * 1.0;
+  } else if (percentage >= 67) {
+    // 2.5 - 3.5 range (67-80%)
+    const position = (81 - percentage) / (81 - 67);
+    return 2.5 + position * 1.0;
+  } else if (percentage >= 50) {
+    // 3.5 - 4.5 range (50-66%)
+    const position = (67 - percentage) / (67 - 50);
+    return 3.5 + position * 1.0;
+  } else if (percentage >= 30) {
+    // 4.5 - 5.5 range (30-49%)
+    const position = (50 - percentage) / (50 - 30);
+    return 4.5 + position * 1.0;
+  } else {
+    // 5.5 - 6.0 range (0-29%)
+    const position = (30 - percentage) / 30;
+    return 5.5 + position * 0.5;
+  }
+}
+
+/**
+ * Convert German grade (1-6) to approximate percentage
+ */
+export function germanGradeToPercentage(grade: number): number {
+  if (grade <= 1.5) return 92 + (1.5 - grade) * 16; // 92-100%
+  if (grade <= 2.5) return 81 + (2.5 - grade) * 11; // 81-91%
+  if (grade <= 3.5) return 67 + (3.5 - grade) * 14; // 67-80%
+  if (grade <= 4.5) return 50 + (4.5 - grade) * 17; // 50-66%
+  if (grade <= 5.5) return 30 + (5.5 - grade) * 20; // 30-49%
+  return Math.max(0, 30 - (grade - 5.5) * 60); // 0-29%
+}
+
+/**
+ * Get German grade description
+ */
+export function getGermanGradeDescription(grade: number): string {
+  if (grade <= 1.5) return "sehr gut (very good)";
+  if (grade <= 2.5) return "gut (good)";
+  if (grade <= 3.5) return "befriedigend (satisfactory)";
+  if (grade <= 4.5) return "ausreichend (sufficient)";
+  if (grade <= 5.5) return "mangelhaft (deficient)";
+  return "ungenügend (insufficient)";
+}
+
+/**
+ * Get color for German grade
+ */
+export function getGermanGradeColor(grade: number): string {
+  if (grade <= 2.0) return "text-green-600";
+  if (grade <= 3.0) return "text-blue-600";
+  if (grade <= 4.0) return "text-yellow-600";
+  if (grade <= 5.0) return "text-orange-600";
+  return "text-red-600";
+}
+
+/**
+ * Format grade based on system
+ */
+export function formatGradeBySystem(
+  percentage: number,
+  system: GradeSystem,
+  decimals: number = 2
+): string {
+  switch (system) {
+    case "german": {
+      const germanGrade = percentageToGermanGradeDetailed(percentage);
+      return germanGrade.toFixed(1);
+    }
+    case "us-letter": {
+      if (percentage >= 90) return "A";
+      if (percentage >= 80) return "B";
+      if (percentage >= 70) return "C";
+      if (percentage >= 60) return "D";
+      return "F";
+    }
+    case "percentage":
+    default:
+      return `${percentage.toFixed(decimals)}%`;
+  }
+}
+
+/**
+ * Get color for grade based on system
+ */
+export function getGradeColorBySystem(
+  percentage: number,
+  system: GradeSystem
+): string {
+  switch (system) {
+    case "german": {
+      const germanGrade = percentageToGermanGradeDetailed(percentage);
+      return getGermanGradeColor(germanGrade);
+    }
+    case "percentage":
+    case "us-letter":
+    default:
+      if (percentage >= 90) return "text-green-600";
+      if (percentage >= 80) return "text-blue-600";
+      if (percentage >= 70) return "text-yellow-600";
+      if (percentage >= 60) return "text-orange-600";
+      return "text-red-600";
+  }
+}
+
+/**
+ * Get description for grade
+ */
+export function getGradeDescription(
+  percentage: number,
+  system: GradeSystem
+): string | null {
+  if (system === "german") {
+    const germanGrade = percentageToGermanGradeDetailed(percentage);
+    return getGermanGradeDescription(germanGrade);
+  }
+  return null;
+}