recipes: add cake form size scaling for ingredient multiplier

Allow recipes to specify a default pan shape (round, rectangular, gugelhupf)
with dimensions. On the recipe page, users can enter their own pan size to
auto-calculate an ingredient multiplier based on the 2D area ratio.

src/lib/components/recipes/IngredientsPage.svelte

@@ -120,9 +120,71 @@ const isEnglish = $derived(data.lang === 'en');
 const labels = $derived({
 	portions: isEnglish ? 'Portions:' : 'Portionen:',
 	adjustAmount: isEnglish ? 'Adjust Amount:' : 'Menge anpassen:',
-	ingredients: isEnglish ? 'Ingredients' : 'Zutaten'
+	ingredients: isEnglish ? 'Ingredients' : 'Zutaten',
+	cakeForm: isEnglish ? 'Cake form:' : 'Backform:',
+	round: isEnglish ? 'Round' : 'Rund',
+	rectangular: isEnglish ? 'Rectangular' : 'Rechteckig',
+	diameter: isEnglish ? 'Diameter' : 'Durchmesser',
+	width: isEnglish ? 'Width' : 'Breite',
+	length: isEnglish ? 'Length' : 'Länge',
+	factor: isEnglish ? 'Factor' : 'Faktor',
 });
 
+// Cake form scaling
+const hasDefaultForm = $derived(!!data.defaultForm?.shape);
+let userFormShape = $state(data.defaultForm?.shape || 'round');
+let userFormDiameter = $state(data.defaultForm?.diameter || 26);
+let userFormWidth = $state(data.defaultForm?.width || 20);
+let userFormLength = $state(data.defaultForm?.length || 30);
+let userFormInnerDiameter = $state(data.defaultForm?.innerDiameter || 8);
+
+function calcArea(shape, diameter, width, length, innerDiameter) {
+	if (shape === 'round') return Math.PI * (diameter / 2) ** 2;
+	if (shape === 'gugelhupf') return Math.PI * ((diameter / 2) ** 2 - (innerDiameter / 2) ** 2);
+	return width * length;
+}
+
+const defaultFormArea = $derived(
+	hasDefaultForm
+		? calcArea(data.defaultForm.shape, data.defaultForm.diameter, data.defaultForm.width, data.defaultForm.length, data.defaultForm.innerDiameter)
+		: 1
+);
+
+const userFormArea = $derived(
+	calcArea(userFormShape, userFormDiameter, userFormWidth, userFormLength, userFormInnerDiameter)
+);
+
+const formMultiplier = $derived(
+	hasDefaultForm && defaultFormArea > 0 ? userFormArea / defaultFormArea : 1
+);
+
+// Track whether multiplier is driven by form or manual buttons
+let formDriven = $state(false);
+
+function applyFormMultiplier() {
+	formDriven = true;
+}
+
+// Reactively update multiplier when form dimensions change and form is driving
+$effect(() => {
+	if (formDriven) {
+		multiplier = formMultiplier;
+		updateUrl(multiplier);
+	}
+});
+
+function updateUrl(value) {
+	if (browser) {
+		const url = new URL(window.location);
+		if (value === 1) {
+			url.searchParams.delete('multiplier');
+		} else {
+			url.searchParams.set('multiplier', String(value));
+		}
+		window.history.replaceState({}, '', url);
+	}
+}
+
 // Multiplier button options
 const multiplierOptions = [
 	{ value: 0.5, label: '<sup>1</sup>/<sub>2</sub>x' },
@@ -176,15 +238,8 @@ function handleMultiplierClick(event, value) {
 	if (browser) {
 		event.preventDefault();
 		multiplier = value;
-		
+		formDriven = false;
-		// Update URL without reloading
+		updateUrl(value);
-		const url = new URL(window.location);
-		if (value === 1) {
-			url.searchParams.delete('multiplier');
-		} else {
-			url.searchParams.set('multiplier', value);
-		}
-		window.history.replaceState({}, '', url);
 	}
 	// If no JS, form will submit normally
 }
@@ -194,15 +249,8 @@ function handleCustomInput(event) {
 		const value = parseFloat(event.target.value);
 		if (!isNaN(value) && value > 0) {
 			multiplier = value;
-			
+			formDriven = false;
-			// Update URL without reloading
+			updateUrl(value);
-			const url = new URL(window.location);
-			if (value === 1) {
-				url.searchParams.delete('multiplier');
-			} else {
-				url.searchParams.set('multiplier', value);
-			}
-			window.history.replaceState({}, '', url);
 		}
 	}
 }
@@ -386,6 +434,53 @@ function adjust_amount(string, multiplier){
 	box-shadow: none;
 }
 
+.cake-form {
+	margin-block: 1rem;
+}
+.cake-form-shape {
+	display: flex;
+	gap: 0.75rem;
+	justify-content: center;
+	margin-bottom: 0.5rem;
+}
+.cake-form-shape label {
+	cursor: pointer;
+	padding: 0.25em 0.6em;
+	border-radius: var(--radius-sm);
+	transition: var(--transition-fast);
+}
+.cake-form-shape input[type="radio"] {
+	display: none;
+}
+.cake-form-selected {
+	background-color: var(--nord9);
+	color: white;
+	font-weight: bold;
+}
+.cake-form-inputs {
+	display: flex;
+	gap: 1rem;
+	justify-content: center;
+	align-items: center;
+	flex-wrap: wrap;
+}
+.cake-form-num {
+	width: 3.5em;
+	padding: 0.2em 0.4em;
+	border: 1px solid var(--nord4);
+	border-radius: var(--radius-sm);
+	text-align: center;
+	font-size: inherit;
+	background: transparent;
+	color: inherit;
+}
+.cake-form-factor {
+	text-align: center;
+	margin-top: 0.4rem;
+	font-weight: bold;
+	color: var(--nord10);
+}
+
 </style>
 {#if data.ingredients}
 <div class=ingredients>
@@ -419,6 +514,42 @@ function adjust_amount(string, multiplier){
 	</span>
 </form>
 
+{#if hasDefaultForm}
+<div class="cake-form">
+	<h3>{labels.cakeForm}</h3>
+	<div class="cake-form-shape">
+		<label class:cake-form-selected={userFormShape === 'round'}>
+			<input type="radio" name="userFormShape" value="round" bind:group={userFormShape} onchange={applyFormMultiplier} />
+			{labels.round}
+		</label>
+		<label class:cake-form-selected={userFormShape === 'rectangular'}>
+			<input type="radio" name="userFormShape" value="rectangular" bind:group={userFormShape} onchange={applyFormMultiplier} />
+			{labels.rectangular}
+		</label>
+		{#if data.defaultForm?.shape === 'gugelhupf'}
+		<label class:cake-form-selected={userFormShape === 'gugelhupf'}>
+			<input type="radio" name="userFormShape" value="gugelhupf" bind:group={userFormShape} onchange={applyFormMultiplier} />
+			Gugelhupf
+		</label>
+		{/if}
+	</div>
+	<div class="cake-form-inputs">
+		{#if userFormShape === 'round'}
+			<label>{labels.diameter}: <input type="number" min="1" step="1" class="cake-form-num" bind:value={userFormDiameter} oninput={applyFormMultiplier} /> cm</label>
+		{:else if userFormShape === 'rectangular'}
+			<label>{labels.width}: <input type="number" min="1" step="1" class="cake-form-num" bind:value={userFormWidth} oninput={applyFormMultiplier} /> cm</label>
+			<label>{labels.length}: <input type="number" min="1" step="1" class="cake-form-num" bind:value={userFormLength} oninput={applyFormMultiplier} /> cm</label>
+		{:else if userFormShape === 'gugelhupf'}
+			<label>{isEnglish ? 'Outer Ø' : 'Außen-Ø'}: <input type="number" min="1" step="1" class="cake-form-num" bind:value={userFormDiameter} oninput={applyFormMultiplier} /> cm</label>
+			<label>{isEnglish ? 'Inner Ø' : 'Innen-Ø'}: <input type="number" min="1" step="1" class="cake-form-num" bind:value={userFormInnerDiameter} oninput={applyFormMultiplier} /> cm</label>
+		{/if}
+	</div>
+	{#if formDriven}
+		<div class="cake-form-factor">→ {labels.factor}: {formMultiplier.toFixed(2)}x</div>
+	{/if}
+</div>
+{/if}
+
 <h2>{labels.ingredients}</h2>
 {#each flattenedIngredients as list, listIndex}
 {#if list.name}

src/models/Recipe.ts

@@ -28,6 +28,13 @@ const RecipeSchema = new mongoose.Schema(
 
 	},
     portions :{type:String, default: ""},
+    defaultForm: {
+      shape: { type: String, enum: ['round', 'rectangular', 'gugelhupf'] },
+      diameter: { type: Number },
+      width: { type: Number },
+      length: { type: Number },
+      innerDiameter: { type: Number },
+    },
     cooking: {type:String, default: ""},
     total_time : {type:String, default: ""},
     ingredients: [{

src/routes/[recipeLang=recipeLang]/edit/[name]/+page.svelte

@@ -82,6 +82,7 @@
 	let datecreated = $state(data.recipe.datecreated);
 	let datemodified = $state(new Date());
 	let isBaseRecipe = $state(data.recipe.isBaseRecipe || false);
+	let defaultForm = $state(data.recipe.defaultForm ? { ...data.recipe.defaultForm } : null);
 	let ingredients = $state(data.recipe.ingredients || []);
 	let instructions = $state(data.recipe.instructions || []);
 
@@ -142,6 +143,7 @@
 			preamble,
 			note,
 			isBaseRecipe,
+			defaultForm,
 		};
 	});
 
@@ -343,6 +345,29 @@
 			background-color: var(--nord6-dark);
 		}
 	}
+	.form-size-section {
+		max-width: 600px;
+		margin: 1rem auto;
+		text-align: center;
+	}
+	.form-size-controls {
+		display: flex;
+		gap: 1.5rem;
+		justify-content: center;
+		margin-bottom: 0.5rem;
+	}
+	.form-size-inputs {
+		display: flex;
+		gap: 1rem;
+		justify-content: center;
+		align-items: center;
+		flex-wrap: wrap;
+	}
+	.form-size-inputs input[type="number"] {
+		width: 4em;
+		display: inline;
+		margin: 0 0.3em;
+	}
 	.error-message {
 		background: var(--nord11);
 		color: var(--nord6);
@@ -422,6 +447,7 @@
 	<input type="hidden" name="icon" value={card_data.icon} />
 	<input type="hidden" name="portions" value={portions_local} />
 	<input type="hidden" name="isBaseRecipe" value={isBaseRecipe ? "true" : "false"} />
+	<input type="hidden" name="defaultForm_json" value={defaultForm ? JSON.stringify(defaultForm) : ''} />
 
 	<div style="text-align: center; margin: 1rem;">
 		<Toggle
@@ -430,6 +456,44 @@
 		/>
 	</div>
 
+	<!-- Default Form (Cake Pan) -->
+	<div class="form-size-section">
+		<h3>Backform (Standard):</h3>
+		<div class="form-size-controls">
+			<label>
+				<input type="radio" name="formShape" value="none" checked={!defaultForm} onchange={() => { defaultForm = null; }} />
+				Keine
+			</label>
+			<label>
+				<input type="radio" name="formShape" value="round" checked={defaultForm?.shape === 'round'} onchange={() => { defaultForm = { shape: 'round', diameter: defaultForm?.diameter || 26 }; }} />
+				Rund
+			</label>
+			<label>
+				<input type="radio" name="formShape" value="rectangular" checked={defaultForm?.shape === 'rectangular'} onchange={() => { defaultForm = { shape: 'rectangular', width: defaultForm?.width || 20, length: defaultForm?.length || 30 }; }} />
+				Rechteckig
+			</label>
+			<label>
+				<input type="radio" name="formShape" value="gugelhupf" checked={defaultForm?.shape === 'gugelhupf'} onchange={() => { defaultForm = { shape: 'gugelhupf', diameter: defaultForm?.diameter || 24, innerDiameter: defaultForm?.innerDiameter || 8 }; }} />
+				Gugelhupf
+			</label>
+		</div>
+		{#if defaultForm?.shape === 'round'}
+			<div class="form-size-inputs">
+				<label>Durchmesser: <input type="number" min="1" step="1" bind:value={defaultForm.diameter} /> cm</label>
+			</div>
+		{:else if defaultForm?.shape === 'rectangular'}
+			<div class="form-size-inputs">
+				<label>Breite: <input type="number" min="1" step="1" bind:value={defaultForm.width} /> cm</label>
+				<label>Länge: <input type="number" min="1" step="1" bind:value={defaultForm.length} /> cm</label>
+			</div>
+		{:else if defaultForm?.shape === 'gugelhupf'}
+			<div class="form-size-inputs">
+				<label>Außen-Ø: <input type="number" min="1" step="1" bind:value={defaultForm.diameter} /> cm</label>
+				<label>Innen-Ø: <input type="number" min="1" step="1" bind:value={defaultForm.innerDiameter} /> cm</label>
+			</div>
+		{/if}
+	</div>
+
 	<!-- Recipe Note Component -->
 	<EditRecipeNote bind:note />
 	<input type="hidden" name="note" value={note} />

src/types/types.ts

@@ -140,6 +140,13 @@ export type RecipeModelType = {
 	  final: string;
 	}
   portions?: string;
+  defaultForm?: {
+    shape: 'round' | 'rectangular' | 'gugelhupf';
+    diameter?: number;
+    width?: number;
+    length?: number;
+    innerDiameter?: number;
+  };
   cooking?: string;
   total_time?: string;
   ingredients?: IngredientItem[];

src/utils/recipeFormHelpers.ts

@@ -48,6 +48,15 @@ export interface RecipeFormData {
 		caption: string;
 	}>;
 
+	// Cake form
+	defaultForm?: {
+		shape: 'round' | 'rectangular' | 'gugelhupf';
+		diameter?: number;
+		width?: number;
+		length?: number;
+		innerDiameter?: number;
+	};
+
 	// Metadata
 	isBaseRecipe?: boolean;
 	datecreated?: Date;
@@ -144,6 +153,20 @@ export function extractRecipeFromFormData(formData: FormData): RecipeFormData {
 		}
 	}
 
+	// Default form (cake pan size)
+	let defaultForm: RecipeFormData['defaultForm'] = undefined;
+	const defaultFormData = formData.get('defaultForm_json')?.toString();
+	if (defaultFormData) {
+		try {
+			const parsed = JSON.parse(defaultFormData);
+			if (parsed && parsed.shape) {
+				defaultForm = parsed;
+			}
+		} catch (error) {
+			console.error('Failed to parse defaultForm:', error);
+		}
+	}
+
 	// Metadata
 	const isBaseRecipe = formData.get('isBaseRecipe') === 'true';
 	const datecreated = formData.get('datecreated')
@@ -189,6 +212,7 @@ export function extractRecipeFromFormData(formData: FormData): RecipeFormData {
 		instructions,
 		add_info,
 		images,
+		defaultForm,
 		isBaseRecipe,
 		datecreated,
 		datemodified,
@@ -343,6 +367,7 @@ export function serializeRecipeForDatabase(data: RecipeFormData): any {
 	if (data.preamble) recipe.preamble = data.preamble;
 	if (data.addendum) recipe.addendum = data.addendum;
 	if (data.note) recipe.note = data.note;
+	if (data.defaultForm) recipe.defaultForm = data.defaultForm;
 
 	// Additional info
 	if (data.add_info && Object.keys(data.add_info).length > 0) {