Checkpoint packed spine spacing

public/js/webgl-book-shape-lab.js

@@ -64,12 +64,23 @@ const NORMAL_FLIP_DURATION = 1800;
 const FAST_FLIP_DURATION = 900;
 const FAST_FLIP_COUNT = 10;
 const FAST_FLIP_OVERLAP = 5;
+const OPEN_SEAM_GAP = 0.003;
+const SUPPORT_ANGLE_STEPS = 720;
+const SUPPORT_ANGLE_CANDIDATES = Array.from({ length: SUPPORT_ANGLE_STEPS }, (_, sample) => {
+    const angle = sample / SUPPORT_ANGLE_STEPS * Math.PI * 2;
+    return {
+        angle,
+        cos: Math.cos(angle),
+        sin: Math.sin(angle)
+    };
+});
 
 let readingProgress = readInitialProgress();
 let pageCount = readInitialPageCount();
 let lastLengthError = 0;
 let lastSpacingError = 0;
 let lastBookModel = null;
+let activeSpineHalf = 0.08;
 let activeFlips = [];
 let pendingPageFlips = 0;
 progressInput.value = readingProgress.toFixed(3);
@@ -188,11 +199,14 @@ function rebuildBook() {
     const pageWidth = 1.62;
     const pageDepth = 2.24;
     const bundleCount = Math.max(4, Math.round(pageCount / 10));
-    const spineWidth = Math.max(0.16, bundleCount * BOOK_PROFILE.bundleSpacing);
+    const spineWidth = calculateSpineWidth(bundleCount);
-    const lines = simulatePageLines(bundleCount, pageWidth, spineWidth);
+    const leftCount = calculateLeftBundleCount(bundleCount);
+    const bundleSpacing = calculateBundleSpacing(bundleCount, spineWidth, leftCount);
+    activeSpineHalf = spineWidth * 0.5;
+    const lines = simulatePageLines(bundleCount, pageWidth, spineWidth, bundleSpacing, leftCount);
     lastLengthError = measureLineLengthError(lines, pageWidth);
-    lastSpacingError = measureStackSpacingError(lines);
+    lastSpacingError = measureStackSpacingError(lines, bundleSpacing);
-    lastBookModel = { coverDepth, pageWidth, pageDepth, bundleCount, spineWidth, lines };
+    lastBookModel = { coverDepth, pageWidth, pageDepth, bundleCount, spineWidth, bundleSpacing, lines };
 
     addCoverAssembly(pageWidth, coverDepth, coverThickness, spineWidth);
     addClothSpine(pageDepth, spineWidth);
@@ -323,17 +337,76 @@ function spineCurvePoint(t, spineWidth) {
     };
 }
 
-function simulatePageLines(bundleCount, pageWidth, spineWidth) {
+function calculateSpineWidth(bundleCount) {
+    const minimumWidth = 0.16;
+    if (bundleCount <= 1) return minimumWidth;
+    const targetArcLength = (bundleCount - 1) * BOOK_PROFILE.bundleSpacing + OPEN_SEAM_GAP;
+    let low = minimumWidth;
+    let high = Math.max(minimumWidth, bundleCount * BOOK_PROFILE.bundleSpacing * 1.4);
+    while (measureSpineArcLength(high) < targetArcLength) {
+        high *= 1.25;
+    }
+    for (let i = 0; i < 24; i += 1) {
+        const mid = (low + high) * 0.5;
+        if (measureSpineArcLength(mid) < targetArcLength) {
+            low = mid;
+        } else {
+            high = mid;
+        }
+    }
+    return high;
+}
+
+function calculateBundleSpacing(bundleCount, spineWidth, leftCount) {
+    const rightCount = bundleCount - leftCount;
+    const stackIntervals = Math.max(0, leftCount - 1) + Math.max(0, rightCount - 1);
+    if (stackIntervals <= 0) return BOOK_PROFILE.bundleSpacing;
+    return Math.max(0.001, (measureSpineArcLength(spineWidth) - OPEN_SEAM_GAP) / stackIntervals);
+}
+
+function measureSpineArcLength(spineWidth) {
+    const steps = 240;
+    let length = 0;
+    let previous = spineCurvePoint(0, spineWidth);
+    for (let i = 1; i <= steps; i += 1) {
+        const point = spineCurvePoint(i / steps, spineWidth);
+        length += Math.hypot(point.x - previous.x, point.y - previous.y);
+        previous = point;
+    }
+    return length;
+}
+
+function calculateLeftBundleCount(bundleCount) {
+    return THREE.MathUtils.clamp(Math.round(bundleCount * readingProgress), 0, bundleCount);
+}
+
+function simulatePageLines(bundleCount, pageWidth, spineWidth, bundleSpacing, leftCount) {
     const lines = [];
     const segments = 24;
     const stepLength = pageWidth / segments;
     const entries = [];
-    const spineSamples = sampleSpineByArc(bundleCount, spineWidth);
+    const spineArc = buildSpineArcSamples(spineWidth);
-    const leftLimit = Math.min(bundleCount - 2, Math.floor((bundleCount - 1) * readingProgress));
+    const rightCount = bundleCount - leftCount;
+    const leftSpan = Math.max(0, leftCount - 1) * bundleSpacing;
+    const rightSpan = Math.max(0, rightCount - 1) * bundleSpacing;
+    const seamLeftLength = leftSpan;
+    const seamRightLength = seamLeftLength + OPEN_SEAM_GAP;
     for (let index = 0; index < bundleCount; index += 1) {
-        const t = spineSamples[index].t;
+        const side = index < leftCount ? -1 : 1;
-        const side = index <= leftLimit ? -1 : 1;
+        const sideRank = side < 0 ? index : index - leftCount;
-        entries.push({ index, t, side });
+        const arcLength = side < 0
+            ? seamLeftLength - (leftCount - 1 - sideRank) * bundleSpacing
+            : seamRightLength + sideRank * bundleSpacing;
+        const point = pointAtSpineArcLength(spineArc, arcLength);
+        entries.push({ index, t: point.t, side });
+    }
+    if (leftCount === 0) {
+        const point = pointAtSpineArcLength(spineArc, seamLeftLength);
+        entries.push({ index: -1, t: point.t, side: -1, isHairPage: true });
+    }
+    if (rightCount === 0) {
+        const point = pointAtSpineArcLength(spineArc, seamRightLength);
+        entries.push({ index: bundleCount, t: point.t, side: 1, isHairPage: true });
     }
     [-1, 1].forEach((side) => {
         const sideEntries = entries.filter((entry) => entry.side === side);
@@ -351,9 +424,9 @@ function simulatePageLines(bundleCount, pageWidth, spineWidth) {
         let lowerLine = null;
         sideEntries.forEach((entry, rank) => {
             const anchor = spineCurvePoint(entry.t, spineWidth);
-            const target = restingTarget(side, pageWidth, rank, sideEntries.length);
+            const target = restingTarget(side, pageWidth, rank, sideEntries.length, bundleSpacing);
-            const points = buildSupportSolvedLine(anchor, target, lowerLine, side, segments, stepLength, bundleCount);
+            const points = buildSupportSolvedLine(anchor, target, lowerLine, side, segments, stepLength, bundleCount, bundleSpacing);
-            const line = { index: entry.index, t: entry.t, side, anchor, points, endpoint: points[points.length - 1] };
+            const line = { index: entry.index, t: entry.t, side, anchor, points, endpoint: points[points.length - 1], isHairPage: entry.isHairPage === true };
             lines.push(line);
             lowerLine = line;
         });
@@ -371,7 +444,7 @@ function measureLineLengthError(lines, pageWidth) {
     }, 0);
 }
 
-function measureStackSpacingError(lines) {
+function measureStackSpacingError(lines, bundleSpacing) {
     let maxViolation = 0;
     [-1, 1].forEach((side) => {
         const sideLines = lines
@@ -383,14 +456,14 @@ function measureStackSpacingError(lines) {
             for (let col = 1; col < upper.points.length; col += 1) {
                 const closest = closestPointOnPolyline(upper.points[col], lower.points);
                 const distance = Math.hypot(upper.points[col].x - closest.x, upper.points[col].y - closest.y);
-                maxViolation = Math.max(maxViolation, Math.max(0, BOOK_PROFILE.bundleSpacing - distance));
+                maxViolation = Math.max(maxViolation, Math.max(0, bundleSpacing - distance));
             }
         }
     });
     return maxViolation;
 }
 
-function sampleSpineByArc(count, spineWidth) {
+function buildSpineArcSamples(spineWidth) {
     const samples = [];
     const steps = 240;
     let length = 0;
@@ -403,21 +476,27 @@ function sampleSpineByArc(count, spineWidth) {
         samples.push({ point, length });
         previous = point;
     }
-    const points = [];
+    return { samples, length, spineWidth };
-    for (let i = 0; i < count; i += 1) {
+}
-        const target = count === 1 ? length * 0.5 : length * (i / (count - 1));
+
-        const found = samples.findIndex((sample) => sample.length >= target);
+function pointAtSpineArcLength(spineArc, targetLength) {
-        if (found <= 0) {
+    const target = THREE.MathUtils.clamp(targetLength, 0, spineArc.length);
-            points.push(samples[0].point);
+    let low = 0;
-            continue;
+    let high = spineArc.samples.length - 1;
+    while (low < high) {
+        const mid = Math.floor((low + high) * 0.5);
+        if (spineArc.samples[mid].length < target) {
+            low = mid + 1;
+        } else {
+            high = mid;
         }
-        const before = samples[found - 1];
+    }
-        const after = samples[found];
+    if (low <= 0) return spineArc.samples[0].point;
+    const before = spineArc.samples[low - 1];
+    const after = spineArc.samples[low];
     const span = after.length - before.length || 1;
     const t = THREE.MathUtils.lerp(before.point.t, after.point.t, (target - before.length) / span);
-        points.push(spineCurvePoint(t, spineWidth));
+    return spineCurvePoint(t, spineArc.spineWidth);
-    }
-    return points;
 }
 
 function initialPageLine(anchor, target, segments) {
@@ -433,47 +512,54 @@ function initialPageLine(anchor, target, segments) {
     return points;
 }
 
-function restingTarget(side, pageWidth, rank, sideCount) {
+function restingTarget(side, pageWidth, rank, sideCount, bundleSpacing) {
     const local = sideCount <= 1 ? 0 : rank / (sideCount - 1);
     const foreCurve = 0.11 * Math.sin(Math.PI * local);
     const x = side * (pageWidth - foreCurve);
-    const y = BOOK_PROFILE.coverThickness + BOOK_PROFILE.paperContactOffset + rank * BOOK_PROFILE.bundleSpacing + 0.002 * Math.sin(Math.PI * local);
+    const y = BOOK_PROFILE.coverThickness + BOOK_PROFILE.paperContactOffset + rank * bundleSpacing + 0.002 * Math.sin(Math.PI * local);
     return { x, y };
 }
 
-function buildSupportSolvedLine(anchor, target, lowerLine, side, segments, stepLength, bundleCount) {
+function buildSupportSolvedLine(anchor, target, lowerLine, side, segments, stepLength, bundleCount, bundleSpacing) {
     const points = [{ x: anchor.x, y: anchor.y }];
     let tangent = coverTangentAtX(anchor.x, side);
     for (let index = 1; index <= segments; index += 1) {
         const u = index / segments;
         const supportTangent = lowerLine ? lineTangentAt(lowerLine.points, index) : coverTangentAtX(points[index - 1].x, side);
-        const point = chooseClosestSupportedPoint(points[index - 1], tangent, supportTangent, target, lowerLine, index, side, stepLength, bundleCount, u);
+        const point = chooseClosestSupportedPoint(points[index - 1], tangent, supportTangent, target, lowerLine, index, side, stepLength, bundleCount, bundleSpacing, u);
         points.push(point);
         tangent = normalizedVector(point.x - points[index - 1].x, point.y - points[index - 1].y);
     }
     return points;
 }
 
-function chooseClosestSupportedPoint(previous, tangent, supportTangent, target, lowerLine, index, side, stepLength, bundleCount, u) {
+function chooseClosestSupportedPoint(previous, tangent, supportTangent, target, lowerLine, index, side, stepLength, bundleCount, bundleSpacing, u) {
     const blendTangent = normalizedVector(tangent.x + supportTangent.x * 2, tangent.y + supportTangent.y * 2);
     const angleHint = Math.atan2(blendTangent.y, blendTangent.x);
     let best = null;
-    let fallback = null;
+    for (const sample of SUPPORT_ANGLE_CANDIDATES) {
-    for (let sample = 0; sample < 720; sample += 1) {
-        const angle = sample / 720 * Math.PI * 2;
         const candidate = {
-            x: previous.x + Math.cos(angle) * stepLength,
+            x: previous.x + sample.cos * stepLength,
-            y: previous.y + Math.sin(angle) * stepLength
+            y: previous.y + sample.sin * stepLength
         };
-        const score = scoreSupportedPoint(candidate, previous, tangent, supportTangent, angle, angleHint, target, lowerLine, index, side, bundleCount, u);
+        const score = scoreSupportedPoint(candidate, previous, tangent, supportTangent, sample.angle, angleHint, target, lowerLine, index, side, bundleCount, bundleSpacing, u);
         if (best === null || score < best.score) best = { point: candidate, score };
-        const fallbackScore = scoreSupportedPoint(candidate, previous, tangent, supportTangent, angle, angleHint, target, lowerLine, index, side, bundleCount, u, true);
+    }
+    if (Number.isFinite(best?.score)) return best.point;
+
+    let fallback = null;
+    for (const sample of SUPPORT_ANGLE_CANDIDATES) {
+        const candidate = {
+            x: previous.x + sample.cos * stepLength,
+            y: previous.y + sample.sin * stepLength
+        };
+        const fallbackScore = scoreSupportedPoint(candidate, previous, tangent, supportTangent, sample.angle, angleHint, target, lowerLine, index, side, bundleCount, bundleSpacing, u, true);
         if (fallback === null || fallbackScore < fallback.score) fallback = { point: candidate, score: fallbackScore };
     }
-    return Number.isFinite(best?.score) ? best.point : fallback.point;
+    return fallback.point;
 }
 
-function scoreSupportedPoint(candidate, previous, tangent, supportTangent, angle, angleHint, target, lowerLine, index, side, bundleCount, u, allowViolation = false) {
+function scoreSupportedPoint(candidate, previous, tangent, supportTangent, angle, angleHint, target, lowerLine, index, side, bundleCount, bundleSpacing, u, allowViolation = false) {
     const backward = Math.max(0, side * (previous.x - candidate.x));
     if (!allowViolation && backward > 0.00001) return Number.POSITIVE_INFINITY;
 
@@ -482,9 +568,9 @@ function scoreSupportedPoint(candidate, previous, tangent, supportTangent, angle
     if (lowerLine) {
         const closest = closestPointOnPolyline(candidate, lowerLine.points);
         const closestDistance = Math.hypot(candidate.x - closest.x, candidate.y - closest.y);
-        supportViolation = Math.max(0, BOOK_PROFILE.bundleSpacing - closestDistance) + Math.max(0, closest.y - candidate.y);
+        supportViolation = Math.max(0, bundleSpacing - closestDistance) + Math.max(0, closest.y - candidate.y);
         if (!allowViolation && supportViolation > 0.00001) return Number.POSITIVE_INFINITY;
-        supportError = closestDistance - BOOK_PROFILE.bundleSpacing;
+        supportError = closestDistance - bundleSpacing;
     } else {
         const floor = coverTopYAtX(candidate.x) + coverClearance(bundleCount);
         supportViolation = Math.max(0, floor - candidate.y);
@@ -636,6 +722,7 @@ function coverClearance(bundleCount) {
 }
 
 function enforceStackConstraints(lines, stepLength, bundleCount) {
+    const bundleSpacing = lastBookModel?.bundleSpacing ?? BOOK_PROFILE.bundleSpacing;
     const iterations = 44;
     [-1, 1].forEach((side) => {
         const sideLines = lines
@@ -655,8 +742,8 @@ function enforceStackConstraints(lines, stepLength, bundleCount) {
                 const upper = sideLines[row];
                 for (let col = 1; col < upper.points.length; col += 1) {
                     const normal = upwardNormalAt(lower.points, col);
-                    const targetX = lower.points[col].x + normal.x * BOOK_PROFILE.bundleSpacing;
+                    const targetX = lower.points[col].x + normal.x * bundleSpacing;
-                    const targetY = lower.points[col].y + normal.y * BOOK_PROFILE.bundleSpacing;
+                    const targetY = lower.points[col].y + normal.y * bundleSpacing;
                     upper.points[col].x = THREE.MathUtils.lerp(upper.points[col].x, targetX, 0.28);
                     upper.points[col].y = Math.max(upper.points[col].y, THREE.MathUtils.lerp(upper.points[col].y, targetY, 0.42));
                 }
@@ -720,7 +807,7 @@ function coverTopYAtX(x) {
 }
 
 function currentSpineHalf() {
-    return Math.max(0.16, Math.round(pageCount / 10) * BOOK_PROFILE.bundleSpacing) * 0.5;
+    return activeSpineHalf;
 }
 
 function addSimulatedStackBodies(lines, depth) {
@@ -735,9 +822,10 @@ function addSimulatedStackBodies(lines, depth) {
 
 function createSinglePageBodyLines(line) {
     const bundleCount = Math.max(4, Math.round(pageCount / 10));
+    const bundleSpacing = lastBookModel?.bundleSpacing ?? BOOK_PROFILE.bundleSpacing;
     const supportPoints = line.points.map((point) => ({
         x: point.x,
-        y: Math.max(coverTopYAtX(point.x) + coverClearance(bundleCount) + BOOK_PROFILE.singlePageCoverGap, point.y - BOOK_PROFILE.bundleSpacing)
+        y: Math.max(coverTopYAtX(point.x) + coverClearance(bundleCount) + BOOK_PROFILE.singlePageCoverGap, point.y - bundleSpacing)
     }));
     return [
         { ...line, points: supportPoints, endpoint: supportPoints[supportPoints.length - 1] },
@@ -951,10 +1039,11 @@ function buildFlippingPageSurface(sourceLine, destinationLine, direction, t, pag
     const baseAngle = startAngle + direction * Math.PI * t;
     const lift = Math.sin(Math.PI * t);
     const curlStrength = direction * 0.48 * lift;
+    const sourceLengths = cumulativeLineLengths(sourceLine.points);
     const surface = [];
     for (let widthIndex = 0; widthIndex <= widthSegments; widthIndex += 1) {
         const u = widthIndex / widthSegments;
-        const radius = lastBookModel.pageWidth * u;
+        const radius = sourceLengths[widthIndex];
         const row = [];
         for (let depthIndex = 0; depthIndex <= depthSegments; depthIndex += 1) {
             const v = depthIndex / depthSegments;
@@ -977,6 +1066,16 @@ function buildFlippingPageSurface(sourceLine, destinationLine, direction, t, pag
     return surface;
 }
 
+function cumulativeLineLengths(points) {
+    const lengths = [0];
+    for (let index = 1; index < points.length; index += 1) {
+        const previous = points[index - 1];
+        const current = points[index];
+        lengths.push(lengths[index - 1] + Math.hypot(current.x - previous.x, current.y - previous.y));
+    }
+    return lengths;
+}
+
 function createRestingPageSurface(points, depthSegments, zFront, zBack) {
     return points.map((point) => {
         const row = [];

public/webgl-book-shape-lab.html

@@ -74,6 +74,6 @@
         <button id="fast_forward" type="button">Fast Forward</button>
         <output id="flip_count">0 / 10</output>
     </div>
-    <script type="module" src="/js/webgl-book-shape-lab.js?v=stack-texture-lines-5"></script>
+    <script type="module" src="/js/webgl-book-shape-lab.js?v=packed-spine-seam-2"></script>
 </body>
 </html>