feat(core): 일체기초 footings for 2·3주형 with per-footing pile grid

- Columns closer than one footing length (10400) share a 일체기초 whose
  length is the outer-column distance + 10400, centred between them (spec §4.6).
- Pile grid is computed from each footing's length (rows across 8150,
  pile count along the length from (length − 1400) / 2250 + 1).
- Blinding concrete follows each combined footing.

Co-Authored-By: Claude Haiku 5.5 <noreply@anthropic.com>

src/core/geometry.ts

@@ -240,21 +240,23 @@ export function buildPier(input: PierInput): PierModel {
   const pileLength = input.pileLengthMm / 1000;
   const pileTip = input.footingBottomEl - pileLength;
 
-  for (const s of colS) {
-    if (input.foundationType === '현장타설말뚝') {
+  if (input.foundationType === '현장타설말뚝') {
+    for (const s of colS) {
       piles.push({ s, n: 0, top: input.footingBottomEl, bottom: pileTip, diameter: DIM.columnDiameter });
-      continue;
     }
-    footings.push({ s, top: footingTop, bottom: input.footingBottomEl, length: DIM.footingL, width: DIM.footingW });
-    blindings.push({
-      s,
-      top: input.footingBottomEl,
-      length: DIM.footingL + DIM.blindingMargin,
-      width: DIM.footingW + DIM.blindingMargin,
-      thickness: DIM.blindingT,
-    });
-    if (input.foundationType === '말뚝기초') {
-      piles.push(...pilesFor(s, input.footingBottomEl, pileLength));
+  } else {
+    for (const g of footingGroups(colS)) {
+      footings.push({ s: g.s, top: footingTop, bottom: input.footingBottomEl, length: g.length, width: DIM.footingW });
+      blindings.push({
+        s: g.s,
+        top: input.footingBottomEl,
+        length: g.length + DIM.blindingMargin,
+        width: DIM.footingW + DIM.blindingMargin,
+        thickness: DIM.blindingT,
+      });
+      if (input.foundationType === '말뚝기초') {
+        piles.push(...pilesFor(g.s, input.footingBottomEl, pileLength, g.length));
+      }
     }
   }
 
@@ -306,7 +308,7 @@ export function buildPier(input: PierInput): PierModel {
       columnHeight: levelBottom - columns[0].bottom,
       soilCover: input.groundEl - (input.foundationType === '현장타설말뚝' ? input.footingBottomEl : footingTop),
       pileCount: piles.length,
-      pileLayout: input.foundationType === '말뚝기초' ? pileLayoutText() : null,
+      pileLayout: input.foundationType === '말뚝기초' ? pileLayoutText(footings[0].length) : null,
       pileTipEl: piles.length ? pileTip : null,
       blockHeightFront,
       blockHeightBack,
@@ -326,30 +328,47 @@ function segmentTop(segments: Segment[], s: number): number {
   return hit.top;
 }
 
+/**
+ * Footings (spec §4.6). Adjacent columns closer than one footing length share a 일체기초 whose length is
+ * the distance between its outer columns + DIM.footingL, centred between them. Other columns get their own footing.
+ */
+export function footingGroups(colS: number[]): { s: number; length: number }[] {
+  const groups: number[][] = [];
+  for (const s of [...colS].sort((a, b) => a - b)) {
+    const last = groups[groups.length - 1];
+    if (last && s - last[last.length - 1] < DIM.footingL) last.push(s);
+    else groups.push([s]);
+  }
+  return groups.map((g) => ({
+    s: (g[0] + g[g.length - 1]) / 2,
+    length: g[g.length - 1] - g[0] + DIM.footingL,
+  }));
+}
+
 /**
  * Piles under one footing (spec §4.6): rows across the footing width, piles along the length,
  * both with an end distance of 0.7 m and an even spacing that never exceeds 2.25 m.
  */
-export function pileGrid(): { countS: number; countN: number; spacingS: number; spacingN: number } {
+export function pileGrid(footingLength: number = DIM.footingL): { countS: number; countN: number; spacingS: number; spacingN: number } {
   const span = (size: number) => Math.floor((size - 2 * DIM.pileEnd) / DIM.pileSpacing) + 1;
-  const countS = span(DIM.footingL);
+  const countS = span(footingLength);
   const countN = span(DIM.footingW);
   return {
     countS,
     countN,
-    spacingS: (DIM.footingL - 2 * DIM.pileEnd) / (countS - 1),
+    spacingS: (footingLength - 2 * DIM.pileEnd) / (countS - 1),
     spacingN: (DIM.footingW - 2 * DIM.pileEnd) / (countN - 1),
   };
 }
 
 /** Display string such as "4@2250 × 3@2250 = 20본" (gaps along the length × gaps across the width). */
-export function pileLayoutText(): string {
-  const g = pileGrid();
+export function pileLayoutText(footingLength: number = DIM.footingL): string {
+  const g = pileGrid(footingLength);
   return `${g.countS - 1}@${Math.round(g.spacingS * 1000)} × ${g.countN - 1}@${Math.round(g.spacingN * 1000)} = ${g.countS * g.countN}본`;
 }
 
-export function pilesFor(s: number, topEl: number, length: number): PileModel[] {
-  const { countS, countN, spacingS, spacingN } = pileGrid();
+export function pilesFor(s: number, topEl: number, length: number, footingLength: number = DIM.footingL): PileModel[] {
+  const { countS, countN, spacingS, spacingN } = pileGrid(footingLength);
   const out: PileModel[] = [];
   for (let i = 0; i < countS; i++) {
     for (let j = 0; j < countN; j++) {