diff --git a/src/components/auth/AutoLogin.jsx b/src/components/auth/AutoLogin.jsx
index b3dcbb6e..5de9ea85 100644
--- a/src/components/auth/AutoLogin.jsx
+++ b/src/components/auth/AutoLogin.jsx
@@ -8,6 +8,7 @@ import { useRecoilState } from 'recoil'
 import { useAxios } from '@/hooks/useAxios'
 import { globalLocaleStore } from '@/store/localeAtom'
 import { useRouter } from 'next/navigation'
+import Cookies from 'js-cookie'
 
 import GlobalSpinner from '@/components/common/spinner/GlobalSpinner'
 
@@ -31,6 +32,7 @@ export default function AutoLoginPage({ autoLoginParam }) {
       setIsLoading(false)
       if (response.data) {
         const res = response.data
+        if (res.sessionId) Cookies.set('sessionId', res.sessionId)
         const result = { ...res, storeLvl: res.groupId === '60000' ? '1' : '2', pwdInitYn: 'Y' }
         setSession(result)
         setSessionState(result)
diff --git a/src/components/auth/Login.jsx b/src/components/auth/Login.jsx
index 7a6ba957..d20f5320 100644
--- a/src/components/auth/Login.jsx
+++ b/src/components/auth/Login.jsx
@@ -48,6 +48,7 @@ export default function Login() {
             post({ url: '/api/login/v1.0/user', data: { loginId: res.data } }).then((response) => {
               setIsLoading(false)
               if (response) {
+                if (response.sessionId) Cookies.set('sessionId', response.sessionId)
                 const result = { ...response, storeLvl: response.groupId === '60000' ? '1' : '2', pwdInitYn: 'Y' }
                 setSession(result)
                 setSessionState(result)
@@ -107,6 +108,7 @@ export default function Login() {
         if (res) {
           setIsLoading(false)
           if (res.data.result.resultCode === 'S') {
+            if (res.data.sessionId) Cookies.set('sessionId', res.data.sessionId)
             setSession(res.data.data)
             setSessionState(res.data.data)
             // ID SAVE 체크되어 있는 경우, 쿠키 저장
diff --git a/src/components/header/Header.jsx b/src/components/header/Header.jsx
index 561b8e47..8c2ccbff 100644
--- a/src/components/header/Header.jsx
+++ b/src/components/header/Header.jsx
@@ -8,7 +8,8 @@ import { useRecoilState, useRecoilValue, useResetRecoilState } from 'recoil'
 import { dimmedStore, sessionStore } from '@/store/commonAtom'
 
 import { useMessage } from '@/hooks/useMessage'
-import { checkSession, logout } from '@/lib/authActions'
+import { checkSession } from '@/lib/authActions'
+import { useLogout } from '@/hooks/useLogout'
 
 import QSelectBox from '@/components/common/select/QSelectBox'
 
@@ -49,6 +50,7 @@ export default function Header(props) {
   const [stuffSearch, setStuffSearch] = useRecoilState(stuffSearchState)
 
   const { closeAll } = usePopup()
+  const { logoutProcess } = useLogout()
 
   const { userSession } = props
   const [sessionState, setSessionState] = useRecoilState(sessionStore)
@@ -372,14 +374,7 @@ export default function Header(props) {
               <div className="sign-out-box">
                 <button
                   className="sign-out"
-                  onClick={() => {
-                    setStuffSearch({
-                      ...stuffSearch,
-                      code: 'DELETE',
-                    })
-                    logout()
-                    router.replace('/login', undefined, { shallow: true })
-                  }}
+                  onClick={() => logoutProcess()}
                 >
                   {getMessage('header.logout')}
                 </button>
diff --git a/src/components/main/ChangePasswordPop.jsx b/src/components/main/ChangePasswordPop.jsx
index 28dc537c..58c22d69 100644
--- a/src/components/main/ChangePasswordPop.jsx
+++ b/src/components/main/ChangePasswordPop.jsx
@@ -5,10 +5,10 @@ import { sessionStore } from '@/store/commonAtom'
 import { useRecoilState, useRecoilValue } from 'recoil'
 import { useAxios } from '@/hooks/useAxios'
 import { globalLocaleStore } from '@/store/localeAtom'
-import { login, logout, setSession } from '@/lib/authActions'
+import { login, setSession } from '@/lib/authActions'
 import { useSwal } from '@/hooks/useSwal'
 import { QcastContext } from '@/app/QcastProvider'
-import { useRouter } from 'next/navigation'
+import { useLogout } from '@/hooks/useLogout'
 
 export default function ChangePasswordPop(props) {
   const globalLocaleState = useRecoilValue(globalLocaleStore)
@@ -19,7 +19,7 @@ export default function ChangePasswordPop(props) {
   const { patch } = useAxios(globalLocaleState)
   const { getMessage } = useMessage()
   const [sessionState, setSessionState] = useRecoilState(sessionStore)
-  const router = useRouter()
+  const { logoutProcess } = useLogout()
   const formInitValue = {
     password1: '',
     password2: '',
@@ -129,15 +129,13 @@ export default function ChangePasswordPop(props) {
           }
         } else {
           setIsGlobalLoading(false)
-          logout()
-          router.replace('/login', undefined, { shallow: true })
+          logoutProcess()
           console.log('code not 200 error')
         }
       })
       .catch((error) => {
         setIsGlobalLoading(false)
-        logout()
-        router.replace('/login', undefined, { shallow: true })
+        logoutProcess()
         console.log('catch::::::::', error)
       })
   }
@@ -209,10 +207,7 @@ export default function ChangePasswordPop(props) {
               <button
                 type="button"
                 className="btn-origin grey"
-                onClick={() => {
-                  logout()
-                  router.replace('/login', undefined, { shallow: true })
-                }}
+                onClick={() => logoutProcess()}
               >
                 {getMessage('main.popup.login.btn2')}
               </button>
diff --git a/src/components/management/StuffDetail.jsx b/src/components/management/StuffDetail.jsx
index 12eef9ff..341e537d 100644
--- a/src/components/management/StuffDetail.jsx
+++ b/src/components/management/StuffDetail.jsx
@@ -1868,7 +1868,7 @@ export default function StuffDetail() {
                         })}
                         {/* 라디오끝 */}
                         <div className="input-wrap mr5" style={{ width: '545px' }}>
-                          <input type="text" className="input-light" {...form.register('objectName')} />
+                          <input type="text" className="input-light" maxLength={50} {...form.register('objectName')} />
                         </div>
                         <div className="select-wrap" style={{ width: '120px' }}>
                           <Select
@@ -2461,7 +2461,7 @@ export default function StuffDetail() {
                             })}
                             {/* 상세라디오끝 */}
                             <div className="input-wrap mr5" style={{ width: '545px' }}>
-                              <input type="text" className="input-light" {...form.register('objectName')} />
+                              <input type="text" className="input-light" maxLength={50} {...form.register('objectName')} />
                             </div>
                             <div className="select-wrap" style={{ width: '120px' }}>
                               <Select
diff --git a/src/hooks/module/useTrestle.js b/src/hooks/module/useTrestle.js
index 19da5b4e..411fc118 100644
--- a/src/hooks/module/useTrestle.js
+++ b/src/hooks/module/useTrestle.js
@@ -799,6 +799,7 @@ export const useTrestle = () => {
       const parent = canvas.getObjects().find((obj) => obj.id === surface.parentId)
       const { directionText, roofMaterial, moduleCompass, surfaceCompass } = parent
       const slope = Number(roofMaterial.pitch)
+      const angle = Number(roofMaterial.angle) || getDegreeByChon(slope)
       const roofMaterialIndex = parent.roofMaterial.index
       const { nameJp: roofMaterialIdMulti } = roofMaterial
       const moduleSelection = moduleSelectionData?.roofConstructions?.find((construction) => construction.roofIndex === roofMaterialIndex)
@@ -836,7 +837,7 @@ export const useTrestle = () => {
         supportMeaker,
         slope: +roofSizeSet === 3 ? 0 : slope,
         classType: currentAngleType === 'slope' ? '0' : '1',
-        angle: +roofSizeSet === 3 ? 0 : getDegreeByChon(slope),
+        angle: +roofSizeSet === 3 ? 0 : angle,
         azimuth: getAzimuth(parent),
         moduleList,
       }
@@ -1122,7 +1123,7 @@ export const useTrestle = () => {
       return
     }
     const roof = canvas.getObjects().find((obj) => obj.id === surface.parentId)
-    const degree = getDegreeByChon(roof.roofMaterial.pitch)
+    const degree = Number(roof.roofMaterial.angle) || getDegreeByChon(roof.roofMaterial.pitch)
     rackIntvlPct = rackIntvlPct === 0 ? 1 : rackIntvlPct // 0인 경우 1로 변경
     rackIntvlPct = 100 / rackIntvlPct // 퍼센트로 변경
     const moduleLeft = lastX ?? left
diff --git a/src/hooks/useLogout.js b/src/hooks/useLogout.js
new file mode 100644
index 00000000..08ef1cc3
--- /dev/null
+++ b/src/hooks/useLogout.js
@@ -0,0 +1,44 @@
+import { useRecoilState, useRecoilValue } from 'recoil'
+import { sessionStore } from '@/store/commonAtom'
+import { globalLocaleStore } from '@/store/localeAtom'
+import { stuffSearchState } from '@/store/stuffAtom'
+import { useAxios } from '@/hooks/useAxios'
+import { logout } from '@/lib/authActions'
+import Cookies from 'js-cookie'
+
+/**
+ * 로그아웃 처리 Hook
+ * - 로그아웃 API 호출 후 성공/실패 상관없이 로그아웃 처리
+ * - Header, ChangePasswordPop 등에서 공통으로 사용
+ */
+export function useLogout() {
+  const [sessionState] = useRecoilState(sessionStore)
+  const [stuffSearch, setStuffSearch] = useRecoilState(stuffSearchState)
+  const globalLocaleState = useRecoilValue(globalLocaleStore)
+  const { promisePost } = useAxios(globalLocaleState)
+
+  const logoutProcess = async () => {
+    const param = {
+      loginId: sessionState.userId,
+      requestId: Cookies.get('sessionId'), // 로그인 시 저장한 sessionId
+    }
+
+    // 로그아웃 API 호출 (실패해도 로그아웃 진행)
+    try {
+      await promisePost({ url: '/api/login/v1.0/logout', data: param })
+    } catch (error) {
+      console.log('logout api error:', error)
+    }
+
+    // 물건검색 상태 초기화
+    setStuffSearch({
+      ...stuffSearch,
+      code: 'DELETE',
+    })
+    Cookies.remove('sessionId') // sessionId 쿠키 삭제
+    await logout() // iron-session 세션 파기
+    window.location.href = '/login' // 로그인 페이지로 이동 (full reload)
+  }
+
+  return { logoutProcess }
+}
diff --git a/src/lib/skeletons/SkeletonBuilder.ts b/src/lib/skeletons/SkeletonBuilder.ts
index 01ddb95b..6466782d 100644
--- a/src/lib/skeletons/SkeletonBuilder.ts
+++ b/src/lib/skeletons/SkeletonBuilder.ts
@@ -253,13 +253,12 @@ export default class SkeletonBuilder {
 	}
 
 	private static CorrectBisectorDirection(bisector: LineParametric2d, beginNextVertex: Vertex, endPreviousVertex: Vertex, beginEdge: Edge, endEdge: Edge) {
-		const beginEdge2 = beginNextVertex.PreviousEdge;
-		const endEdge2 = endPreviousVertex.NextEdge;
+		// Use the vertex's actual edges — chain edges can become stale
+		// when previous iterations of MultiSplitEvent modify the LAV
+		const actualBeginEdge = beginNextVertex.PreviousEdge;
+		const actualEndEdge = endPreviousVertex.NextEdge;
 
-		if (beginEdge !== beginEdge2 || endEdge !== endEdge2)
-			throw new Error();
-
-		if (beginEdge.Norm.Dot(endEdge.Norm) < -0.97) {
+		if (actualBeginEdge.Norm.Dot(actualEndEdge.Norm) < -0.97) {
 			const n1 = PrimitiveUtils.FromTo(endPreviousVertex.Point, bisector.A).Normalized();
 			const n2 = PrimitiveUtils.FromTo(bisector.A, beginNextVertex.Point).Normalized();
 			const bisectorPrediction = this.CalcVectorBisector(n1, n2);
@@ -887,7 +886,7 @@ export default class SkeletonBuilder {
 	private static GetEdgeInLav(lav: CircularList<Vertex>, oppositeEdge: Edge): Vertex {
 		for (const node of lav.Iterate())
 			if (oppositeEdge === node.PreviousEdge ||
-				oppositeEdge === node.Previous.Next)
+				oppositeEdge === (node.Previous as Vertex).NextEdge)
 				return node;
 
 		return null;
diff --git a/src/util/skeleton-utils.js b/src/util/skeleton-utils.js
index 17374edd..ae92a224 100644
--- a/src/util/skeleton-utils.js
+++ b/src/util/skeleton-utils.js
@@ -16,6 +16,39 @@ import wallLine from '@/components/floor-plan/modal/wallLineOffset/type/WallLine
  */
 const EPSILON = 0.1
 
+/**
+ * 오목(concave) 폴리곤인지 판별합니다.
+ * cross product의 부호가 혼재하면 오목 폴리곤입니다.
+ */
+const isConcavePolygon = (points) => {
+  if (!points || points.length < 4) return false
+  let positive = 0, negative = 0
+  for (let i = 0; i < points.length; i++) {
+    const prev = points[(i - 1 + points.length) % points.length]
+    const curr = points[i]
+    const next = points[(i + 1) % points.length]
+    const cross = (curr.x - prev.x) * (next.y - curr.y) - (curr.y - prev.y) * (next.x - curr.x)
+    if (cross > 0) positive++
+    else if (cross < 0) negative++
+  }
+  return positive > 0 && negative > 0
+}
+
+/**
+ * 오목 폴리곤에만 미세한 perturbation을 적용하여 동시 이벤트(MultiSplitEvent)를 방지합니다.
+ * 대칭적 변 길이(예: 45.5, 45.5)가 동일 거리의 이벤트를 만들어 LAV 불일치 오류를 유발하므로
+ * 각 꼭짓점에 인덱스 기반 미세 오프셋을 적용하면 이벤트가 개별 SplitEvent로 처리됩니다.
+ * 볼록 폴리곤은 이 문제가 없으므로 원본을 그대로 반환합니다.
+ */
+const perturbPolygonPoints = (points, eps = 1e-4) => {
+  if (!points || points.length < 3) return points
+  if (!isConcavePolygon(points)) return points
+  return points.map((p, i) => ({
+    x: p.x + (i + 1) * eps,
+    y: p.y + (i + 1) * eps
+  }))
+}
+
 export const drawSkeletonRidgeRoof = (roofId, canvas, textMode) => {
 
   // 2. 스켈레톤 생성 및 그리기
@@ -503,11 +536,13 @@ export const skeletonBuilder = (roofId, canvas, textMode) => {
   // changRoofLinePoints를 roof.skeletonPoints에 저장 (roof.points 원본은 유지)
   roof.skeletonPoints = changRoofLinePoints.map(p => ({ x: p.x, y: p.y }))
 
-  const geoJSONPolygon = toGeoJSON(changRoofLinePoints)
+  const perturbedPoints = perturbPolygonPoints(changRoofLinePoints)
+  const geoJSONPolygon = toGeoJSON(perturbedPoints)
 
   try {
     // SkeletonBuilder는 닫히지 않은 폴리곤을 기대하므로 마지막 점 제거
     geoJSONPolygon.pop()
+    console.log('[SkeletonBuilder] geoJSONPolygon:', JSON.stringify(geoJSONPolygon, null, 2))
     const skeleton = SkeletonBuilder.BuildFromGeoJSON([[geoJSONPolygon]])
 
     // 스켈레톤 데이터를 기반으로 내부선 생성