{"topic":{"id":6314,"title":"4.2.2 的这个公式，v − (N · v) · N 意思是 N 和 v 的点积再乘 N 吗？","slug":"topic","userId":304,"categoryId":56,"createdAt":"2023-10-08 08:45:24.245372","bumpedAt":"2023-10-08 12:43:19.978794","views":232,"postsCount":2,"highestPostNumber":2,"likeCount":0,"closed":true,"pinned":false,"pinnedGlobally":false,"pinnedAt":null,"pinnedUntil":null,"isBanner":false,"excerpt":"4.2.2 的这个公式，意思是 N 和 v 的点积再乘 N 吗？","deletedAt":null,"isAnonymous":false,"isPrivate":false,"isMembersOnly":false,"category":{"id":56,"name":"计算机图形学","slug":"cg","color":"92278F"},"author":{"id":304,"username":"rarabura","name":"raraBura","avatarUrl":null},"realAuthor":{"id":304,"username":"rarabura","name":"raraBura","avatarUrl":null},"tags":[]},"posts":[{"id":13044,"postNumber":1,"raw":"4.2.2 的这个公式，\n![屏幕截图 2023-10-08 164457|690x177](/uploads/image/89/95/899534339e91e41f7908911be205b57aebf7abd5b22fb9b6ab5da8e9fa70d3cf.avif)\n意思是 N 和 v 的点积再乘 N 吗？","cooked":"

4.2.2 的这个公式，
\n $\"屏幕截图$
\n意思是 N 和 v 的点积再乘 N 吗？

\n","createdAt":"2023-10-08 08:45:24.350771","updatedAt":"2023-10-09 15:23:55.541359","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":28,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":2,"publicVersion":2,"deletedAt":null,"isAnonymous":false,"user":{"id":304,"username":"rarabura","name":"raraBura","avatarUrl":null,"admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":13090,"postNumber":2,"raw":"是的。\n\n你可以这么想：首先我们的目的是让顶点只沿它的切向移动，而原本的方向 $\\mathbf{v}$ 可以分解为切向和法向两部分；现在我们知道顶点处的法线（沿法向的单位向量），那么想要求出方向 $\\mathbf{v}$ 的切向分量自然要用 $\\mathbf{v}$ 减去它的法向分量。\n\n而根据线性代数的知识，点积 $\\mathbf{N\\cdot v}$ 是法向分量的模长， $(\\mathbf{N\\cdot v})\\cdot\\mathbf{N}$ 就是在法向上的投影，即法向分量。用 $\\mathbf{v}$ 减去它，就得到了我们要的切向分量。","cooked":"

是的。

你可以这么想：首先我们的目的是让顶点只沿它的切向移动，而原本的方向 $\\mathbf{v}$ 可以分解为切向和法向两部分；现在我们知道顶点处的法线（沿法向的单位向量），那么想要求出方向 $\\mathbf{v}$ 的切向分量自然要用 $\\mathbf{v}$ 减去它的法向分量。

而根据线性代数的知识，点积 $\\mathbf{N\\cdot v}$ 是法向分量的模长， $(\\mathbf{N\\cdot v})\\cdot\\mathbf{N}$ 就是在法向上的投影，即法向分量。用 $\\mathbf{v}$ 减去它，就得到了我们要的切向分量。

\n","createdAt":"2023-10-08 12:43:19.978794","updatedAt":"2023-10-08 12:43:19.978794","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":162,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":1381,"username":"greyishsong","name":"greyishsong","avatarUrl":"/uploads/image/da/bc/dabc731b0311f59850625bbeb55ed969fcfac0430c5ef0f68441e5466b7aa496.avif","admin":false,"moderator":true,"signatureRaw":null,"signatureCooked":null}}],"hasMore":false,"lastReadPostNumber":1,"hasUrlPostNumber":false}