{"id":3186,"date":"2023-09-01T00:00:13","date_gmt":"2023-08-31T16:00:13","guid":{"rendered":"https:\/\/www.caiqinyi.cn\/?p=3186"},"modified":"2025-02-26T10:59:09","modified_gmt":"2025-02-26T02:59:09","slug":"auto_lod_group","status":"publish","type":"post","link":"https:\/\/www.caiqinyi.cn\/index.php\/2023\/09\/01\/auto_lod_group\/","title":{"rendered":"Auto LOD Group"},"content":{"rendered":"<p><script type=\"text\/javascript\" async src=\"https:\/\/www.caiqinyi.cn\/wp-content\/MathJax\/MathJax.js?config=TeX-AMS_CHTML\">\n<\/script><br \/>\n<script type=\"text\/x-mathjax-config\">\n    MathJax.Hub.Config({\n        tex2jax: {inlineMath: [['$','$']]},\n        TeX: {equationNumbers: {autoNumber: [\"AMS\"], useLabelIds: true}},\n        \"HTML-CSS\": {linebreaks: {automatic: true}},\n        SVG: {linebreaks: {automatic: true}}\n    });\n<\/script><\/p>\n<p>\u5b66\u5b8c\u4ee3\u6570\u62d3\u6251\u5df2\u7ecf\u6709\u4e00\u6bb5\u65f6\u95f4\u4e86, \u5c3d\u7ba1\u5185\u5bb9\u5df2\u7ecf\u5fd8\u4e86\u4e0d\u5c11\u4e86, \u4f46\u4e00\u76f4\u5fc3\u5fc3\u5ff5\u5ff5\u5c06\u4ee3\u6570\u62d3\u6251\u7684\u601d\u60f3\u5e94\u7528\u81f3\u6e38\u620f\u5f00\u53d1\u4e2d. \u7ec8\u4e8e\u5728\u524d\u6bb5\u65f6\u95f4, \u81ea\u5df1\u5b8c\u6210\u4e86\u4e00\u4e2a\u540d\u4e3aAuto LOD Group\u7684UE5\u63d2\u4ef6\u521d\u7248, \u5229\u7528\u95ed\u66f2\u9762\u5206\u7c7b\u5b9a\u7406\u8bbe\u7f6e\u6e38\u620f\u5f00\u53d1\u8fc7\u7a0b\u4e2d\u4f7f\u7528\u5230\u7684Mesh\u7684LOD Group. \u7531\u4e8e\u4e0d\u540c\u7f8e\u672f\u540c\u5b66\u8bbe\u7f6eMesh\u7684LOD Group\u7684\u6807\u51c6\u53ef\u80fd\u662f\u4e0d\u4e00\u81f4\u7684, \u4f1a\u4f7f\u5f97\u6e38\u620f\u5f00\u53d1\u8fc7\u7a0b\u4e2d\u5bf9\u4e8eLOD Group\u7684\u7ba1\u7406\u53d8\u5f97\u5341\u5206\u6df7\u4e71, \u800cAuto LOD Group\u4fbf\u53ef\u4ee5\u5e2e\u52a9\u5b9e\u73b0LOD Group\u7684\u81ea\u52a8\u5316\u8bbe\u7f6e, \u4e25\u683c\u4fdd\u8bc1\u4e86LOD Group\u7684\u8bbe\u7f6e\u6807\u51c6\u7684\u4e00\u81f4\u6027. \u9650\u4e8e\u6240\u5728\u9879\u76ee\u7684\u4fdd\u5bc6\u6027, \u63a5\u4e0b\u6765\u4ec5\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e0bAuto LOD Group\u7684\u7b97\u6cd5\u601d\u60f3.<\/p>\n<p><!--more--><\/p>\n<p><strong>\u53c2\u8003\u6750\u6599<\/strong><br \/>\n1. <a href=\"https:\/\/math.fandom.com\/zh\/wiki\/%E9%97%AD%E6%9B%B2%E9%9D%A2%E5%88%86%E7%B1%BB%E5%AE%9A%E7%90%86?variant=zh\">\u95ed\u66f2\u9762\u5206\u7c7b\u5b9a\u7406<\/a><br \/>\n2. <a href=\"https:\/\/www.zhihu.com\/question\/26699192\/answer\/33715531\">\u5982\u4f55\u76f4\u89c2\uff0c\u51c6\u786e\u5730\u89e3\u91ca\uff02\u4e8f\u683c\uff02\u3002\uff1f<\/a><br \/>\n3. <a href=\"https:\/\/www.caiqinyi.cn\/index.php\/2023\/06\/17\/geometry_processing_model_simplification_course_notes\/\">\u51e0\u4f55\u5904\u7406\u548c\u6a21\u578b\u7b80\u5316\u8bfe\u7a0b\u7b14\u8bb0<\/a><\/p>\n<p><strong>1. \u95ed\u66f2\u9762\u5206\u7c7b\u5b9a\u7406<\/strong><\/p>\n<p>\u9996\u5148\u590d\u4e60\u4e00\u4e0b\u95ed\u66f2\u9762\u5206\u7c7b\u5b9a\u7406.<br \/>\n$\\\\$ <strong>\u95ed\u66f2\u9762\u5206\u7c7b\u5b9a\u7406<\/strong> \u4e00\u4e2a\u4e8c\u7ef4\u95ed\u66f2\u9762, \u5b83\u662f\u4e14\u53ea\u80fd\u662f\u4ee5\u4e0b\u4e09\u79cd\u7c7b\u578b\u4e4b\u4e00:<br \/>\n$\\\\$ 1) \u7403\u9762: $\\mathbb{S}^2$, \u8fd9\u65f6\u4e3a\u53ef\u5b9a\u5411\u95ed\u66f2\u9762.<br \/>\n$\\\\$ 2) $n$\u4e2a\u73af\u9762\u4f5c\u8fde\u901a\u548c: $n \\mathbb{T}^2$\u578b, \u8fd9\u65f6\u4e3a\u53ef\u5b9a\u5411\u95ed\u66f2\u9762.<br \/>\n$\\\\$ 3) $m$\u4e2a\u5c04\u5f71\u5e73\u9762\u4f5c\u8fde\u901a\u548c: $m \\mathbb{P}^2$\u578b, \u8fd9\u65f6\u4e3a\u4e0d\u53ef\u5b9a\u5411\u95ed\u66f2\u9762.<br \/>\n$\\\\$ \u8fd9\u4e2a\u5b9a\u7406\u8574\u542b\u4e86\u5bf9\u4efb\u610f\u7684\u6b63\u6574\u6570$m$, $n$, \u8fd9\u4e9b\u4e0d\u540c\u7c7b\u578b\u7684\u95ed\u66f2\u9762\u662f\u4e0d\u4ea4\u7684, \u8fd9\u4e2a\u4e0d\u4ea4\u6027\u7684\u8bc1\u660e\u9700\u8981\u7528\u5230\u57fa\u672c\u7fa4\u7684\u76f8\u5173\u7406\u8bba. \u53ef\u5b9a\u5411\u6027\u662f\u62d3\u6251\u4e0d\u53d8\u91cf.<\/p>\n<p>\u4e0a\u8ff0\u4e09\u7c7b\u66f2\u9762\u7684Euler\u793a\u6027\u6570\u548c\u4e8f\u683c\u5982\u4e0b:<br \/>\n$\\\\$ 1) $\\mathbb{S}^2$, Euler\u793a\u6027\u6570\u662f2, \u4e8f\u683c\u662f0.<br \/>\n$\\\\$ 2) $n \\mathbb{T}^2$, Euler\u793a\u6027\u6570\u662f$2 &#8211; 2n$, (\u53ef\u5b9a\u5411) \u4e8f\u683c\u662f$n$.<br \/>\n$\\\\$ 3) $m \\mathbb{P}^2$, Euler\u793a\u6027\u6570\u662f$2 &#8211; m$, (\u4e0d\u53ef\u5b9a\u5411) \u4e8f\u683c\u662f$m$.<br \/>\n$\\\\$ Euler\u793a\u6027\u6570\u548c\u4e8f\u683c\u662f\u62d3\u6251\u4e0d\u53d8\u91cf.<\/p>\n<p>\u6ce8: \u4e00\u4e2a\u66f2\u9762\u505a\u8fde\u901a\u548c\u88ab\u89c6\u4e3a\u8fd8\u662f\u8fd9\u4e2a\u66f2\u9762\u81ea\u8eab.<\/p>\n<p><strong>2. \u4e8f\u683c\u8ba1\u7b97<\/strong><\/p>\n<p>\u4e00\u822c\u6765\u8bf4, \u6e38\u620f\u5f00\u53d1\u6240\u4f7f\u7528\u7684Mesh\u7684\u8fde\u901a\u5206\u652f\u6570(\u5373\u7b2c0\u4e2aBetti\u6570) \u4e0d\u4e00\u5b9a\u4e3a1, \u4e14\u53ef\u80fd\u662f\u5e26\u6d1e\u7684. \u6b64\u5904\u6d1e\u7684\u6570\u91cf\u4e0d\u4e00\u5b9a\u4e3a\u4e8f\u683c, \u56e0\u4e3a\u4e8f\u683c\u5bf9\u5e94\u7684\u6d1e\u5fc5\u987b\u662f\u7a7f\u900f\u578b\u7684, \u4e0d\u7a7f\u900f\u7684\u6d1e\u518d\u6df1\u4e5f\u4e0d\u884c(\u8be6\u89c1\u53c2\u8003\u6750\u65992). \u56e0\u6b64, \u5728\u8ba1\u7b97\u4e8f\u683c\u65f6, \u5fc5\u987b\u8003\u8651\u7b2c0\u4e2aBetti\u6570\u4e0e\u8fb9\u754c\u7684\u8fde\u901a\u5206\u652f\u6570(\u5373\u6d1e\u7684\u6570\u91cf). \u7b14\u8005\u6240\u4f7f\u7528\u7684\u8ba1\u7b97\u4e8f\u683c\u7684\u516c\u5f0f\u4e3a:<br \/>\n$\\\\$ 1) \u5f53Mesh\u7684\u9690\u85cf\u66f2\u9762\u4e3a\u53ef\u5b9a\u5411\u66f2\u9762\u65f6, $$v &#8211; e + f = 2s &#8211; 2g &#8211; h.$$$\\\\$ 2) \u5f53Mesh\u7684\u9690\u85cf\u66f2\u9762\u4e3a\u4e0d\u53ef\u5b9a\u5411\u66f2\u9762\u65f6, $$v &#8211; e + f = 2s &#8211; g &#8211; h.$$\u5176\u4e2d, $s$\u4e3a\u7b2c0\u4e2aBetti\u6570, $g$\u4e3a\u4e8f\u683c, $h$\u4e3a\u8fb9\u754c\u7684\u8fde\u901a\u5206\u652f\u6570.<br \/>\n$\\\\$ <strong>\u8bc1:<\/strong> \u4ec5\u8bc11). \u4e0d\u59a8\u8bbeMesh\u7684\u6240\u6709\u8fde\u901a\u5206\u652f\u7684\u9876\u70b9\u6570\u5206\u522b\u4e3a$v_1$, $\\cdots$, $v_s$, \u8fb9\u6570\u5206\u522b\u4e3a$e_1$, $\\cdots$, $e_s$, \u9762\u6570\u5206\u522b\u4e3a$f_1$, $\\cdots$, $f_s$, \u8fb9\u754c\u7684\u8fde\u901a\u5206\u652f\u6570\u5206\u522b\u4e3a$h_1$, $\\cdots$, $h_s$, \u8003\u8651\u8fde\u901a\u5206\u652f$C_i$, \u5176\u4e8f\u683c\u8ba1\u7b97\u516c\u5f0f\u4e3a$$v_i &#8211; e_i + f_i = 2 &#8211; 2g_i &#8211; h_i,$$\u5176\u4e2d, \u7528\u8be5\u8fde\u901a\u5206\u652f$C_i$\u7684\u6b27\u62c9\u793a\u6027\u6570$v_i &#8211; e_i + f_i$\u52a0\u4e0a\u8fb9\u754c\u7684\u8fde\u901a\u5206\u652f\u6570$h_i$\u7684\u64cd\u4f5c\u53ef\u89c6\u4e3a\u4ec5\u7528\u4e00\u4e2a\u9762\u8fdb\u884c\u8865\u6d1e. \u53c8Mesh\u7684\u4e8f\u683c$g$\u4e3a\u5176\u6240\u6709\u8fde\u901a\u5206\u652f$\\{ C_i \\}_{i = 1}^s$\u7684\u4e8f\u683c$\\{ g_i \\}_{i = 1}^s$\u4e4b\u548c, \u6545\u5176\u4e8f\u683c\u8ba1\u7b97\u516c\u5f0f\u4e3a$${\\textstyle \\sum_{i = 1}^{s}} v_i &#8211; {\\textstyle \\sum_{i = 1}^{s}} e_i + {\\textstyle \\sum_{i = 1}^{s}} f_i = 2s &#8211; 2{\\textstyle \\sum_{i = 1}^{s}} g_i &#8211; {\\textstyle \\sum_{i = 1}^{s}} h_i,$$\u4e0a\u5f0f\u53ef\u7b80\u8bb0\u4e3a$$v &#8211; e + f = 2s &#8211; 2g &#8211; h.$$\u4ece\u800c, \u547d\u9898\u5f97\u8bc1. \u7c7b\u4f3c\u53ef\u5f972).<br \/>\n$\\\\$ \u6b64\u5916, \u501f\u52a9\u5e76\u67e5\u96c6\u8fd9\u4e2a\u5f3a\u6709\u529b\u7684\u6570\u636e\u7ed3\u6784, \u4e5f\u53ef\u4ee5\u8f83\u5feb\u901f\u5ea6\u5730\u8ba1\u7b97\u51faMesh\u7684\u7b2c0\u4e2aBetti\u6570, \u8fb9\u754c\u7684\u8fde\u901a\u5206\u652f\u6570\u4e0e\u53ef\u5b9a\u5411\u6027. <\/p>\n<p><strong>3. \u4e8f\u683c\u5230LOD Group\u7684\u6620\u5c04<\/strong><\/p>\n<p>\u5b9e\u9645\u4e0a, \u5404\u4e2a\u9879\u76ee\u7ec4\u5bf9\u4e8eLOD Group\u7684\u8bbe\u7f6e\u89c4\u5219\u53ef\u80fd\u662f\u5404\u4e0d\u76f8\u540c\u7684. \u7b14\u8005\u5c06Mesh\u7684\u4e8f\u683c$g$\u5230\u5176LOD Group\u7684\u6620\u5c04\u5b9a\u4e49\u5982\u4e0b:$$f: (g, b, s) \\mapsto LOD \\ Group,$$\u5176\u4e2d, $b$\u4e3aMesh\u7684\u7684Bounding Sphere\u7684\u534a\u5f84, $s$\u4e3aMesh\u91c7\u7528\u7684Shading Model. \u4e4b\u6240\u4ee5\u8fd8\u9700\u8981\u8003\u8651Mesh\u91c7\u7528\u7684Shading Model, \u662f\u56e0\u4e3a\u4e0a\u8ff0\u7684\u4e8f\u683c\u8ba1\u7b97\u662f\u4e0d\u8003\u8651\u6750\u8d28\u4ea7\u751f\u7684\u4e8f\u683c\u7684. \u76ee\u524d, \u7b14\u8005\u89c2\u5bdf\u5230Two Sided Foliage Shading Model\u4f1a\u4ea7\u751f\u4e00\u5b9a\u6570\u91cf\u7684\u4e8f\u683c, \u5bf9\u4e8e\u91c7\u7528\u4e86Two Sided Foliage Shading Model\u7684Mesh, \u4f1a\u76f4\u63a5\u5c06\u5176LOD Group\u8bbe\u7f6e\u4e3aFoliage\u76f8\u5173\u7684LOD Group.<\/p>\n<p><strong>4. \u5e94\u7528<\/strong><\/p>\n<p>\u5206\u7c7b\u95ee\u9898\u4e00\u76f4\u662f\u6570\u5b66\u7814\u7a76\u7684\u57fa\u672c\u95ee\u9898\u4e4b\u4e00, \u5728\u5229\u7528\u95ed\u66f2\u9762\u5206\u7c7b\u5b9a\u7406\u4e0eLOD Group\u5bf9\u6e38\u620f\u5f00\u53d1\u8fc7\u7a0b\u4e2d\u4f7f\u7528\u5230\u7684Mesh\u8fdb\u884c\u5206\u7c7b\u540e, \u6211\u4eec\u4fbf\u53ef\u4ee5\u9488\u5bf9\u6bcf\u4e00\u7c7bMesh\u8fdb\u884c\u7279\u5b9a\u7684\u4f18\u5316. \u5982<br \/>\n$\\\\$ 1) \u5bf9\u4e8e\u9ad8\u4e8f\u683c, LOD Group\u4e3aFoliage, Deco\u6216Small Prop\u7684Mesh, \u7531\u4e8e\u5176\u5f88\u96be\u5728\u906e\u6321\u5254\u9664\u4e2d\u53d1\u6325\u4f5c\u7528, \u90a3\u4e48\u53ef\u4ee5\u5173\u95ed\u5bf9\u5e94\u7684Actor Settings\u4e0a\u7684Use as Occluder\u9009\u9879. \u5c24\u5176\u662f\u5bf9\u4e8eLOD Group\u4e3aFoliage\u7684Mesh, \u8fd8\u53ef\u4ee5\u542f\u7528Nanite\u8fdb\u884c\u6e32\u67d3(\u5206Cluster\u6e32\u67d3, \u5254\u9664\u6548\u7387\u66f4\u9ad8).<br \/>\n$\\\\$ 2) \u5bf9\u4e8eLOD Group\u4e3aVista\u7684Mesh, \u53ef\u4ee5\u5c06\u5176\u7ed8\u5236\u5230\u5929\u7a7a\u76d2\u4e0a(\u5f85\u9a8c\u8bc1&#8230;).<\/p>\n<p><strong>5. \u672a\u6765\u5de5\u4f5c<\/strong><\/p>\n<p>\u76ee\u524dAuto LOD Group\u7b97\u6cd5\u5df2\u7ecf\u5728\u7b14\u8005\u9879\u76ee\u5185\u987a\u5229\u843d\u5730, \u4e5f\u53d6\u5f97\u4e86\u8fd8\u7b97\u4e0d\u9519\u7684\u81ea\u52a8\u5316\u6548\u679c. \u4f46\u4f9d\u65e7\u5b58\u5728\u4e00\u4e9b\u4e0d\u8db3\u7b49\u5f85\u89e3\u51b3, \u5982:<br \/>\n$\\\\$ 1) \u5b9e\u9645\u4e0a, \u76ee\u524d\u8ba1\u7b97\u5f97\u5230\u7684Mesh\u7684\u603b\u4e8f\u683c\u6570\u91cf\u533a\u5206\u610f\u4e49\u4e0d\u5927. \u5c24\u5176\u662f\u5bf9\u4e8e\u975e\u6d41\u5f62\u7684Mesh, \u5fc5\u987b\u5bf9\u5176\u8fdb\u884cManifold-Connected(MC) \u5206\u89e3\u5f97\u5230MC\u590d\u5f62(\u53c2\u8003\u8bba\u6587Hui A, De Floriani L. A two-level topological decomposition for non-manifold simplicial shapes[C]\/\/Proceedings of the 2007 ACM symposium on Solid and physical modeling. 2007: 355-360.), \u6bd4\u8f83\u5176\u6bcf\u4e00\u4e2aMC Component\u7684\u4e8f\u683c(\u53c2\u8003\u8bba\u6587Heisserman J A. A generalized Euler-Poincar\u00e9 equation[J]. 1991.), \u8fd9\u6837\u5728Mesh\u7684\u5206\u7c7b\u95ee\u9898\u4e0a\u624d\u66f4\u5177\u533a\u5206\u4ef7\u503c.<br \/>\n$\\\\$ 2) \u8ba1\u7b97Mesh\u7684\u6750\u8d28\u4ea7\u751f\u7684\u4e8f\u683c.<br \/>\n$\\\\$ 3) \u8ba1\u7b97Mesh\u7684Handle\u4e0eTunnel(\u53c2\u8003\u8bba\u6587Dey T K, Fan F, Wang Y. An efficient computation of handle and tunnel loops via Reeb graphs[J]. ACM Transactions on Graphics (TOG), 2013, 32(4): 1-10. \u6216\u8bb8\u53ef\u4ee5\u7528\u81f3Portal Culling\u4e2d?).<br \/>\n$\\\\$ \u6700\u540e, \u4e5f\u5e0c\u671b\u80fd\u591f\u5c06\u4ee3\u6570\u62d3\u6251\u66f4\u6df1\u5c42\u6b21\u7684\u601d\u60f3\u5e94\u7528\u81f3\u6e38\u620f\u5f00\u53d1\u4e2d. \u4e0d\u5fd8\u521d\u5fc3, \u4ee5\u5b66\u672f\u4e4b\u5fc3\u5e94\u5de5\u4e1a\u4e4b\u4e8b(\u0e07 \u2022_\u2022)\u0e07~<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b66\u5b8c\u4ee3\u6570\u62d3\u6251\u5df2\u7ecf\u6709\u4e00\u6bb5\u65f6\u95f4\u4e86, \u5c3d\u7ba1\u5185\u5bb9\u5df2\u7ecf\u5fd8\u4e86\u4e0d\u5c11\u4e86, \u4f46\u4e00\u76f4\u5fc3\u5fc3\u5ff5\u5ff5\u5c06\u4ee3\u6570\u62d3\u6251\u7684\u601d\u60f3\u5e94\u7528\u81f3\u6e38\u620f\u5f00\u53d1\u4e2d. \u7ec8 &hellip; <a href=\"https:\/\/www.caiqinyi.cn\/index.php\/2023\/09\/01\/auto_lod_group\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Auto LOD Group<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,24,9,5],"tags":[],"_links":{"self":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/3186"}],"collection":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/comments?post=3186"}],"version-history":[{"count":17,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/3186\/revisions"}],"predecessor-version":[{"id":3600,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/3186\/revisions\/3600"}],"wp:attachment":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/media?parent=3186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/categories?post=3186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/tags?post=3186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}