{"id":138,"date":"2021-10-22T11:50:49","date_gmt":"2021-10-22T03:50:49","guid":{"rendered":"https:\/\/playerzhou.com\/blog\/?p=138"},"modified":"2021-10-22T11:50:49","modified_gmt":"2021-10-22T03:50:49","slug":"%e7%ba%bf%e6%80%a7bvh%e6%a0%91%e5%b9%b6%e8%a1%8c%e6%9e%84%e5%bb%ba%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/playerzhou.com\/blog\/?p=138","title":{"rendered":"\u7ebf\u6027BVH\u6811\u5e76\u884c\u6784\u5efa\u65b9\u6cd5"},"content":{"rendered":"<h1>\u7ebf\u6027BVH\u6811\u5e76\u884c\u6784\u5efa\u65b9\u6cd5<\/h1>\n<h2>\u80cc\u666f<\/h2>\n<ul>\n<li>\u4f20\u7edfBVH\u6811\u91c7\u7528\u9012\u5f52\u7684\u65b9\u5f0f\u5b9e\u73b0\uff0c\u4e0d\u5229\u4e8e\u5e76\u884c\u5b9e\u73b0<\/li>\n<\/ul>\n<h2>\u524d\u7f6e\u6b65\u9aa4<\/h2>\n<h3>\u6784\u9020\u4e00\u4e2a\u6392\u5e8f\u597d\u7684\u53f6\u5b50\u8282\u70b9\u5e8f\u5217<\/h3>\n<h4>\u76ee\u7684<\/h4>\n<ul>\n<li>\u6709\u5229\u4e8e\u5408\u5e76\u64cd\u4f5c\uff0c\u7531\u4e8e\u53f6\u8282\u70b9\u5df2\u7ecf\u6392\u5e8f\u5b8c\u6bd5\uff0c\u53ea\u9700\u5408\u5e76\u76f8\u90bb\u53f6\u8282\u70b9\u6216\u975e\u53f6\u8282\u70b9\u5373\u53ef\u6784\u9020\u51fa\u65b0\u7684\u7236\u8282\u70b9<\/li>\n<li>\u4e0d\u9700\u8981\u91cd\u65b0\u8fdb\u884c\u6392\u5e8f\u64cd\u4f5c\u6765\u6784\u9020\u5212\u5206\uff0c\u4ece\u800c\u4f7f\u5f97\u6784\u5efa\u65e0\u6cd5\u5e76\u884c\u5316<\/li>\n<\/ul>\n<h4>\u8981\u6c42<\/h4>\n<ul>\n<li>\u76f8\u90bb\u53f6\u5b50\u8282\u70b9\u8981\u5c3d\u53ef\u80fd\u9760\u8fd1<\/li>\n<\/ul>\n<h4>\u505a\u6cd5<\/h4>\n<ul>\n<li>\u6bcf\u4e00\u4e2aAABB\u63d0\u4f9b\u4e00\u4e2apoint\uff08\u8fd9\u91cc\u91c7\u7528\u5305\u56f4\u76d2\u91cd\u5fc3\uff09<\/li>\n<li>\u5c06\u8be5point\u5750\u6807\u8f6c\u6362\u4e3aMorton Code<\/li>\n<li>\u6839\u636eMorton Code\u8fdb\u884c\u6392\u5e8f<\/li>\n<\/ul>\n<h4>\u539f\u7406<\/h4>\n<ul>\n<li>\u76f8\u5f53\u4e8e\u5c06\u7a7a\u95f4\u5212\u5206\u6210\u4e00\u4e2a\u4e2a\u4f53\u7d20\uff0c\u6bcf\u4e00\u4e2aMorton Code\u4ee3\u8868\u4e00\u4e2a\u4f53\u7d20<\/li>\n<li>\u53ef\u7c7b\u6bd4\u4e8e2D\u7a7a\u95f4\u4e2d\u7684Z\u578b\u66f2\u7ebf\uff0c\u5927\u90e8\u5206\u76f8\u4e34\u7f16\u7801\u7684\u4f53\u7d20\u5728\u7a7a\u95f4\u4e2d\u76f8\u90bb<\/li>\n<li>\u53ef\u901a\u8fc7\u524d\u7f00\u5c06\u82e5\u5e72\u4e2a\u5c0f\u4f53\u7d20\u5408\u5e76\u6210\u5927\u4f53\u7d20\uff0c\u7b26\u5408BVH\u6811\u7684\u5408\u5e76\u9700\u6c42<\/li>\n<\/ul>\n<h4>\u7f3a\u70b9<\/h4>\n<ul>\n<li>\u8be5\u5212\u5206\u65b9\u5f0f\u5047\u5b9a\u7edd\u5927\u90e8\u5206\u4e09\u89d2\u9762\u7247\u8db3\u591f\u5c0f\uff0c\u4ec5\u5b58\u5728\u4e8epoint\u9644\u8fd1\u7684\u51e0\u4e2a\u4f53\u7d20\u5185<\/li>\n<li>\u5bf9\u4e8e\u90e8\u5206\u5927\u7684\u4e09\u89d2\u9762\u7247\uff0c\u67e5\u8be2\u6548\u679c\u8f83\u5dee\uff0c\u4f46\u4f9d\u65e7\u80fd\u591f\u4fdd\u8bc1\u9c81\u68d2\u6027<\/li>\n<\/ul>\n<h3>BVH\u6811\u5408\u5e76\u6807\u51c6<\/h3>\n<ul>\n<li>\u6839\u636e\u524d\u7f00\u548c\u8fdb\u884c\u5408\u5e76\uff0c\u6709\u76f8\u540c\u524d\u7f00\u548c\u7684\u7684\u8282\u70b9\u5c5e\u4e8e\u540c\u4e00\u4e2a\u975e\u53f6\u8282\u70b9<\/li>\n<li>\u4ece\u5e95\u5411\u4e0a\u524d\u7f00\u548c\u9010\u6e10\u53d8\u5c0f\uff0c\u4ece\u800c\u6784\u5efa\u51fa\u6811\u7684\u5c42\u7ea7\u3001<\/li>\n<li>\u5982\u56fe\u6240\u793a<img src=\"https:\/\/playerzhou.com\/blog\/wp-content\/uploads\/2021\/10\/tree.png\" alt=\"tree\" \/><\/li>\n<\/ul>\n<h2>\u6784\u5efa\u7b97\u6cd5<\/h2>\n<h3>\u4f2a\u4ee3\u7801<\/h3>\n<p><img src=\"https:\/\/playerzhou.com\/blog\/wp-content\/uploads\/2021\/10\/code.png\" alt=\"code\" \/><\/p>\n<h3>\u6982\u5ff5\u89e3\u91ca<\/h3>\n<ul>\n<li>\n<p>\u53f6\u5b50\u8282\u70b9<\/p>\n<ul>\n<li>\u6bcf\u4e00\u4e2a\u7269\u4f53\u4f5c\u4e3a\u6700\u5c0f\u5355\u5143\u5b58\u50a8\u5728\u53f6\u5b50\u8282\u70b9\u4e2d<\/li>\n<li>\u540c\u65f6\u5b58\u50a8\u7269\u4f53\u7684\u5305\u56f4\u76d2\u4fe1\u606f\uff0c\u5305\u62ecMorton Code<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u975e\u53f6\u8282\u70b9<\/p>\n<ul>\n<li>\u901a\u8fc7\u5408\u5e76\u53f6\u5b50\u8282\u70b9\/\u975e\u53f6\u8282\u70b9\u5f97\u5230<\/li>\n<li>\u5b58\u50a8\u5408\u5e76\u540e\u7684\u5305\u56f4\u76d2\u4fe1\u606f\uff0c\u5305\u62ecMorton Code\u524d\u7f00<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u8282\u70b9\u5b58\u50a8<\/p>\n<ul>\n<li>\u4f7f\u7528\u4e24\u4e2a\u6570\u7ec4\u5206\u522b\u5b58\u50a8\u53f6\u5b50\u8282\u70b9\u548c\u975e\u53f6\u8282\u70b9<\/li>\n<li>\u6570\u7ec4L\uff1a\u5b58\u50a8\u53f6\u5b50\u8282\u70b9\u7684\u6570\u7ec4<\/li>\n<li>\u6570\u7ec4I\uff1a\u5b58\u50a8\u975e\u53f6\u8282\u70b9\u7684\u6570\u7ec4<\/li>\n<li>N\uff1a\u53f6\u5b50\u8282\u70b9\u6570\u7ec4\u5927\u5c0f\uff0cN-1\uff1a\u975e\u53f6\u8282\u70b9\u6570\u7ec4\u5927\u5c0f<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u4e0b\u6807<\/p>\n<ul>\n<li>\u53f6\u5b50\u8282\u70b9\u4e0b\u6807\uff1a\u4ee3\u8868\u5728L\u4e2d\u7684\u4f4d\u7f6e<\/li>\n<li>\u975e\u53f6\u8282\u70b9\u4e0b\u6807<\/li>\n<li>\u4ee3\u8868\u5728I\u4e2d\u4f4d\u7f6e<\/li>\n<li>\u6839\u8282\u70b9\u4e0b\u6807=0<\/li>\n<li>\u82e5\u8be5\u975e\u53f6\u8282\u70b9\u4e3a\u5176\u7236\u8282\u70b9\u7684\u5de6\u5b69\u5b50\uff0c\u5219\u975e\u53f6\u8282\u70b9\u4e0b\u6807=\u6240\u5305\u542b\u6700\u53f3\u7aef\u53f6\u5b50\u8282\u70b9\u7684\u4e0b\u6807<\/li>\n<li>\u82e5\u8be5\u975e\u53f6\u8282\u70b9\u4e3a\u5176\u7236\u8282\u70b9\u7684\u53f3\u5b69\u5b50\uff0c\u5219\u975e\u53f6\u8282\u70b9\u4e0b\u6807=\u6240\u5305\u542b\u6700\u5de6\u7aef\u53f6\u5b50\u8282\u70b9\u7684\u4e0b\u6807<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u03b4(i, j)\uff1a<\/p>\n<ul>\n<li>\u8fd4\u56deL[i]\u548cL[j]\u8282\u70b9\u7684Morton Code\u7684\u6700\u957f\u516c\u5171\u524d\u7f00\u957f\u5ea6<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u5206\u5272\u4f4d\u7f6e\u03b3<\/p>\n<ul>\n<li>\u82e5\u975e\u53f6\u8282\u70b9K\u6240\u5305\u542b\u7684\u53f6\u8282\u70b9\u4e0b\u6807\u8303\u56f4\u4e3a[l,r]<\/li>\n<li>\u5219\u5176\u5de6\u53f3\u5b50\u6811\u5305\u542b\u7684\u53f6\u8282\u70b9\u4e0b\u6807\u8303\u56f4\u5206\u522b\u4e3a[l,\u03b3]\uff0c[\u03b3+1,r]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b97\u6cd5\u89e3\u6790<\/h3>\n<pre><code>\/\/ \u8be5\u7b97\u6cd5\u7684\u76ee\u7684\u662f\u627e\u5230I[i]\u7684\u5de6\u53f3\u5b50\u6811\uff0c\u4ece\u800c\u5c06\u5176\u5408\u5e76\nfor each internal node with index i \u2208 [0,n n 2] in parallel\n    \/\/ Determine direction of the range (+1 or -1)\n    \/\/ \u5224\u65ad\u65b9\u5411\uff0c\u82e5i\u4e3a\u5de6\u5b69\u5b50\uff0cL[i]\u4e3aI[i]\u6700\u53f3\u5143\u7d20\uff0c\u5219d=1\uff0c\u82e5i\u4e3a\u53f3\u5b69\u5b50\uff0cL[i]\u4e3aI[i]\u6700\u5de6\u5143\u7d20\uff0cd=-1\n    d \u2190 sign(\u03b4(i,i+1) ) \u03b4(i,i i 1))\n    \/\/ Compute upper bound for the length of the range\n    \/\/ \u8ba1\u7b97\u524d\u7f00\u957f\u5ea6\u7684\u4e0b\u754c\uff0c\u7531\u4e8ei-d\u5fc5\u7136\u4e0d\u5c5e\u4e8ei\u5b50\u6811\uff0c\u5047\u8bbei\u5b50\u6811\u7684\u524d\u7f00\u4e3a\u03b4_i\uff0c\u56e0\u6b64\u03b4(i,i-d)&lt;\u03b4_i\n    \u03b4_min \u2190 \u03b4(i,i-d)\n    l_max \u2190 2\n    \/\/ \u7531\u4e8ei\u5b50\u6811\u5185\u7684\u524d\u7f00\u957f\u5ea6\u5fc5\u7136\u5927\u4e8e\u03b4_min\uff0c\u56e0\u6b64\u82e5\u03b4(i,i+lmax*d)&lt;=\u03b4_min,\u5219i+lmax*d\u4e0d\u5728i\u5b50\u6811\u4e2d\n    \/\/ \u56e0\u6b64\u8be5\u5faa\u73af\u627e\u5230\u4e00\u4e2a\u4e0b\u754c\uff0c\u5373i\u5b50\u6811\u7684\u53e6\u4e00\u4e2a\u7aef\u70b9\u5fc5\u7136\u5c5e\u4e8e[i,i+lmax*d)\n    while \u03b4(i,i+lmax*d) &gt; \u03b4_min do\n        lmax \u2190 lmax*2\n    \/\/ Find the other end using binary search\n    \/\/ \u4f7f\u7528\u4e8c\u5206\u67e5\u627e\u627e\u5230I[i]\u7684\u53e6\u4e00\u4e2a\u7aef\u70b9j\n    l \u2190 0\n    for t \u2190 {lmax\/2,lmax\/4,...,1} do\n        if \u03b4(i,i+ (l +t)\u00b7 d) &gt; \u03b4min then\n            l \u2190 l +t\n    j \u2190 i+l \u00b7 d\n    \/\/ Find the split position using binary search\n    \/\/ \u63a5\u4e0b\u6765\u67e5\u627eI[i]\u7684\u5212\u5206\u4f4d\u7f6e\u03b3\n    \/\/ \u540c\u6837\u4f7f\u7528\u4e8c\u5206\u67e5\u627e\u7684\u65b9\u5f0f\u67e5\u627e\uff0c\u8fd9\u91cc\u7531\u4e8e\u65b9\u5411\u95ee\u9898\uff0c\u6700\u540e\u8fd8\u8981\u8fdb\u884c\u5904\u7406\u4e00\u4e0b\n    \/\/ \u82e5d=1\uff0c\u5219\u67e5\u627e\u5230\u7684\u7ed3\u679c\u662f\u03b3\uff0c\u53cd\u4e4b\u5219\u662f\u03b3+1\uff0c\u6545\u6b64\u65f6\u9700\u8981\u518d\u51cf\u53bb1\n    \u03b4node \u2190 \u03b4(i, j)\n    s \u2190 0\n    for t \u2190 {l\/2, l\/4,...,1} do\n        if \u03b4(i,i+ (s+t)\u00b7 d) &gt; \u03b4node then\n            s \u2190 s+t\n    \u03b3 \u2190 i+s\u00b7 d +min(d,0)\n    \/\/ Output child pointers\n    \/\/ \u5224\u65ad\u5b50\u8282\u70b9\u5c5e\u4e8eI\u6570\u7ec4\u8fd8\u662fL\u6570\u7ec4\n    if min(i, j) = \u03b3 then left \u2190 L\u03b3 else left \u2190 I\u03b3\n    if max(i, j) = \u03b3+1 then right \u2190 L\u03b3+1 else right \u2190 I\u03b3+1\n    \/\/ \u5408\u5e76\u7ed3\u679c\n    Ii \u2190 (left,right)\nend for<\/code><\/pre>\n<h2>\u540e\u7f6e\u6b65\u9aa4<\/h2>\n<h4>\u5408\u5e76AABB<\/h4>\n<ul>\n<li>\u5e76\u884c\u4ece\u6240\u6709\u53f6\u5b50\u8282\u70b9\u51fa\u53d1\u8fdb\u884c\u8fed\u4ee3\u66f4\u65b0<\/li>\n<li>\u4e3a\u6bcf\u4e2a\u975e\u53f6\u8282\u70b9\u8bbe\u7f6e\u6807\u8bb0\u4f4d<\/li>\n<li>\u6bcf\u6b21\u8bbf\u95ee\u5230\u975e\u53f6\u8282\u70b9\uff0c\u91c7\u7528\u539f\u5b50\u64cd\u4f5c\u5c06\u5176\u9012\u589e\uff0c\u82e5\u8bbf\u95ee\u975e\u53f6\u8282\u70b9\u4e24\u6b21\u5219\u5408\u5e76\u8be5\u8282\u70b9\u7684\u4e24\u4e2a\u5b50\u8282\u70b9\uff08\u7531\u4e8e\u6bcf\u4e2a\u975e\u53f6\u8282\u70b9\u6709\u4e14\u53ea\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\uff0c\u56e0\u6b64\u8fd9\u6837\u53ef\u4ee5\u4fdd\u8bc1\u5b50\u8282\u70b9\u7684aabb\u90fd\u5df2\u66f4\u65b0\u5b8c\u6bd5\uff09\uff0c\u53cd\u4e4b\u5219\u7ed3\u675f\u8fed\u4ee3<\/li>\n<li>\u7ee7\u7eed\u8fed\u4ee3\u8be5\u8282\u70b9\u7684\u7236\u8282\u70b9<\/li>\n<li>\u7f3a\u70b9\uff1a\u6bcf\u6b21\u8fed\u4ee3\u540e\uff0c\u5c31\u6709\u4e00\u534a\u7ebf\u7a0b\u7ed3\u675f\u8fed\u4ee3\u95f2\u7f6e\uff0c\u4f46\u8be5\u64cd\u4f5c\u8017\u65f6\u4e0d\u5927\uff0c\u8fd9\u6837\u7684\u635f\u5931\u662f\u53ef\u4ee5\u63a5\u53d7\u7684<\/li>\n<\/ul>\n<h2>\u67e5\u8be2<\/h2>\n<ul>\n<li>\u53ef\u91c7\u7528BFS\u6216DFS\u7684\u65b9\u5f0f\u8fdb\u884c\u67e5\u8be2\uff0c\u82e5\u67e5\u5230\u67d0\u4e00\u4e2a\u5305\u56f4\u76d2\u76f8\u4ea4\uff0c\u5219\u7ee7\u7eed\u67e5\u8be2\u5176\u5b50\u8282\u70b9\u662f\u5426\u76f8\u4ea4\uff0c\u76f4\u81f3\u67e5\u8be2\u5230\u53f6\u5b50\u8282\u70b9<\/li>\n<\/ul>\n<h2>\u53c2\u8003\u6587\u732e<\/h2>\n<ul>\n<li><a href=\"https:\/\/developer.nvidia.com\/blog\/parallelforall\/wp-content\/uploads\/2012\/11\/karras2012hpg_paper.pdf\">Maximizing Parallelism in the Construction of BVHs, Octrees, and k-d Trees<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u7ebf\u6027BVH\u6811\u5e76\u884c\u6784\u5efa\u65b9\u6cd5 \u80cc\u666f \u4f20\u7edfBVH\u6811\u91c7\u7528\u9012\u5f52\u7684\u65b9\u5f0f\u5b9e\u73b0\uff0c\u4e0d\u5229\u4e8e\u5e76\u884c\u5b9e\u73b0 \u524d\u7f6e\u6b65\u9aa4 \u6784\u9020\u4e00\u4e2a\u6392\u5e8f\u597d\u7684\u53f6\u5b50 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[14],"tags":[],"_links":{"self":[{"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/138"}],"collection":[{"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=138"}],"version-history":[{"count":1,"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/138\/revisions"}],"predecessor-version":[{"id":141,"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/138\/revisions\/141"}],"wp:attachment":[{"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/playerzhou.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}