{"id":803,"date":"2023-11-01T11:46:34","date_gmt":"2023-11-01T03:46:34","guid":{"rendered":"http:\/\/www.forillusion.com\/?p=803"},"modified":"2025-02-14T11:39:18","modified_gmt":"2025-02-14T03:39:18","slug":"games101-l05-rasterization1-triangles","status":"publish","type":"post","link":"https:\/\/www.forillusion.com\/index.php\/games101-l05-rasterization1-triangles\/","title":{"rendered":"GAMES101-L05 \u5149\u6805\u5316\uff08\u4e09\u89d2\u5f62\u7684\u79bb\u6563\u5316\uff09"},"content":{"rendered":"\n<p><div class=\"has-toc have-toc\"><\/div><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u89c6\u9525<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9a\u4e49<\/h3>\n\n\n\n<p>\u5bbd\u5ea6\uff1a[latex]width[\/latex]<br>\u9ad8\u5ea6\uff1a[latex]height[\/latex]<\/p>\n\n\n\n<p>\u8fd1\u5e73\u9762\uff1a[latex]zNear[\/latex]<br>\u8fdc\u5e73\u9762\uff1a[latex]zFar[\/latex]<br>\u5782\u76f4\u53ef\u89c6\u89d2\uff1a\u957f\u65b9\u5f62\u4e0a\u4e0b\u4e2d\u70b9\u4e0e\u76f8\u673a\u8fde\u7ebf\u7684\u89d2\u5ea6\uff0c[latex]fovY[\/latex](Vertical Field of View)<br>\u5bbd\u9ad8\u6bd4\uff1a[latex]aspect[\/latex]<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\"   class=\"lazyload\" data-src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image.png\" src=\"https:\/\/cdn.forillusion.com\/moezx\/img\/svg\/loader\/trans.ajax-spinner-preloader.svg\" onerror=\"imgError(this)\"  alt=\"\" class=\"wp-image-816\"\/><\/figure >\n<noscript><img decoding=\"async\" src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image.png\" alt=\"\" class=\"wp-image-816\"\/><\/figure><\/noscript>\n\n\n\n<h3 class=\"wp-block-heading\">\u89c6\u9525\u4f53\u8f6c\u6362\u5230\u89c6\u666f\u4f53<\/h3>\n\n\n\n<p>\u9700\u8981\u8ba1\u7b97\u51fa\u89c6\u666f\u4f53\u7684l,r,t,b,n,f\u4fe1\u606f<br>\u7531\u4e8e\u5728\u6b64\u4e4b\u524d\u7684\u89c6\u56fe\u53d8\u6362\uff0c\u89c6\u666f\u4f53n\u3001f\u5e73\u9762\u7684\u4e2d\u5fc3\u5c31\u5728Z\u8f74\u4e0a\uff0c\u800c\u89c6\u9525\u4f53\u7684\u8fd1\u5e73\u9762\u548c\u8fdc\u5e73\u9762\u5c31\u662f\u89c6\u666f\u4f53\u7684n,f\u3002<\/p>\n\n\n\n<p>\u89c6\u9525\u4f53\u53c2\u6570\u548c\u89c6\u666f\u4f53\u5b58\u5728\u4ee5\u4e0b\u5173\u7cfb\uff1a<br>[latex]\\tan \\frac{\\text {fov } Y}{2}=\\frac{t}{|n|}[\/latex]<br>[latex]\\text{aspect}=\\frac{r}{t}[\/latex]<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"613\" height=\"251\"   class=\"lazyload\" data-src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-1.png\" src=\"https:\/\/cdn.forillusion.com\/moezx\/img\/svg\/loader\/trans.ajax-spinner-preloader.svg\" onerror=\"imgError(this)\"  alt=\"\" class=\"wp-image-820\" srcset=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-1.png 613w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-1-300x123.png 300w\" sizes=\"auto, (max-width: 613px) 100vw, 613px\" \/><\/figure >\n<noscript><img loading=\"lazy\" decoding=\"async\" width=\"613\" height=\"251\" src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-1.png\" alt=\"\" class=\"wp-image-820\" srcset=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-1.png 613w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-1-300x123.png 300w\" sizes=\"auto, (max-width: 613px) 100vw, 613px\" \/><\/figure><\/noscript>\n\n\n\n<p>\u6240\u4ee5\uff1a<br>[latex]n=zNear[\/latex]<br>[latex]f=zFar[\/latex]<br>[latex]t=tan(\\frac{fovY}{2} )\\times n[\/latex]<br>[latex]b=-t[\/latex]<br>[latex]r=aspect\\times t[\/latex]<br>[latex]l=-r[\/latex]<br><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5149\u6805\u5316<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5c4f\u5e55<\/h3>\n\n\n\n<p>\u4e8c\u7ef4\u6570\u7ec4<br>\u6570\u7ec4\u5927\u5c0f\uff1a\u5206\u8fa8\u7387<br>\u5178\u578b\u7684\u5149\u6805\u663e\u793a\u5668<\/p>\n\n\n\n<p>\u5149\u6805\u5316\uff1a\u5728\u5c4f\u5e55\u4e0a\u7ed8\u56fe<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5c4f\u5e55\u5750\u6807\u7cfb<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\"   class=\"lazyload\" data-src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-2.png\" src=\"https:\/\/cdn.forillusion.com\/moezx\/img\/svg\/loader\/trans.ajax-spinner-preloader.svg\" onerror=\"imgError(this)\"  alt=\"\" class=\"wp-image-821\" width=\"401\" height=\"307\" srcset=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-2.png 515w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-2-300x230.png 300w\" sizes=\"auto, (max-width: 401px) 100vw, 401px\" \/><\/figure >\n<noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-2.png\" alt=\"\" class=\"wp-image-821\" width=\"401\" height=\"307\" srcset=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-2.png 515w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-2-300x230.png 300w\" sizes=\"auto, (max-width: 401px) 100vw, 401px\" \/><\/figure><\/noscript>\n\n\n\n<p>\u5c4f\u5e55\u7684\u5de6\u4e0b\u89d2\u4e3a\u539f\u70b9<br>\u84dd\u8272\u50cf\u7d20\u4e3a [latex](2,1)[\/latex]<br>\u7528\u50cf\u7d20\u7684\u5de6\u4e0b\u89d2\u6765\u8868\u793a\u50cf\u7d20\uff0c\u50cf\u7d20 [latex](x,y)[\/latex] \u7684\u4e2d\u5fc3\u5728 [latex](x+0.5,y+0.5)[\/latex]<br>\u6240\u6709\u7684\u50cf\u7d20\u5750\u6807\u4ece [latex](0,0)[\/latex] \u5230 [latex](width-1,height-1)[\/latex]<br>\u6574\u4e2a\u5c4f\u5e55\u4f1a\u8986\u76d6 [latex](0,0)[\/latex] \u5230 [latex](width,height)[\/latex]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u89c6\u53e3\u53d8\u6362<\/h3>\n\n\n\n<p>\u5c06\u6b63\u4ea4\u6295\u5f71\u663e\u793a\u5230\u5c4f\u5e55<\/p>\n\n\n\n<p>1.\u5ffd\u7565z\u5750\u6807<br>2.\u5c06[latex][-1,1]^2[\/latex]\u62c9\u4f38\u5230[latex][0,width]\\times[0,height][\/latex]<br>[latex]<br>M_{\\text {viewport }}=<br>\\begin{bmatrix}<br>\\frac{{ width }}{2} &amp; 0 &amp; 0 &amp; \\frac{{ width }}{2} \\\\<br>0 &amp; \\frac{{ height }}{2} &amp; 0 &amp; \\frac{{ height }}{2} \\\\<br>0 &amp; 0 &amp; 1 &amp; 0 \\\\<br>0 &amp; 0 &amp; 0 &amp; 1<br>\\end{bmatrix}<br>[\/latex]<br><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5149\u6805\u5316<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u91c7\u6837<\/h4>\n\n\n\n<p>\u91c7\u6837\u5c31\u662f\u83b7\u53d6\u6bcf\u4e2a\u70b9\u7684\u51fd\u6570\u503c<br>\u91c7\u6837\u662f\u5bf9\u51fd\u6570\u7684\u79bb\u6563\u5316<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>for (int x = 0; x &lt; xmax; ++x)\n    output&#91;x] = f(x); <\/code><\/pre>\n\n\n\n<p>\u5149\u6805\u5316\u5c31\u662f2D\u7684\u91c7\u6837<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u5149\u6805\u5316<\/h4>\n\n\n\n<p>\u5224\u65ad\u5c4f\u5e55\u4e0a\u7684\u50cf\u7d20\u662f\u5426\u5728\u4e09\u89d2\u5f62\u5185\u90e8<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"316\"   class=\"lazyload\" data-src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4-1024x316.png\" src=\"https:\/\/cdn.forillusion.com\/moezx\/img\/svg\/loader\/trans.ajax-spinner-preloader.svg\" onerror=\"imgError(this)\"  alt=\"\" class=\"wp-image-828\" srcset=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4-1024x316.png 1024w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4-300x93.png 300w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4-768x237.png 768w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4.png 1402w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure >\n<noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"316\" src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4-1024x316.png\" alt=\"\" class=\"wp-image-828\" srcset=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4-1024x316.png 1024w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4-300x93.png 300w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4-768x237.png 768w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-4.png 1402w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/noscript>\n\n\n\n<p>[latex]<br>\\text { inside }(t, x, y) \\begin{cases}1 &amp; \\text { Point }(x, y) \\text { in triangle } t \\\\ 0 &amp; \\text { otherwise }\\end{cases}<br>[\/latex]<\/p>\n\n\n\n<p>\u5149\u6805\u5316=\u5bf92D\u6307\u793a\u5668\u51fd\u6570\u8fdb\u884c\u91c7\u6837<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>for (int x = 0; x &lt; xmax; ++x)\n   for (int y = 0; y &lt; ymax; ++y)\n       image&#91;x]&#91;y] = inside(tri,\n x + 0.5, \ny + 0.5); <\/code><\/pre>\n\n\n\n<p>inside\u51fd\u6570\uff1a\u5229\u7528\u53c9\u4e58\u5224\u65ad\u50cf\u7d20\u70b9\u7684\u4e2d\u5fc3\u662f\u5426\u5728\u4e09\u89d2\u5f62\u5185\u90e8<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\"   class=\"lazyload\" data-src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-3.png\" src=\"https:\/\/cdn.forillusion.com\/moezx\/img\/svg\/loader\/trans.ajax-spinner-preloader.svg\" onerror=\"imgError(this)\"  alt=\"\" class=\"wp-image-829\" width=\"459\" height=\"1005\"\/><figcaption>\u6837\u672c (x,y) \u7684\u4f4d\u7f6e<\/figcaption><\/figure >\n<noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-3.png\" alt=\"\" class=\"wp-image-829\" width=\"459\" height=\"1005\"\/><figcaption>\u6837\u672c (x,y) \u7684\u4f4d\u7f6e<\/figcaption><\/figure><\/noscript>\n\n\n\n<h4 class=\"wp-block-heading\">\u4f18\u5316<\/h4>\n\n\n\n<p>\u539f\u672c\u662f\u5224\u65ad\u5c4f\u5e55\u4e0a\u6240\u6709\u7684\u50cf\u7d20\u662f\u5426\u5728\u4e09\u89d2\u5f62\u5185\u90e8\uff0c\u53ef\u4ee5\u4f7f\u7528\u5305\u56f4\u76d2\u6765\u53ea\u5224\u65ad\u4e09\u89d2\u5f62\u5468\u56f4\u7684\u50cf\u7d20\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\"   class=\"lazyload\" data-src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-5.png\" src=\"https:\/\/cdn.forillusion.com\/moezx\/img\/svg\/loader\/trans.ajax-spinner-preloader.svg\" onerror=\"imgError(this)\"  alt=\"\" class=\"wp-image-832\" width=\"352\" height=\"313\" srcset=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-5.png 517w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-5-300x267.png 300w\" sizes=\"auto, (max-width: 352px) 100vw, 352px\" \/><\/figure >\n<noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-5.png\" alt=\"\" class=\"wp-image-832\" width=\"352\" height=\"313\" srcset=\"https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-5.png 517w, https:\/\/cos.forillusion.top\/wp-content\/uploads\/2023\/11\/image-5-300x267.png 300w\" sizes=\"auto, (max-width: 352px) 100vw, 352px\" \/><\/figure><\/noscript>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u89c6\u9525 \u5b9a\u4e49 \u5bbd\u5ea6\uff1a[latex]width[\/latex]\u9ad8\u5ea6\uff1a[latex]height[\/latex] \u8fd1\u5e73\u9762\uff1a[latex] &#8230;<\/p>","protected":false},"author":1,"featured_media":804,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-803","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/803","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=803"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/803\/revisions"}],"predecessor-version":[{"id":1759,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/803\/revisions\/1759"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/804"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}