![\"\u30c8\u30fc\u30e9\u30b9\"](\"wp-content\/uploads\/2012\/03\/out_1151-300x300.png\")
<\/p>\n\n\u30c8\u30fc\u30e9\u30b9\u306f3DCG\u3067\u306f\u3088\u304f\u898b\u304b\u3051\u308b\u7acb\u4f53\u3067\u3059\u304c\u4ea4\u5dee\u5224\u5b9a\u306f\u7d50\u69cb\u8907\u96d1\u3067\u3059\uff0e<\/p>\n\n
<\/p>\n\n
x-z\u5e73\u9762\u306b\u7f6e\u304b\u308c\u3066\u308b\u30c8\u30fc\u30e9\u30b9\u306e\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\uff0e<\/p>\n\n
\u3053\u308c\u306b\u534a\u76f4\u7dda\\({\\bf x}={\\bf p}+t{\\bf d}\\)\u3092\u4ee3\u5165\u3057\u3066$$t$$\u306b\u95a2\u3057\u3066\u6574\u7406\u3059\u308b\u308f\u3051\u3067\u3059\uff0e<\/p>\n\n
(1)\u306f\u89e3\u6790\u8868\u793a\u306a\u308f\u3051\u3067\u3059\u304c\uff0c\u8a08\u7b97\u304c\u5927\u5909\u306a\u306e\u3067\uff0c\u3053\u308c\u3092\u7121\u7406\u77e2\u7406<\/strong>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u3057\u3066\u307f\u307e\u3059\uff0e<\/p>\n\n \u305f\u3060\u3057<\/p>\n\n \u3067\u3059\uff0e<\/p>\n\n (2)\u306f\u30c8\u30fc\u30e9\u30b9\u306e\u4e2d\u5fc3\u304c\u539f\u70b9\u306b\u3042\u308b\u3053\u3068\u3092\u524d\u63d0\u3068\u3057\u3066\u3044\u308b\u306e\u3067\uff0c\u4e2d\u5fc3\u304c$${\\bf c}$$\u3067\u3042\u308b\u3068\u3059\u308b\u3068\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n \u3053\u308c\u306b<\/p>\n\n \u3092\u4ee3\u5165\u3057\u307e\u3059\uff0e\u305d\u308c\u3067\u3082\u5927\u5909\u306a\u306e\u3067\u90e8\u5206\u90e8\u5206\u306b\u5206\u3051\u3066\u8a08\u7b97\u3057\u307e\u3059\uff0e<\/p>\n\n $$ \\sqrt{(left-side)}=|{\\bf p}+t{\\bf d}-{\\bf c}|^{2}+R^{2}-r^{2} $$<\/p>\n\n \u3053\u306e\u5f0f\u306e\u4e00\u90e8\u306f\u5148\u65e5\u306e\u7403\u306e\u5f0f<\/a>\u3068\u540c\u3058\u306a\u306e\u3067\u8a08\u7b97\u3092\u7701\u7565\u3057\u307e\u3059\uff0e<\/p>\n\n $$ \\sqrt{(left-side)}=|{\\bf d}|^{2}t^{2}+2\\left({\\bf d}\\cdot({\\bf p}-{\\bf c})\\right)t+|{\\bf p}-{\\bf c}|^{2}+R^{2}-r^{2} $$<\/p>\n\n \u3053\u3053\u3067$$ C_{1}=|{\\bf d}|^{2} $$, $$ C_{2}=2\\left({\\bf d}\\cdot({\\bf p}-{\\bf c})\\right) $$, $$ C_{3}=|{\\bf p}-{\\bf c}|^{2}+R^{2}-r^{2} $$\u3068\u7f6e\u3044\u3066<\/p>\n\n $$ \\sqrt{(left-side)}=C_{1}t^{2}+C_{2}t+C_{3} $$ $$ (right-side)=4R^{2}|({\\bf p}+t{\\bf d}-{\\bf c}){\\bf M}|^{2} $$\n$$ =4R^{2}|{\\bf pM} + t{\\bf dM} – {\\bf cM}|^{2} $$<\/p>\n\n \u7d50\u5c40\u3053\u3061\u3089\u3082$${\\bf M}$$\u304c\u639b\u304b\u3063\u3066\u3044\u308b\u4ee5\u5916\u306f\u5148\u65e5\u306e\u7403\u306e\u5f0f<\/a>\u3068\u540c\u3058\u3067\u3059\uff0e<\/p>\n\n $$ =4R^{2}|{\\bf dM}|^{2}t^{2} + 8R^{2}\\left({\\bf dM}\\cdot(({\\bf p} – {\\bf c}){\\bf M})\\right)t + 4R^{2}|({\\bf p} – {\\bf c}){\\bf M}|^{2} $$<\/p>\n\n $$ C_{4}=4R^{2}|{\\bf dM}|^{2} $$, $$ C_{5}=8R^{2}\\left({\\bf dM}\\cdot(({\\bf p} – {\\bf c}){\\bf M})\\right) $$,\n$$ C_{6}=4R^{2}|({\\bf p} – {\\bf c}){\\bf M}|^{2} $$\u3068\u7f6e\u3044\u3066\uff0c<\/p>\n\n $$ (right-side)=C_{4}t^{2}+C_{5}t+C_{6} $$<\/p>\n\n \u5de6\u53f3\u3092\u5143\u306b\u623b\u3057\u3066\uff0c<\/p>\n\n $$ C_{1}^2t^{4} + 2C_{1}C_{2}t^{3} + \\left(2C_{1}C_{3} + C_{2}^{2}\\right)t^{2} + 2C_{2}C_{3}t + C_{3}^{2}=C_{4}t^{2}+C_{5}t+C_{6} $$<\/p>\n\n $$t$$\u306b\u95a2\u3057\u3066\u6574\u7406\u3057\u3066\uff0c<\/p>\n\n $$ C_{1}^2t^{4} + 2C_{1}C_{2}t^{3} + \\left(2C_{1}C_{3} + C_{2}^{2} -C_{4}\\right)t^{2} + (2C_{2}C_{3}-C_{5})t + C_{3}^{2}-C_{6}=0 $$<\/p>\n\n \u307e\u3068\u3081\u308b\u3068,<\/p>\n\n $$ At^{4} + Bt^{3} + Ct^{2} + Dt + E = 0 $$<\/p>\n\n $$ A=C_{1}^{2} $$ $$ C_{1}=|{\\bf d}|^{2} $$ \u3053\u306e\u56db\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u3051\u3070\u4ea4\u70b9(\u6700\u5927\u30674\u3064)\u304c\u6c42\u307e\u308a\u307e\u3059\uff0e\n\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306f\u3068\u3066\u3082\u96e3\u3057\u3044\u306e\u3067\u6b21\u56de\u66f8\u304d\u307e\u3059\uff0e<\/p>\n\n \u53c2\u8003 :<\/p>\n\n \u30c8\u30fc\u30e9\u30b9\u306f3DCG\u3067\u306f\u3088\u304f\u898b\u304b\u3051\u308b\u7acb\u4f53\u3067\u3059\u304c\u4ea4\u5dee\u5224\u5b9a\u306f\u7d50\u69cb\u8907\u96d1\u3067\u3059\uff0e x-z\u5e73\u9762\u306b\u7f6e\u304b\u308c\u3066\u308b\u30c8\u30fc\u30e9\u30b9\u306e\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\uff0e \u3053\u308c\u306b\u534a\u76f4\u7dda\u3092\u4ee3\u5165\u3057\u3066$$t$$\u306b\u95a2\u3057\u3066\u6574\u7406\u3059\u308b\u308f\u3051\u3067\u3059\uff0e (1)\u306f\u89e3\u6790\u8868\u793a\u306a\u308f\u3051\u3067\u3059 […]<\/p>","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts\/78"}],"collection":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=78"}],"version-history":[{"count":90,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts\/78\/revisions"}],"predecessor-version":[{"id":148,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts\/78\/revisions\/148"}],"wp:attachment":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=78"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=78"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=78"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\\(\n(|{\\bf x}|^{2}+R^{2}-r^{2})^{2}=4R^{2}|{\\bf x}{\\bf M}|^2 \\ldots (2)\n\\)<\/div>\n\n\\({\\bf M}=\\left(\\begin{array} \\\\ 1 & 0 & 0 \\\\ 0 & 0 & 0 \\\\ 0 & 0 & 1 \\end{array}\\right)\\)<\/div>\n\n\\((|{\\bf x}-{\\bf c}|^{2}+R^{2}-r^{2})^{2}=4R^{2}|({\\bf x}-{\\bf c}){\\bf M}|^2 \\ldots (2)’\\)<\/div>\n\n\\({\\bf x}={\\bf p}+t{\\bf d}\\)<\/div>\n\n
\n$$ (left-side)=\\left(C_{1}t^{2}+C_{2}t+C_{3}\\right)^{2} $$\n$$ =C_{1}^2t^{4} + 2C_{1}t^{2}\\left(C_{2}t+C_{3}\\right) + \\left(C_{2}t+C_{3}\\right)^{2} $$\n$$ =C_{1}^2t^{4} + 2C_{1}C_{2}t^{3} + 2C_{1}C_{3}t^{2} + C_{2}^{2}t^{2} + 2C_{2}C_{3}t + C_{3}^{2} $$\n$$ =C_{1}^2t^{4} + 2C_{1}C_{2}t^{3} + \\left(2C_{1}C_{3} + C_{2}^{2}\\right)t^{2} + 2C_{2}C_{3}t + C_{3}^{2} $$<\/p>\n\n
\n$$ B=2C_{1}C_{2} $$
\n$$ C=2C_{1}C_{3} + C_{2}^{2} -C_{4} $$
\n$$ D=2C_{2}C_{3}-C_{5} $$
\n$$ E=C_{3}^{2}-C_{6} $$
<\/p>\n\n
\n$$ C_{2}=2\\left({\\bf d}\\cdot({\\bf p}-{\\bf c})\\right) $$
\n$$ C_{3}=|{\\bf p}-{\\bf c}|^{2}+R^{2}-r^{2} $$
\n$$ C_{4}=4R^{2}|{\\bf dM}|^{2} $$
\n$$ C_{5}=8R^{2}\\left({\\bf dM}\\cdot(({\\bf p} – {\\bf c}){\\bf M})\\right) $$
\n$$ C_{6}=4R^{2}|({\\bf p} – {\\bf c}){\\bf M}|^{2} $$
<\/p>\n\n
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