锘??xml version="1.0" encoding="utf-8" standalone="yes"?>久久人做人爽一区二区三区 ,2020久久精品亚洲热综合一本,久久久久免费精品国产http://www.shnenglu.com/deane/category/5616.html 鍓嶈繘......zh-cnWed, 13 May 2009 08:06:04 GMTWed, 13 May 2009 08:06:04 GMT60鍫嗘帓搴?/title><link>http://www.shnenglu.com/deane/articles/82548.html</link><dc:creator>鏉庨槼</dc:creator><author>鏉庨槼</author><pubDate>Mon, 11 May 2009 03:57:00 GMT</pubDate><guid>http://www.shnenglu.com/deane/articles/82548.html</guid><wfw:comment>http://www.shnenglu.com/deane/comments/82548.html</wfw:comment><comments>http://www.shnenglu.com/deane/articles/82548.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/deane/comments/commentRss/82548.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/deane/services/trackbacks/82548.html</trackback:ping><description><![CDATA[<p><br>1銆?鍫嗘帓搴忓畾涔?br>    銆n涓叧閿瓧搴忓垪Kl錛孠2錛?#8230;錛孠n縐頒負鍫嗭紝褰撲笖浠呭綋璇ュ簭鍒楁弧瓚沖涓嬫ц川(綆縐頒負鍫嗘ц川)錛?br>    銆(1) ki≤K2i涓攌i≤K2i+1 鎴?2)Ki≥K2i涓攌i≥K2i+1(1≤i≤  )</p> <p>    銆鑻ュ皢姝ゅ簭鍒楁墍瀛樺偍鐨勫悜閲廟[1..n]鐪嬪仛鏄竴媯靛畬鍏ㄤ簩鍙夋爲鐨勫瓨鍌ㄧ粨鏋勶紝鍒欏爢瀹炶川涓婃槸婊¤凍濡備笅鎬ц川鐨勫畬鍏ㄤ簩鍙夋爲錛氭爲涓換涓闈炲彾緇撶偣鐨勫叧閿瓧鍧囦笉澶т簬(鎴栦笉灝忎簬)鍏跺乏鍙沖瀛?鑻ュ瓨鍦?緇撶偣鐨勫叧閿瓧銆?br>銆愪緥銆戝叧閿瓧搴忓垪(10錛?5錛?6錛?5錛?0錛?0)鍜?70錛?6錛?0錛?5錛?5錛?0)鍒嗗埆婊¤凍鍫嗘ц川(1)鍜?2)</p> <p>2銆佸ぇ鏍瑰爢鍜屽皬鏍瑰爢<br>    銆鏍圭粨鐐?浜︾О涓哄爢欏?鐨勫叧閿瓧鏄爢閲屾墍鏈夌粨鐐瑰叧閿瓧涓渶灝忚呯殑鍫嗙О涓哄皬鏍瑰爢銆?br>    銆鏍圭粨鐐?浜︾О涓哄爢欏?鐨勫叧閿瓧鏄爢閲屾墍鏈夌粨鐐瑰叧閿瓧涓渶澶ц咃紝縐頒負澶ф牴鍫嗐?br>  娉ㄦ剰錛?br>    銆鈶犲爢涓換涓瀛愭爲浜︽槸鍫嗐?br>   銆 鈶′互涓婅璁虹殑鍫嗗疄闄呬笂鏄簩鍙夊爢(Binary Heap)錛岀被浼煎湴鍙畾涔塳鍙夊爢銆?/p> <p>3銆佸爢鎺掑簭鐗圭偣<br>    銆鍫嗘帓搴?HeapSort)鏄竴鏍戝艦閫夋嫨鎺掑簭銆?br>    銆鍫嗘帓搴忕殑鐗圭偣鏄細鍦ㄦ帓搴忚繃紼嬩腑錛屽皢R[l..n]鐪嬫垚鏄竴媯靛畬鍏ㄤ簩鍙夋爲鐨勯『搴忓瓨鍌ㄧ粨鏋勶紝鍒╃敤瀹屽叏浜屽弶鏍戜腑鍙屼翰緇撶偣鍜屽瀛愮粨鐐逛箣闂寸殑鍐呭湪鍏崇郴銆愬弬瑙佷簩鍙夋爲鐨勯『搴忓瓨鍌ㄧ粨鏋勩戯紝鍦ㄥ綋鍓嶆棤搴忓尯涓夋嫨鍏抽敭瀛楁渶澶?鎴栨渶灝?鐨勮褰曘?/p> <p>4銆佸爢鎺掑簭涓庣洿鎺ユ彃鍏ユ帓搴忕殑鍖哄埆<br>    銆鐩存帴閫夋嫨鎺掑簭涓紝涓轟簡浠嶳[1..n]涓夊嚭鍏抽敭瀛楁渶灝忕殑璁板綍錛屽繀欏昏繘琛宯-1嬈℃瘮杈冿紝鐒跺悗鍦≧[2..n]涓夊嚭鍏抽敭瀛楁渶灝忕殑璁板綍錛屽張闇瑕佸仛n-2嬈?姣旇緝銆備簨瀹炰笂錛屽悗闈㈢殑n-2嬈℃瘮杈冧腑錛屾湁璁稿姣旇緝鍙兘鍦ㄥ墠闈㈢殑n-1嬈℃瘮杈冧腑宸茬粡鍋氳繃錛屼絾鐢變簬鍓嶄竴瓚熸帓搴忔椂鏈繚鐣欒繖浜涙瘮杈冪粨鏋滐紝鎵浠ュ悗涓瓚熸帓搴忔椂鍙堥噸澶嶆墽 琛屼簡榪欎簺姣旇緝鎿嶄綔銆?br>    銆鍫嗘帓搴忓彲閫氳繃鏍戝艦緇撴瀯淇濆瓨閮ㄥ垎姣旇緝緇撴灉錛屽彲鍑忓皯姣旇緝嬈℃暟銆?/p> <p>5銆佸爢鎺掑簭<br>    鍫嗘帓搴忓埄鐢ㄤ簡澶ф牴鍫?鎴栧皬鏍瑰爢)鍫嗛《璁板綍鐨勫叧閿瓧鏈澶?鎴栨渶灝?榪欎竴鐗瑰緛錛屼嬌寰楀湪褰撳墠鏃犲簭鍖轟腑閫夊彇鏈澶?鎴栨渶灝?鍏抽敭瀛楃殑璁板綍鍙樺緱綆鍗曘?/p> <p>錛?錛夌敤澶ф牴鍫嗘帓搴忕殑鍩烘湰鎬濇兂<br>鈶?鍏堝皢鍒濆鏂囦歡R[1..n]寤烘垚涓涓ぇ鏍瑰爢錛屾鍫嗕負鍒濆鐨勬棤搴忓尯<br>鈶?鍐嶅皢鍏抽敭瀛楁渶澶х殑璁板綍R[1](鍗沖爢欏?鍜屾棤搴忓尯鐨勬渶鍚庝竴涓褰昍[n]浜ゆ崲錛岀敱姝ゅ緱鍒版柊鐨勬棤搴忓尯R[1..n-1]鍜屾湁搴忓尯R[n]錛屼笖婊¤凍R[1..n-1].keys≤R[n].key<br>鈶?鐢變簬浜ゆ崲鍚庢柊鐨勬牴R[1]鍙兘榪濆弽鍫嗘ц川錛屾晠搴斿皢褰撳墠鏃犲簭鍖篟[1..n-1]璋冩暣涓哄爢銆傜劧鍚庡啀嬈″皢R[1..n-1]涓叧閿瓧鏈澶х殑璁板綍R[1]鍜岃鍖?闂寸殑鏈鍚庝竴涓褰昍[n-1]浜ゆ崲錛岀敱姝ゅ緱鍒版柊鐨勬棤搴忓尯R[1..n-2]鍜屾湁搴忓尯R[n-1..n]錛屼笖浠嶆弧瓚沖叧緋籖[1..n-2].keys≤R [n-1..n].keys錛屽悓鏍瘋灝哛[1..n-2]璋冩暣涓哄爢銆?br>    ……<br>鐩村埌鏃犲簭鍖哄彧鏈変竴涓厓绱犱負姝€?/p> <p>錛?錛夊ぇ鏍瑰爢鎺掑簭綆楁硶鐨勫熀鏈搷浣滐細<br>鈶?鍒濆鍖栨搷浣滐細灝哛[1..n]鏋勯犱負鍒濆鍫嗭紱<br>鈶?姣忎竴瓚熸帓搴忕殑鍩烘湰鎿嶄綔錛氬皢褰撳墠鏃犲簭鍖虹殑鍫嗛《璁板綍R[1]鍜岃鍖洪棿鐨勬渶鍚庝竴涓褰曚氦鎹紝鐒跺悗灝嗘柊鐨勬棤搴忓尯璋冩暣涓哄爢(浜︾О閲嶅緩鍫?銆?br>  娉ㄦ剰錛?br>鈶犲彧闇鍋歯-1瓚熸帓搴忥紝閫夊嚭杈冨ぇ鐨刵-1涓叧閿瓧鍗沖彲浠ヤ嬌寰楁枃浠墮掑鏈夊簭銆?br>鈶$敤灝忔牴鍫嗘帓搴忎笌鍒╃敤澶ф牴鍫嗙被浼鹼紝鍙笉榪囧叾鎺掑簭緇撴灉鏄掑噺鏈夊簭鐨勩傚爢鎺掑簭鍜岀洿鎺ラ夋嫨鎺掑簭鐩稿弽錛氬湪浠諱綍鏃跺埢錛屽爢鎺掑簭涓棤搴忓尯鎬繪槸鍦ㄦ湁搴忓尯涔嬪墠錛屼笖鏈夊簭鍖烘槸鍦ㄥ師鍚戦噺鐨勫熬閮ㄧ敱鍚庡線鍓嶉愭鎵╁ぇ鑷蟲暣涓悜閲忎負姝€?/p> <p>錛?錛夊爢鎺掑簭鐨勭畻娉曪細<br>  void HeapSort(SeqIAst R)<br>   { //瀵筊[1..n]榪涜鍫嗘帓搴忥紝涓嶅Θ鐢≧[0]鍋氭殏瀛樺崟鍏?br>    int i錛?br>    BuildHeap(R)錛?//灝哛[1-n]寤烘垚鍒濆鍫?br>    for(i=n;i>1錛沬--){ //瀵瑰綋鍓嶆棤搴忓尯R[1..i]榪涜鍫嗘帓搴忥紝鍏卞仛n-1瓚熴?br>      R[0]=R[1]錛汻[1]=R[i];R[i]=R[0]錛?//灝嗗爢欏跺拰鍫嗕腑鏈鍚庝竴涓褰曚氦鎹?br>銆    Heapify(R錛?錛宨-1)錛?//灝哛[1..i-1]閲嶆柊璋冩暣涓哄爢錛屼粎鏈塕[1]鍙兘榪濆弽鍫嗘ц川<br>     } //endfor<br>   } //HeapSort</p> <p>錛?錛?BuildHeap鍜孒eapify鍑芥暟鐨勫疄鐜?br>銆鍥犱負鏋勯犲垵濮嬪爢蹇呴』浣跨敤鍒拌皟鏁村爢鐨勬搷浣滐紝鍏堣璁篐eapify鐨勫疄鐜般?br>鈶?Heapify鍑芥暟鎬濇兂鏂規硶<br>銆 姣忚稛鎺掑簭寮濮嬪墠R[l..i]鏄互R[1]涓烘牴鐨勫爢錛屽湪R[1]涓嶳[i]浜ゆ崲鍚庯紝鏂扮殑鏃犲簭鍖篟[1..i-1]涓彧鏈塕[1]鐨勫煎彂鐢熶簡鍙樺寲錛屾晠闄 [1]鍙兘榪濆弽鍫嗘ц川澶栵紝鍏朵綑浠諱綍緇撶偣涓烘牴鐨勫瓙鏍戝潎鏄爢銆傚洜姝わ紝褰撹璋冩暣鍖洪棿鏄疪[low..high]鏃訛紝鍙』璋冩暣浠[low]涓烘牴鐨勬爲鍗沖彲銆?br>"絳涢夋硶"璋冩暣鍫?br>銆 R[low]鐨勫乏銆佸彸瀛愭爲(鑻ュ瓨鍦?鍧囧凡鏄爢錛岃繖涓ゆ5瀛愭爲鐨勬牴R[2low]鍜孯[2low+1]鍒嗗埆鏄悇鑷瓙鏍戜腑鍏抽敭瀛楁渶澶х殑緇撶偣銆傝嫢R[low]. key涓嶅皬浜庤繖涓や釜瀛╁瓙緇撶偣鐨勫叧閿瓧錛屽垯R[low]鏈繚鍙嶅爢鎬ц川錛屼互R[low]涓烘牴鐨勬爲宸叉槸鍫嗭紝鏃犻』璋冩暣錛涘惁鍒欏繀欏誨皢R[low]鍜屽畠鐨勪袱涓瀛愮粨鐐?涓叧閿瓧杈冨ぇ鑰呰繘琛屼氦鎹紝鍗砇[low]涓嶳[large](R[large].key=max(R[2low].key錛孯[2low+1]. key))浜ゆ崲銆備氦鎹㈠悗鍙堝彲鑳戒嬌緇撶偣R[large]榪濆弽鍫嗘ц川錛屽悓鏍風敱浜庤緇撶偣鐨勪袱媯靛瓙鏍?鑻ュ瓨鍦?浠嶇劧鏄爢錛屾晠鍙噸澶嶄笂榪扮殑璋冩暣榪囩▼錛屽浠 [large]涓烘牴鐨勬爲榪涜璋冩暣銆傛榪囩▼鐩磋嚦褰撳墠琚皟鏁寸殑緇撶偣宸叉弧瓚沖爢鎬ц川錛屾垨鑰呰緇撶偣宸叉槸鍙跺瓙涓烘銆備笂榪拌繃紼嬪氨璞¤繃絳涘瓙涓鏍鳳紝鎶婅緝灝忕殑鍏抽敭瀛楅愬眰絳涗笅 鍘伙紝鑰屽皢杈冨ぇ鐨勫叧閿瓧閫愬眰閫変笂鏉ャ傚洜姝わ紝鏈変漢灝嗘鏂規硶縐頒負"絳涢夋硶"銆?br>  銆 鍏蜂綋鐨勭畻娉曘愬弬瑙佹暀鏉愩?/p> <p>鈶uildHeap鐨勫疄鐜?br>銆銆瑕佸皢鍒濆鏂囦歡R[l..n]璋冩暣涓轟竴涓ぇ鏍瑰爢錛屽氨蹇呴』灝嗗畠鎵瀵瑰簲鐨勫畬鍏ㄤ簩鍙夋爲涓互姣忎竴緇撶偣涓烘牴鐨勫瓙鏍戦兘璋冩暣涓哄爢銆?br>銆銆鏄劇劧鍙湁涓涓粨鐐圭殑鏍戞槸鍫嗭紝鑰屽湪瀹屽叏浜屽弶鏍戜腑錛屾墍鏈夊簭鍙?鐨勭粨鐐歸兘鏄彾瀛愶紝鍥犳浠ヨ繖浜涚粨鐐逛負鏍圭殑瀛愭爲鍧囧凡鏄爢銆傝繖鏍鳳紝鎴戜滑鍙渶渚濇灝嗕互搴忓彿涓?錛?nbsp; -1錛?#8230;錛?鐨勭粨鐐逛綔涓烘牴鐨勫瓙鏍戦兘璋冩暣涓哄爢鍗沖彲銆?br>   銆 鍏蜂綋綆楁硶銆愬弬瑙佹暀鏉愩戙?/p> <p>5銆佸ぇ欏跺爢鎺掑簭瀹炵幇</p> <p> </p> <p>void HeapSort ( Elem R[], int n ) ...{<br>// 瀵硅褰曞簭鍒桼[1..n]榪涜鍫嗘帓搴忋?br>for ( i=n/2; i>0; --i )<br>                    // 鎶奟[1..n]寤烘垚澶ч《鍫?br>   HeapAdjust ( R, i, n );<br>for ( i=n; i>1; --i ) ...{<br>R[1]←→R;          <br>        // 灝嗗爢欏惰褰曞拰褰撳墠鏈粡鎺掑簭瀛愬簭鍒?br>        // R[1..i]涓渶鍚庝竴涓褰曠浉浜掍氦鎹?br>HeapAdjust(R, 1, i-1);            <br>        // 灝哛[1..i-1] 閲嶆柊璋冩暣涓哄ぇ欏跺爢<br>}<br>} // HeapSort<br>鍏朵腑絳涢夌殑綆楁硶濡備笅鎵紺恒備負灝哛[s..m]璋冩暣涓?#8220;澶ч《鍫?#8221;錛岀畻娉曚腑“絳涢?#8221;搴旀部鍏抽敭瀛楄緝澶х殑瀛╁瓙緇撶偣鍚戜笅榪涜銆?br>void HeapAdjust (Elem R[], int s, int m) ...{<br>// 宸茬煡R[s..m]涓褰曠殑鍏抽敭瀛楅櫎R[s].key涔?br>// 澶栧潎婊¤凍鍫嗙殑瀹氫箟錛屾湰鍑芥暟璋冩暣R[s] 鐨勫叧<br>// 閿瓧錛屼嬌R[s..m]鎴愪負涓涓ぇ欏跺爢錛堝鍏朵腑<br>// 璁板綍鐨勫叧閿瓧鑰岃█錛?br>rc = R[s];<br>for ( j=2*s; j<=m; j*=2 ) ...{// 娌縦ey杈冨ぇ鐨勫瀛愮粨鐐瑰悜涓嬬瓫閫?br>    if ( j<m && R[j].key<R[j+1].key)  ++j;<br>    if ( rc.key >= R[j].key )  break; // rc搴旀彃鍏ュ湪浣嶇疆s涓?br>    R[s] = R[j];  s = j;<br>}<br>    R[s] = rc; // 鎻掑叆<br>} // HeapAdjust </p> <p>6銆?綆楁硶鍒嗘瀽<br>    銆鍫嗘帓搴忕殑鏃墮棿錛屼富瑕佺敱寤虹珛鍒濆鍫嗗拰鍙嶅閲嶅緩鍫嗚繖涓ら儴鍒嗙殑鏃墮棿寮閿鏋勬垚錛屽畠浠潎鏄氳繃璋冪敤Heapify瀹炵幇鐨勩?br>  銆  鍫嗘帓搴忕殑鏈鍧忔椂闂村鏉傚害涓篛(nlgn)銆傚爢鎺掑簭鐨勫鉤鍧囨ц兘杈冩帴榪戜簬鏈鍧忔ц兘銆?br>    銆鐢變簬寤哄垵濮嬪爢鎵闇鐨勬瘮杈冩鏁拌緝澶氾紝鎵浠ュ爢鎺掑簭涓嶉傚疁浜庤褰曟暟杈冨皯鐨勬枃浠躲?br>    銆鍫嗘帓搴忔槸灝卞湴鎺掑簭錛岃緟鍔╃┖闂翠負O(1)錛?br>    銆瀹冩槸涓嶇ǔ瀹氱殑鎺掑簭鏂規硶銆?/p> <p> <br></p> <img src ="http://www.shnenglu.com/deane/aggbug/82548.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/deane/" target="_blank">鏉庨槼</a> 2009-05-11 11:57 <a href="http://www.shnenglu.com/deane/articles/82548.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item><item><title>鍥懼艦鍖呭惈鍒ゅ畾綆楁硶http://www.shnenglu.com/deane/articles/38111.html鏉庨槼鏉庨槼Sun, 09 Dec 2007 12:26:00 GMThttp://www.shnenglu.com/deane/articles/38111.htmlhttp://www.shnenglu.com/deane/comments/38111.htmlhttp://www.shnenglu.com/deane/articles/38111.html#Feedback0http://www.shnenglu.com/deane/comments/commentRss/38111.htmlhttp://www.shnenglu.com/deane/services/trackbacks/38111.html  
     鍦ㄨ繘琛屽浘褰㈡眰浜ゆ椂錛屽父甯擱渶瑕佸垽瀹氫袱涓浘褰㈤棿鏄惁鏈夊寘鍚叧緋匯傚鐐規槸鍚﹀寘鍚湪綰挎銆佸鉤闈㈠尯鍩熴佷笁緇村艦浣撲腑錛岀嚎孌墊槸鍚﹀寘鍚湪騫抽潰鍖哄煙銆佷笁緇村艦浣撲腑錛岀瓑絳夈傝澶氬寘鍚垽瀹氶棶棰樺彲杞寲涓虹偣鐨勫寘鍚垽瀹氶棶棰橈紝濡傚垽鏂嚎孌墊槸鍚﹀湪騫抽潰涓婂彲浠ヨ漿鍖栦負鍒ゆ柇鍏朵袱绔偣鏄惁鍦ㄥ鉤闈笂銆傚洜姝や笅闈富瑕佽璁哄叧浜庣偣鐨勫寘鍚垽瀹氱畻娉曘?/font>

鍒ゆ柇鐐逛笌綰挎鐨勫寘鍚叧緋伙紝涔熷氨鏄垽鏂偣涓庣嚎鐨勬渶鐭窛紱繪槸鍚︿綅浜庡宸寖鍥村唴銆傞犲瀷涓父鐢ㄧ殑綰挎鏈変笁縐嶏細

錛?錛夌洿綰挎錛岋紙2錛夊渾閿ユ洸綰挎錛堜富瑕佹槸鍦嗗姬錛夛紝錛?錛夊弬鏁版洸綰匡紙涓昏鏄疊ezier錛孊鏍鋒潯涓嶯URBS鏇茬嚎錛夈傜偣涓庨潰鐨勫寘鍚垽瀹氫篃綾諱技鍦板垎涓轟笁縐嶆儏鍐點備笅闈㈠垎鍒璁恒?/font>

1銆佺偣涓庣洿綰挎鐨勫寘鍚垽瀹?/font>

鍋囪鐐瑰潗鏍囦負P(x, y, z)錛岀洿綰挎绔偣涓篜1(x1, y1, z1)錛孭2(x2,y2,z2)錛屽垯鐐筆鍒扮嚎孌礟1P2鐨勮窛紱葷殑騫蟲柟涓?/font>

d2=(x-x1)2+(y-y1)2+(z-z1)2-[(x2-x1)(x-x1)+(y2-y1)(y-y1)+(z2-z1)(z-z1)]2/[(x2-x1)2+(y2-y1)2+(z2-z1)2]

褰揹2<a2鏃訛紝璁や負鐐瑰湪綰挎錛堟垨鍏跺歡闀跨嚎錛変笂錛岃繖鏃惰繕闇榪涗竴姝ュ垽鏂偣鏄惁钀藉湪鐩寸嚎孌電殑鏈夋晥鍖洪棿鍐呫傚彧瑕佸鍧愭爣鍒嗛噺榪涜姣旇緝錛屽亣璁劇嚎孌典袱绔偣鐨剎鍒嗛噺涓嶇瓑錛堝惁鍒欐墍鏈夊垎閲忓潎鐩哥瓑錛岄偅涔堢嚎孌典袱绔偣閲嶅悎錛岀嚎孌甸鍖栦負涓鐐癸級錛岄偅涔堝綋x-x1涓巟-x2鍙嶅彿鏃訛紝鐐筆鍦ㄧ嚎孌電殑鏈夋晥鍖洪棿鍐呫?/font>

2銆佺偣涓庡渾閿ユ洸綰挎鐨勫寘鍚垽瀹?/font>

浠ュ渾寮т負渚嬶紝鍋囪鐐圭殑鍧愭爣涓?x, y, z)錛屽渾寮х殑涓績涓猴紙x0, y0, z0錛夛紝鍗婂緞涓簉錛岃搗濮嬭a1錛岀粓姝㈣a2銆傝繖浜涜搴﹂兘鏄浉瀵逛簬灞閮ㄥ潗鏍囩郴x杞磋岃█銆傚渾寮ф墍鍦ㄥ鉤闈負

銆銆銆銆ax+by+cz+d=0

鍏堝垽鏂偣鏄惁鍦ㄨ騫抽潰涓婏紝鑻ヤ笉鍦紝鍒欑偣涓嶅彲鑳借鍖呭惈銆傝嫢鍦紝鍒欓氳繃鍧愭爣鍙樻崲錛屾妸闂杞崲鍒頒簩緇寸殑闂銆?/font>

緇欏畾涓績涓猴紙x0, y0錛夛紝鍗婂緞涓簉錛岃搗濮嬭a1錛岀粓姝㈣a2鐨勫渾寮э紝瀵瑰鉤闈笂涓鐐筆錛坸, y錛夛紝鍒ゆ柇P鏄惁鍦ㄥ渾寮т笂錛屽彲鍒嗕簩姝ヨ繘琛屻傜涓姝ュ垽鏂璓鏄惁鍦ㄥ渾蹇冧負錛坸0, y0錛夛紝鍗婂緞涓簉鐨勫渾鐨勫渾鍛ㄤ笂錛屽嵆涓嬪紡鏄惁鎴愮珛錛?/font>

銆銆銆銆

絎簩姝ュ垽鏂璓鏄惁鍦ㄦ湁鏁堢殑鍦嗗姬孌靛唴銆?/font>

3銆佺偣涓庡弬鏁版洸綰跨殑鍖呭惈鍒ゅ畾

璁劇偣鍧愭爣涓篜(x, y, z)錛屽弬鏁版洸綰夸負Q(t)=(x(t), y(t), z(t))銆傜偣涔熷弬鏁版洸綰跨殑姹備氦璁$畻鍖呮嫭涓変釜姝ラ錛?/font>

錛?錛夎綆楀弬鏁皌鍊鹼紝浣縋鍒癚(t)鐨勮窛紱繪渶灝忥紱

錛?錛夊垽鏂璽鏄惁鍦ㄦ湁鏁堝弬鏁板尯闂村唴錛堥氬父涓篬0錛?]錛夛紱

錛?錛夊垽鏂璔(t)涓嶱鐨勮窛紱繪槸鍚﹀皬浜巃 銆傝嫢錛?錛夛紝錛?錛夋鐨勫垽鏂潎涓?#8220;鏄?#8221;錛屽垯鐐瑰湪鏇茬嚎涓婏紱鍚﹀垯鐐逛笉鍦ㄦ洸綰夸笂銆?/font>

絎竴姝ュ簲璁$畻t錛屼嬌寰梶P-Q(t)|鏈灝忥紝

鍗?R(t)=(P-Q(t))(P-Q(t))=|P-Q(t)|2鏈灝?/font>

鏍規嵁寰Н鍒嗙煡璇嗭紝鍦ㄨ澶凴'(t)=0鍗?/font>

Q'(t)[P-Q(t)]=0

鐢ㄦ暟鍊兼柟娉曡В鍑簍鍊鹼紝鍐嶄唬鍏ユ洸綰垮弬鏁版柟紼嬪彲姹傚嚭鏇茬嚎涓婂搴旂偣鐨勫潗鏍囥傜錛?錛夈侊紙3錛夋鐨勫鐞嗘瘮杈冪畝鍗曪紝涓嶅啀璇﹁堪銆?/font>

4銆佺偣涓庡鉤闈㈠尯鍩熺殑鍖呭惈鍒ゅ畾

璁劇偣鍧愭爣涓篜(x, y, z)錛屽鉤闈㈡柟紼嬩負ax+by+cz+d=0銆傚垯鐐瑰埌騫抽潰鐨勮窛紱諱負

銆銆銆銆d=

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鍒ゆ柇騫抽潰涓婁竴涓偣鏄惁鍖呭惈鍦ㄥ悓騫抽潰鐨勪竴涓杈瑰艦鍐咃紝鏈夎澶氱綆楁硶錛岃繖閲屼粎浠嬬粛甯哥敤鐨勪笁縐嶏細鍙夌Н鍒ゆ柇娉曘佸す瑙掍箣鍜屾楠屾硶浠ュ強浜ょ偣璁℃暟媯楠屾硶銆?/font>

錛?錛夊弶縐垽鏂硶

鍋囪鍒ゆ柇鐐逛負P0銆傚杈瑰艦欏剁偣鎸夐『搴忔帓鍒椾負P1P2…Pn銆傚鍥?.5.2鎵紺恒備護Vi=Pi-P0, i=1, 2, …, n, Vn+1=V1銆?/font>

閭d箞錛孭0鍦ㄥ杈瑰艦鍐呯殑鍏呰鏉′歡鏄弶縐疺iXVi+1(i=1, 2, …, n)鐨勭鍙風浉鍚屻傚弶縐垽鏂硶浠呴傜敤浜庡嚫澶氳竟褰€傚綋澶氳竟褰負鍑規椂錛屽敖綆$偣鍦ㄥ杈瑰艦鍐呬篃涓嶈兘淇濊瘉涓婅堪鍙夌Н絎﹀彿閮界浉鍚屻傝繖鏃跺彲閲囩敤鍚庨潰浠嬬粛鐨勪袱縐嶆柟娉曘?/font>

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鍥?.5.2 鍙夌Н鍒ゆ柇娉?/font>

錛?錛夊す瑙掍箣鍜屾楠屾硶

鍋囪鏌愬鉤闈笂鏈夌偣P0鍜屽杈瑰艦P1P2P3P4P5錛屽鍥?.5.3鎵紺恒傚皢鐐筆0鍒嗗埆涓嶱i鐩歌繛錛屾瀯鎴愬悜閲廣i=P-P0銆傚亣璁捐 PiP0Pi+1=ai銆傚鏋?img height=45 src="file:///F:/杞歡寮鍙?娓告垙寮鍙?鏁板/2.5.3鍖呭惈鍒ゅ畾綆楁硶.files/Image101.gif" width=38>=0錛屽垯鐐筆0鍦ㄥ杈瑰艦涔嬪錛屽鍥?.5.3(a)鎵紺恒傚鏋?img height=45 src="file:///F:/杞歡寮鍙?娓告垙寮鍙?鏁板/2.5.3鍖呭惈鍒ゅ畾綆楁硶.files/Image102.gif" width=38>=2π錛屽垯鐐筆0鍦ㄥ杈瑰艦涔嬪唴錛屽鍥?.5.3(b)鎵紺恒俛i鍙氳繃涓嬪垪鍏紡璁$畻錛氫護Si=Vi? Vi+1, Ci=Vi·Vi+1錛屽垯tg(ai)=Si/Ci錛屾墍浠i=arctg(Si/Ci)涓?/font>

ai鐨勭鍙峰嵆浠h〃瑙掑害鐨勬柟鍚戙?/font>

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鍥?.5.3 澶硅涔嬪拰媯楠屾硶

鍦ㄥ杈瑰艦杈規暟涓嶅お澶氾紙<44錛夌殑鎯呭喌涓嬶紝鍙互閲囩敤涓嬪垪榪戜技鍏紡璁$畻ai銆?/font>

銆銆銆銆褰?|Si|≤|Ci|

銆銆褰?|Si|>|Ci|

鍏朵腑d=0.0355573涓哄父鏁般傚綋Σαi≥π

鏃訛紝鍙垽P0鍦ㄥ杈瑰艦鍐呫傚綋Σαi錛?#960; 鏃訛紝鍙垽P0鍦ㄥ杈瑰艦澶栥傝瘉鏄庣暐銆?/font>

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鏉庨槼 2007-12-09 20:26 鍙戣〃璇勮
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