
#1                   澭߷Ʒ˵

    1Ϊް߷ƷϵĹΪչ棬˷ֽƷ͹ַչͼ㡣߷Ʒǽľ߷ֳɵȷְϣǶεĽ棬βۣмӹ򵥡Թ˵ļҪ󲻸ߡɱ͵ŵ㣬ȷϴʱɽӽ״
    2ʾͼdΪ޵ھbΪĺȡҪdb>0ɲȷ롣
    3޾߷ֳn1ȷ֣γ߷ֳn2ȷÿһߵʵn1n2ֵɲ߸ֱ;ҪԶȡ4n1n2ֵԽչͼľԽߣչͼĹӦӡ˹һȡn1n2=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬n1n2ֵȡһЩ
    4ĽƷʽѡһԲڶΣһԲΣûɸʵҪӦťת
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)һ߶Σȵls߶ηֳn2ȷݣÿݳȵm2
    (2)ȷֵ߶ε໭ֱߣͼڸֱ϶Գȡms(1)ms(n2/2+1)ȡ
    (3)ù⻬ȡĸ㣬ΪһƬչͼ軭n1ƬͬչͼƴɽƵޡ


#2                   澭߷˵

    1Ϊް߷ϵĹΪչ棬ÿ߰ߴϣһӹʱѹӵİ취ʹм칰״ѹӷӹҪдѹģߣԹ˵ļҪߣɱôʹַϣݹҪ󣬹˵ļˮƽ豸״Լɱĸߵȷ
    2ʾͼdΪ޵ھd1Ϊ޶ԲֱbΪĺȡҪd1>=0b>0d>d1ɲȷ롣
    3ڼӹķͬϳߴв죬ǱȽϴĲ죬ڱչϵtԷûݼӹʵʾϡtֵΪ01ֵ֮t=0ʱʾӹûӳģȫİ취棻t=1ʱʾֱߴϣӹҪôѹİ취չĻ棬0<t<1ʱչߴ֮䣬ʱɸݾѡϳߴչϵ
    4޾߷ֳn1ȷ֣γ߷ֳn2ȷÿһߵʵn1n2ֵɲ߸ֱ;ҪԶȡn1ֵݼӹҪȷn2ֵԽչͼľԽߣչͼĹӦӡ˹һȡn2=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬n2ֵȡһЩ
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ԲֱrsΪ뾶Բɵչͼ
    (2)һ߶Σȵlp߶ηֳn2ȷݣÿݳȵm1
    (3)ȷֵ߶ε໭ֱߣ˵㴦ͼrpΪ뾶ڸֱ߼Բ϶Գȡma(1)ma(n2/2+1)ȡ
    (4)ù⻬ȡĸ㣬ΪһƬչͼ軭n1ƬͬչͼڹӹȫﵽҪʵʱʵһƴʱٸʵȥಿ֡
    (5)ԲƬϾѹӹƴԲޡ


#3                   γ߷Ʒ˵

    1Ϊްγ߷ƷϵĹΪչ棬ýƷܽƵ״Ʒǽγ߷ֳɵȷְԲ׶ϣɸԲ׶̨ӵĽ棬βۣмӹ򵥡Թ˵ļҪ󲻸ߡɱ͵ŵ㣬ȷϴʱɽӽ״
    2ʾͼdΪ޵ھbΪĺȡҪdb>0ɲȷ롣
    3޷ʱγ߷ֳn1ȷֱ֣ϴΪ˽Լֲģ߷򻹿ɷֳn2ȷϣn1n2ֵɲ߸ֱ;ҪԶ,n1ȡ2n2ȡڵ1Сڵ48n1n2ֵԽ,չͼľԽߣչͼĹӦӡ˹һȡn1n2=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬n1n2ֵȡһЩ
    4Բİ뾶ݵȷı仯ı䣬Ϊd*sin(180/n1)/2ԲڼӹʱҪѹѹӷӹʱ踨ӹȡøЧ
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ԲֱrsΪ뾶Բɵչͼ
    (2)Բ׶ֱ̨ra(1)ra(n1/2-1)Ϊ뾶⻡rb(1)rb(n1/2-1)Ϊ뾶ڻٷֱla(1)la(n1/2-1)ȡ⻡ҳlb(1)lb(n1/2-1)ȡ⻡Խȡ⻡ԲĻߣֱ߼ΧΪϵչͼ
    (3)Բ׶̨軭n1/2-1ֲͬչͼÿ2n2ƴɽƵޡ


#4                   γ߷˵

    1Ϊްγ߷ֿ鹰ϵĹΪչ棬˹ÿ߸չϵͬ治ͬߴϣһӹʱѹӵİ취ʹмչ״ӹԹ˵ļҪߣɱôѹӷӹҪдѹģߣʹַϣݹҪ󣬹˵ļˮƽ豸״ɱĸߵȷ
    2ʾͼdΪ޵ھbΪĺȡҪdb>0ɲȷ롣
    3޷ʱγ߷ֳn1ȷֿ飬ͬʱ߷ֳn2ȷÿһߵʵn1n2ֵɲ߸ֱ;ҪԶ, n1ȡ2n2ȡڵ3Сڵ48n1n2ֵݹľȺͼӹ豸״ȷÿһ飬γ߷趨˵ȷnnȡڵ6Сڵ48nֵԽ,չͼľԽߣչͼĹӦӡ˹һȡn=1016ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    4Բİ뾶ݵȷı仯ı䣬Ϊd*sin(180/n1)/2ԲڼӹʱҪѹѹӹ⣬踨ӹȡøЧ
    5ڼӹķͬϳߴв죬ڱչϵtԷûݼӹʵʾϡtֵΪ01ֵ֮t=0ʱʾӹûӳģȫİ취棻t=1ʱʾֱߴϣӹҪôѹİ취չĻ棬0<t<1ʱչߴ֮䣬ʱɸݾѡϳߴչϵ
    6չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ԲֱrpΪ뾶Բɵչͼ
    (2)ϷȻһ߶Σȵlp߶˵㰴ͼֱrc(1)rc(n1/2-1)Ϊ뾶⻡rd(1)rd(n1/2-1)Ϊ뾶ڻma(1)ma(n+1)ԳȷԲĿȡ
    (3)Բ˵㴹ֱߣ߶Ϊnȷ֣ÿȷֳΪLu(i)߶ε໭ֱߣֱڸֱ϶ӦԳȡma(1)ma(n+1)ȡ
    (4)ù⻬ȡĸ㣬ΪһƬϵչͼn1/2-1չϣÿ軭2*n2ƬͬչͼΪչ棬κϷԴﵽ׼ȷҪʵʱʵһƴʱٸʵȥಿ֡
    (5)ԲƬϾѹӻƴԲޡ


#5                   Բƫཻ˵

    1ΪԲƫཻƫ漰ԲֱĺȿȡֵĹԲܵչͼչͼǰϣõԲֳոơ
    2ͼd1ΪԲֱd2ΪԲֱܵLΪԲܵĳȣphΪԲƫĸ߶ȣb1Ϊ׶ܰĺȣb2ΪԲܰĺȣɲȷ롣Ҫd1>d2>0ph<(d1-d2)/2,L>d1/2b1b2>0
    3Բܳnȷߵʵnֵ4ɲ߸ԲֱҪȷ롣nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    4ԲչͼֱӸڰϣɲչʾͼ·
    (1)һ߶ΣȵS߶ηֳnȷݣÿݳȵm
    (2)ȷֵ㻭߶εĴֱߣڸֱȡLa(1)La(n/2+1)
    (3)ù⻬ȡĸ㣬ΪԲܵչͼ


#6                   ȾȾҶƬ˵

    1ΪȾȾҶƬĹҶƬΪչ棬ӹͬչͼҪҲͬƬҶƬѹƷӹչͼ㡣öƬҶƬӺƵķӹھ⾶ҪӦСֵӦݾ;ȷ
    2ʾͼd1ΪҶƬ⾶d2ΪҶƬھpΪҶƬݾ࣬bΪĺȡҪd1d2pb>0ɲȷ롣
    3չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ⶨһԭooΪԲģRs1Rs2Ϊ뾶ֱ𻭻
    (2)Rs1Ļȡ㣬һȡҳLxҲչǶaȷԲнǡҳǶȷ󣬰ͼֱߵԭoRs1Rs2ֱΧΪҶƬչͼ


#7                   Ǳ侶ȾҶƬ˵

    1ΪҶƬھݾǶֵ⾶𽥱ҶƬСбı侶ȾҶƬĹҶƬΪչ棬ӹͬչͼҪҲͬƬҶƬѹƷӹչͼ㡣öƬҶƬӺƵķӹھ⾶ҪӦСֵӦݾ;ȷ
    2ʾͼdΪҶƬھd1ΪһƬҶƬС⾶d2ΪһƬҶƬĴ⾶ҲǵڶƬҶƬС⾶d3ΪڶƬҶƬĴ⾶ƣpΪҶƬݾ࣬a1ΪҶƬбǣa2ΪҶƬбǶȣbΪĺȣtΪҪϵҶƬҪd1>d>030>=a1>030>=a2>=0pb>00<t<=4d2d3룬֪ݼóɲȷ롣
    3չͼΪչҶƬܳnȷÿһչ뾶ʵnֵɼȷnֵԽչͼľԽߣչͼĹӦӡ˹һȡn=24~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    4չͼ߿ֱӸڰϣչͼ1ΪСҶƬչͼչͼ2ΪڶҶƬչͼơϿɲչʾͼ·
    (1)ⶨһԭooΪԲģrs1rs2ֱΪ뾶Բ
    (2)Rs2Ļȡ㣬һȡҳLxҲչǶaȷԲнǡҳǶȷ󣬰ͼֱߵԭo
    (3)Rs2󻡲ֳַnȷ֣ÿҳΪmϸȷֱֵߵԭo
    (4)oΪԲģڸȷηֱȡra(1)ra(n+1)뾶Ȼͼù⻬Ӹ㣬߼Rs1ԲΧɵΪƬҶƬչͼ


#8                   ȾҶƬ˵

    1ΪҶƬھݾǶֵ⾶𽥱ı侶ȾҶƬĹҶƬΪչ棬ӹͬչͼҪҲͬƬҶƬѹƷӹչͼ㡣öƬҶƬӺƵķӹھ⾶ҪӦСֵӦݾ;ȷ
    2ʾͼd1ΪҶƬ⾶d2ΪҶƬھp1ΪһƬҶƬݾ࣬p2ΪڶƬҶƬݾ࣬bΪĺȡҪd1>d2>0p2>p1>0b>0ɲȷ롣
    3ҶƬǵƬϵģҶƬݾʵʱֻp1Լϵqp2ΪοֵҪq=p2/p1>1ÿƬ벻ͬݾp1ɵõͬչͼ
    4չͼΪչҶƬܳnȷÿһչ뾶ʵnֵɼȷnֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ⶨһԭooΪԲģrs2Ϊ뾶Բ
    (2)Rs2Ļȡ㣬һȡҳLxҲչǶaȷԲнǡҳǶȷ󣬰ͼֱߵԭo
    (3)Rs2󻡲ֳַnȷ֣ÿҳΪmϸȷֱֵߵԭo
    (4)oΪԲģڸȷζӦȡra(1)ra(n+1)Rb(1)Rb(n+1)뾶Ȼͼù⻬Ӹ㣬ΧɵΪƬҶƬչͼ


#9                   侶ҶƬ˵

    1ΪҶƬھǶֵ⾶ݾఴ𽥱ı侶ҶƬĹҶƬΪչ棬ӹͬչͼҪҲͬƬҶƬѹƷӹչͼ㡣öƬҶƬӺƵķӹھ⾶ҪӦСֵӦݾ;ȷ
    2ʾͼdΪҶƬھd1ΪһƬҶƬС⾶d2ΪһƬҶƬĴ⾶ͬʱҲǵڶƬҶƬС⾶d3ΪڶƬҶƬĴ⾶p1ΪһƬҶƬݾ࣬p2ΪڶƬҶƬݾ࣬bΪĺȡҪd3>d2>d1>d>0p2>p1>0b>0ɲȷ롣
    3ҶƬǵƬϵģÿƬҶƬʵʱʾͼʲôţС⾶Ϊd1⾶Ϊd2ݾֻp1Լϵqp2ΪοֵҪq=p2/p1>1ÿƬ벻ͬd1d2p1ɵõͬչͼ
    4չͼΪչҶƬܳnȷÿһչ뾶ʵnֵɼȷnֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ⶨһԭooΪԲģrs2Ϊ뾶Բ
    (2)Rs2Ļȡ㣬һȡҳLxҲչǶaȷԲнǡҳǶȷ󣬰ͼֱߵԭo
    (3)Rs2󻡲ֳַnȷ֣ÿҳΪmϸȷֱֵߵԭo
    (4)oΪԲģڸȷζӦȡra(1)ra(n+1)Rb(1)Rb(n+1)뾶Ȼͼù⻬Ӹ㣬ΧɵΪƬҶƬչͼ


#10                   ׶ȵȾҶƬ˵

    1ΪҶƬھ⾶ͬ׶ȣݾǶֵͬ׶ȾҶƬĹҶƬΪչ棬ӹͬչͼҪҲͬƬҶƬѹƷӹչͼ㡣öƬҶƬӺƵķӹھ⾶ҪӦСֵӦݾ;ȷ
    2ʾͼd1d4ֱΪһƬҶƬС⾶ھd2d5ֱΪһƬҶƬĴ⾶ھͬʱҲǵڶƬҶƬС⾶ھd3d6ΪڶƬҶƬĴ⾶ھpΪҶƬݾ࣬bΪĺȡҪd3>d2>d1>0d6>d5>d4>0pb>0ɲȷ롣
    3ҶƬǵƬϵģÿƬҶƬʵʱʾͼʲôţС⾶Ϊd1ھΪd4⾶Ϊd2ھΪd5Ҫd5-d4>0d1-d4>0d2-d1>0ÿƬ벻ͬd1d2d4d5ɵõͬչͼ
    4չͼΪչҶƬܳnȷÿһչ뾶ʵnֵɼȷnֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ⶨһԭooΪԲģrs2Ϊ뾶Բ
    (2)Rs2Ļȡ㣬һȡҳLxҲչǶaȷԲнǡҳǶȷ󣬰ͼֱߵԭo
    (3)Rs2󻡲ֳַnȷ֣ÿҳΪmϸȷֱֵߵԭo
    (4)oΪԲģڸȷζӦȡra(1)ra(n+1)Rb(1)Rb(n+1)뾶Ȼͼù⻬Ӹ㣬ΧɵΪƬҶƬչͼ


#11                   ͬ׶ҶƬ˵

    1ΪҶƬھ⾶ͬ׶ȣݾఴ𽥱ͬ׶ҶƬҶƬΪչ棬ӹͬչͼҪҲͬƬҶƬѹƷӹչͼ㡣öƬҶƬӺƵķӹھ⾶ҪӦСֵӦݾ;ȷ
    2ʾͼd1d4ֱΪһƬҶƬС⾶ھd2d5ֱΪһƬҶƬĴ⾶ھͬʱҲǵڶƬҶƬС⾶ھd3d6ΪڶƬҶƬĴ⾶ھp1ΪһƬҶƬݾ࣬p2ΪڶƬҶƬݾ࣬bΪĺȡҪd3>d2>d1>0d6>d5>d4>0p2>p1>0qb>0ɲȷ롣
    3ҶƬǵƬϵģÿƬҶƬʵʱʾͼʲôţС⾶Ϊd1ھΪd4⾶Ϊd2ھΪd5Ҫd5-d4=d2-d1>0ݾֻp1Լϵqp2ΪοֵҪq=p2/p1>1ÿƬ벻ͬd1d2d4d5q1ɵõͬչͼ
    4չͼΪչҶƬܳnȷÿһչ뾶ʵnֵɼȷnֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ⶨһԭooΪԲģrs2Ϊ뾶Բ
    (2)Rs2Ļȡ㣬һȡҳLxҲչǶaȷԲнǡҳǶȷ󣬰ͼֱߵԭo
    (3)Rs2󻡲ֳַnȷ֣ÿҳΪmϸȷֱֵߵԭo
    (4)oΪԲģڸȷζӦȡra(1)ra(n+1)Rb(1)Rb(n+1)뾶Ȼͼù⻬Ӹ㣬ΧɵΪƬҶƬչͼ


#12                   ϿǷ˵

    1ΪɢʽϿǣϿĽڣͬ뾶ͬԲĵԲӷڹɡ
    2ʾͼеR1R2R3ΪϿǵڰ뾶B1B2ΪϿǲͬԲĵˮƽʹֱƫWΪڿȣEΪڵ߾룬hΪϿǵĸ߶ȣbΪĺȡҪR1hB1b>0B2>=0E>Sqr((R1+b)^2-(R3+B1-w-b)^2)R2R3룬R1B1B2óR2=R1+B1R3=R2+B2ҪR3+B1-R1<W<R3B2ֵϿǵİ뾶B2>0ʱ뾶B2=0ʱ뾶ɲ߸ͼֽйȷ롣
    3ϿչͼӲͼӰַûɸͼֽҪϰϣչͼֱϾƣϿǿɲչʾͼ·
    (1)໥ֱߣԽΪһԲģB1B2ͼȷڶԲġ
    (2)R1Ϊ뾶Բ1ΪԲĻԲˮƽߣR2Ϊ뾶Բ2ΪԲĻԲ90㣬R3Ϊ뾶Բ3ΪԲĻԲ90㣬R3߻ˮƽߵĴֱߣ߾ΪEԴֱΪ׼Wֱ߽R1ߣɵõϿǵչͼ
    (3)ҪӲϿչͼR1R2R3bW+2*b˳ͼɡ


#13                   ϿԲܹ˵

    1ΪĽϿԲܵĹ壬ϲϿͬ뾶ͬԲĵԲӷڹɣ²ΪȫյԲڡ
    2ʾͼеR1ΪԲڵڰ뾶R2R3ΪϿǽߵڰ뾶LwΪϿǲͬԲĵˮƽʹֱƫL1Ϊ0ǰĿȣL2Ϊڵ߾룬aΪϿǽ߽ӵĽǶȣhΪĸ߶ȣbΪĺȡҪR1hLWb>0L2>=00<=L1<=r1ɲ߸ͼֽйȷ롣ʾͼеR2R3aû룬R1LwԶR2=R1+LR3=R2+(L^2+W^2)^0.5a=Atn(w/L)
    3ܳnȷʵnֵ4ɲ߸ֱҪȷnֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    4չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶Σ䳤ΪLa(n/2+1)
    (2)߶ұ϶˵ΪԲģmp1Ϊ뾶Բ¶˵ΪԲģLb(n/2)Ϊ뾶ཻȻ¶˵ΪԲģmp2Ϊ뾶ǰ潻ΪԲģLa(n/2)Ϊ뾶ཻ߶¶˵ΪԲģm2Ϊ뾶Բ϶˵ΪԲģLb(n/2+1)Ϊ뾶ཻȻ϶˵ΪԲģm1Ϊ뾶ǰ潻ΪԲģLa(n/2+2)Ϊ뾶ཻ
    (3)ͼ߶ұ˳򻭳La(n/2)La(1)Lb(n/2)Lb(1)߶ν㣻߶˳򻭳La(n/2+2)La(n+1)Lb(n/2+1)Lb(n)߶ν㡣
    (4)ͼұ߽La(1)߻һΪLpΪhp1ľΣ߽La(n+1)߻һΪL2Ϊhp2ľΡ
    (5)ͼֱ߻⻬Ӹ㣬ɵõĹչͼ


#14                            ְʽԲͷ˵

    1ΪְʽԲܷͷһΪԲͷͷĽǸֳߴԲҲǰԲֱܿΪڵ0ʵΪչ棬ƽչͼʵȫһҪôѹӵİ취չģķﵽߴҪʱӦһӹɺ
    2ʾͼdΪͷֱd1ΪͷмϲֱֵLΪͷĳȣL1ΪͷֱͲֳȣbΪĺȡҪdLb>0d1L1>=0ɲ߸Ҫȷ롣
    3ͷ߷ֳn1ȷ֣γ߷ֳn2ȷÿһߵʵn1n2ֵɲ߸ֱ;ҪԶȡ4n1n2ֵԽչͼľԽߣչͼĹӦӡ˹һȡn1n2=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬n1n2ֵȡһЩ
    4ڼӹķͬϳߴв죬ڱչϵtԷûݼӹʵʾϡtֵ01ֵ֮t=0ʱʾӹûӳģȫİ취棻t=1ʱʾֱߴϣӹҪչĵİ취棬0<t<1ʱչߴ֮䣬t=0.3ʱʱߴͬ
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ԲֱrsΪ뾶ԲɵչͼΪһ
    (2)һ߶Σȵlp+L1߶ȡL1Ⱥֳn2ȷݣÿݳȵm1
    (3)ȷֵ߶ε໭ֱߣ˵㴦ͼrpΪ뾶ڸֱ߼Բ϶Գȡma(1)ma(n2/2+1)ȡ
    (4)ù⻬ȡĸ㣬ΪͷܱһƬչͼ軭n1Ƭͬչͼ
    (5)ԲƬϾѹƴԲķͷ


#15                          ʽԲͷ˵

    1ΪʽԲԲͷͷĽǸֳߴԲҲǰԲֱܿΪڵ0ʵΪչ棬ƽչͼʵȫһҪôѹӵİ취չģķﵽߴҪʱӦһӹɺ
    2ʾͼdΪͷֱLΪͷĳȣL1ΪͷֱͲֳȣbΪĺȡҪdLb>0L1>=0ɲ߸Ҫȷ롣
    3ڼӹķͬϳߴв죬ڱչϵtԷûݼӹʵʾϡtֵ01ֵ֮t=0ʱʾӹûӳģȫİ취棻t=1ʱʾֱߴϣӹҪչĵİ취棬0<t<1ʱչߴ֮䣬t=0.3ʱʱߴͬ
    4ֱrsΪ뾶Բɵչͼչͼ߿ֱӸڰϡ


#16                      ԲƽͬĻӹܷ˵

    1Ϊ¾ΪˮƽĳԲΣڵغϣԲĳȡȿȡֵͼͲͼΪͬ뾶Բӵӹܡ
    2ʾͼL1ΪϳԲڱ߳ȣw1ΪϳԲڱ߿ȣL2Ϊ³Բڱ߳ȣw2Ϊ³Բڱ߿ȣhΪӹܸ߶ȣbΪĺȣR1R2ֱΪͲӵԲ뾶ҪL1>w1>0L2>w2>0hb>0R1=(h^2+(l1-l2)^2/4)/(l1-l2)R2=(h^2+(w1-w2)^2/4)/(w1-w2)֪ݼóû롣
    3ڱǲչ棬Ϊ˵õȽԲ棬ɰѹԲֳַtȷϣtֵǴ1ûɸݾȵҪͼӹȷ룻ÿΰбԲ׶̨չ㣬ǽչʵҪߴһʱرע⣬ɲҪ˷ѡ
    4³ԲڰԲnȷߵʵnֵ2ɲ߸ݳԲ뾶ߴ缰Ҫȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5ԲֶֺεչͼбԲ׶̨չͼһͬԲĲͬ뾶ȡߵʵչͼtԲչͼмƽ尴һϡֱӸڰϣɲչʾͼ·
    (һ)Բչͼ
    (1)ⶨһԭ㣬ԭ㻭һ߶ΣȵRa(in1/2+1)
    (2)Ra(in1/2)Ϊ뾶ԭ㣬ma(i)Ϊ뾶Ra(in1/2+1)һ˷ֱ߶໭ཻԭ㼰ΪԲģRa(in1/2-1)ma(i)Ϊ뾶һ㣬˳λ㣻
    (3)Ӹԭ㻭ֱߣٴԭڸ߶϶ӦȡRb(i,1)~Rb(i,n/2+1)ȣ
    (4)ͼԹ⻬ཻ㣬Ϊչͼ
    ()չͼ
    (1)ƽ߶Σhpƽֳ֮tȷ֣ÿݳȵm
    (2)߶м仭һֱߣ²߶ζԳƴֱȡlpȣȻڸȷζԳȡLa(1)La(t)ȣ
    (3)ͼԹ⻬Ӹ㣬Ϊչͼ
    6ԲֶεչͼΪչϣt/2Բչͼмƽ԰ֶεķϣϽṩϣɲչʾͼ·
    (1)ⶨһԭ㣬ԭ㻭໥ֱߣxᣬy᣻
    (2)1ixݣxϻƽyĸߣȻڸ߷ֱӦyȡ㣻
    (3)ͼԹ⻬Ӹ㣬Ϊչͼ


#17                   Բܼа壨һ˵

    1Ϊ̶Բܵļа壬²ΪԲϲΪбֱ壬Գͬļаһп˨ӣмһڼнԲܡ
    2ʾͼеDΪаֱH1H2ΪԲĵ˨˨Ĵֱ룬H3Ϊ˨׵˵ĸ߶ȣH4Ϊ˨׵а䴦ľ룬LΪаƷĳȣBLΪаĿȣE1Ϊаľ룬rΪа䴦ǰ뾶d1Ϊݿ׵ֱbΪаĺȡҪܴﵽʹЧӰΪãɲ߸ͼֽйȷ룬ʾ롣
    3аչͼ밴ͼгߴֱףһа干顣



#18                   Բܼа壨˵

    1Ϊ̶Բܵļа壬²ΪԲԳͬļаһп˨ӣмһڼнԲܡʽһףһֻһס
    2ʾͼеDΪаֱH1ΪԲĵ˨Ĵֱ룬H2Ϊ˨׼ľ룬H3Ϊ˨׵˵ĸ߶ȣLΪаƷĳȣBLΪаĿȣE1Ϊаľ룬rΪа䴦ǰ뾶d1Ϊݿ׵ֱbΪаĺȡаϲֻһףֻҪH20ɣҪܴﵽʹЧӰΪãɲ߸ͼֽйȷ룬ʾ롣
    3аչͼ밴ͼгߴֱףһа干顣



#19                   Ͽǲ弰Բܹ˵

    1ΪĽϿǵĲ弰ԲܵĹ壬ϲϿͬ뾶ͬԲĵԲӷڹɣ²ΪȫյԲڣΪһߡ
    2Ͽֲͬ״ѡܣһԲͬ뾶ĽɣÿԲתǶΪ90㣻һͬ뾶ĽɣR2R3м׼ԽνӣûR4·ѡѡͬ״вͬļչʽûҪѡ
    3ԲʾͼеR1ΪԲڵڰ뾶R2R3R4ΪϿǽߵڰ뾶LwΪϿǲͬԲĵˮƽʹֱƫL1ΪǰԲܵĿȣL2ΪϿǷڵֱ峤ȣpΪϿǽR4Բƫľ룬h1ΪϿǲܸ߶ȣh2Ϊĸ߶ȣbΪĺȡҪR1h2b>0LWL2>=00=<L1<r10=<p<r1h1>h2L=0ĽߵϿǣw=0ǰԲ뽥ߵϿǡɲ߸ͼֽйȷ롣ʾͼеR2R3R4û룬R1LwpԶԲĵԲĵĻͬûƫľpR2R3ͽaҲ룬ݼó
    4ܳnȷʵnֵ4ɲ߸ֱҪȷnֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    չͼһ(ģ
    (1)һˮƽ߶Σ䳤ΪLphp1LeֱΪ뾶߶˵ΪԲĻཻ
    (2)߶߶˵ΪԲģmΪ뾶ԲԽΪԲģpa(1)Ϊ뾶ཻȻ½ΪԲģLa(1)Ϊ뾶ǰ潻ΪԲģm1Ϊ뾶ཻ
    (3)ͼ߶˳򻭳La(1)La(n/4)mpa(1)pa(n/4)m1߶ν㣻ٽ˳򻭳Lb(1)Lb(n/4)mpb(1)pb(n/4)m2ԼLc(1)Lc(n/4)mpc(1)pc(n/4)m3߶ν㡣
    (4)ͼ߽Lc(1)p+L2LxL2LeΪ뾶㡣
    (5)ͼֱ߻⻬Ӹ㣬ɵõԲܹչͼ
    ԲĵչͼһĻһֻLc(i)Pc(i)ݲչʾͼչͼ
    չͼ
    (1)һˮƽ߶Σ䳤ΪL2+Ls1߶˻ȷֱΪh1-h2h1Ĵֱߣh1-h2߶ζ˵㻭ȵL2ˮƽ߶ΣӸ߶μh1߶εĶ˵㣬ΪϿǲչͼ    




#20                   ԲƫֱԲͷ˵

    1ΪԲԲͷƫֱƫԲͷֱ߶ȼԲֱȡĺȿȡֵвʽʽཻʽѡ񣬻аϺͳƷѡ񣬲ɸҪӲǿ塣ԲܼǿչͼԲͷչͼйعϣõԲֳոơ
    2ͼd1h1ΪԲͷֱڸ߶ȣd2ΪԲֱܵh2ΪԲܿھԲͷڵĸ߶ȣpΪԲԲͷƫľ룬b1ΪԲͷĺȣb2ΪԲܰĺȣbtΪϺȣbzΪǿȣwzΪǿȡɲȷ롣Ҫd1>d2>00<p<(d1-d2)/2h2>h1>0b1b2btwz>0Ҫʾ
    3Բܳnȷߵʵnֵ4ɲ߸ԲֱҪȷ롣nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    4Բͷཻʽвʽʽ֣ʽԲܲͷڱڼ㣬ʽԲܽӴͷڼ㣬ʱʽĿڴһЩԲܵĳҲһЩʱݼӹϰߺҪѡ
    5ӲǿĹܣӲǿ塯ťӲǿ棬ýв⣬˲ǿĺȺͿbzwzɸҪ롣
    6չͼƽ߷ϣԲֳܷƽ߽мݸϷʽͬͬѡϣ԰ĵΪֱչȣ߿ɸչͼֱڰϻϣѡƷϣԲ⾶ϺbtΪֱ㣬ϣȻڳƷ⻭ϡɲչʾͼ·
    (һ)ԲϷ
    (1)һ߶ΣȵS2߶ηֳnȷݣÿݳȵm2
    (2)ȷֵ㻭߶εĴֱߣڸֱϰͼȡhc(1)~hc(n/2+1)ȣ
    (3)ͼù⻬ȡĸ㣬ΪԲܵչͼ
    ()ǿϷ
    (1)⻭һֱߣ߶ȴlb(n/2)ȡһΪ߻׼㣻
    (2)ͼߴӻ׼Lb(1)Lb(n/2)㳤ȣ߶ԳƻLb(1)Lb(n/2)һƽߴֱߣȻڸƽ϶ӦԳȡma(1)ma(n/2)ȣ
    (3)÷յĹ⻬Ӹ㣬Ϊ֧ܵĸڡ
    (4)ԸڸΪ׼ȡǿwzõӦĸ㣬÷յĹ⻬Ӹ㣬Ϊǿͼ



#21                      ƽͬĳԲιܷ˵

    1Ϊ¾ΪˮƽмֱĳԲΣڵغϣԲĳȡڹ涨ΧڿȡֵͼΪβͬ뾶ԲӣͼΪֱӵĻιܡ
    2ʾͼL1w1lp1ֱΪ³Բڱ߰볤ȡȡֱȣL2w2lp2ֱΪϳԲڱ߰볤ȡȡֱȣhΪӹܸܵ߶ȣh1Ϊ߶ȣh2Ϊϻĸ߶ȣR1R2ֱΪ²ϲӵԲ뾶涨R1Բ¿ڵӳϣR2ԲԲϿڵˮƽϣpΪߵˮƽ룬bΪĺȡҪL1>w1>0L2>w2>0h>=h1lp2>lp1R2h2p֪ݼóû롣
    3ڱǲչ棬Ϊ˵õȽԲ棬ɰѹԲ²ֳַt1t2ȷϣt1t2ֵǴ0ûɸݾȵҪͼӹȷ룻ÿΰƽƫԲ׶̨չ㣬ǽչҪߴһƫʱرע⣬ɲҪ˷ѡ
    4Բڰ뻡nȷߵʵnֵ2ɲ߸ݳԲ뾶ߴ缰Ҫȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=12~24ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5ԲֶֺεչͼƽƫԲ׶̨չͼһ׶ܸߡߡȷηչͼt1+t2Բչͼмƽ尴һϡֱӸڰϣɲչʾͼ·
    (һ)Բչͼ
    (1)ⶨһԭ㣬ԭ㻭һ߶Σȵeha(i1)
    (2)eha(i1)߶϶˵ΪԲģma(i)Ϊ뾶߶ֱ𻭻߶¶˵ΪԲģehb(i,1)Ϊ뾶ཻ߶¶˵ΪԲģms(i)Ϊ뾶߶ֱ𻭻ǰΪԲģeha(i,2)Ϊ뾶ཻóһ㣬˳λ㣻
    (3)ͼԹ⻬ཻ㣬Ϊչͼ
    ()չͼ
    (1)ƽ߶Σhp²߶Ϊ׼һƽߣhp1hp1ƽ²ֳ֮t1ȷ֣ÿݳȵm1hp1ƽϲֳ֮t2ȷ֣ÿݳȵm2
    (2)߶м仭һֱߣ²߶ζԳƴֱȡlp1ȣȻڸȷζԳȡLa(1)La(t1+t2)ȣ
    (3)ͼԹ⻬Ӹ㣬Ϊչͼ
    ()ϲֱͲչͼΪһΣ밴ͼʾߴ续ϼɡ


#22                   ԲϷ˵

    1ΪԲ༰๹ϣҲɷֳɵȷϣ׺ͰԲڳ֮ѡҲԲϡ
    2ʾͼеd1d2ֱΪԲڡֱd3Ϊ׻ԲԲĵĶԱֱdΪϵԲֱRΪԲ׵İ뾶nΪ׻򿪳׵tΪԲϵķֿҪd1t>0n>=0d2>d3>d1tnΪt>1n>0ʱnܱtɲ߸ͼֽйȷ룬ҪʾĺȲ룬ΰĲϡ
    3п׷ʽѡܣԲסť뷨Բ棬ڳסťԲԲڳ棬ֱdʾڳRʾ⣬ߴͬ
    4չͼͬչͼ׼ľעȥ׵ֱ͵ȷıעt>1ʱ˵ȷֽǶȡԲĻҳıעԱûϣɸչͼֱϼɡ


#23                   ھ߷˵

    1ΪĲּڰ߷ϵĹΪչ棬ÿ߰ߴϣһӹʱѹӵİ취ʹм칰״ѹӷӹҪдѹģߣԹ˵ļҪߣɱôʹַϣݹҪ󣬹˵ļˮƽ豸״Լɱĸߵȷ
    2ʾͼRΪڵڰ뾶hΪԲ߶ȣd1ΪڶԲֱbΪĺȡҪRb>0R>h>0d1>=0ɲȷ롣
    3ΪʺϲͬûҪ󣬱˻ʽѡܣȻťչͼĸʵߵȳģнϴԵĲϿô˷ϣ⻬ƽ޲ťչͼļߵȳ߱Գͷϰ뾶ȽϴڸֽĵϣʱʵɵõʣʱɸݾѡϷʽ
    4еn1Ϊھ߷ķֿn2Ϊγ߷ϵȷn1n2ֵɲ߸ֱ;ҪԶȡn1ֵƺͼӹҪȷn2ֵԽչͼľԽߣչͼĹӦӡ˹һȡn2=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬n2ֵȡһЩ
    5չͼ߿ֱӸڰϣɲչʾͼ·
    (1)ԲֱrsΪ뾶Բɵչͼ
    (2)һ߶Σȵls߶ηֳn2ȷ֣ÿݳȵm2
    (3)ȷֵ߶ε໭ֱߣⴹֱ߶˵㰴ͼrp1Ϊ뾶d1>0ڴֱ߶˵rp2Ϊ뾶ڸֱ߼Բ϶Գȡms(1)ms(n2+1)ȡ
    (4)ù⻬ȡĸ㣬ΪһƬչͼ軭n1ƬͬչͼڹӹȫﵽҪʵʱʵһƴʱٸʵȥಿ֡
    (5)ԲƬϾѹӹƴԲڡ


#24                   ׶ܽƷ˵

    1ΪķҶǰĽƷṹԲ׶ܣֻԲɵģչͼԲĳһΪ߼㣬ʵϵ¿ھСڱעֱϼӹ׶ܺ󣬻Ҫѹģѹӻֹôչܴﵽͼֽߴ磻
    2ͼd1d2Ϊ׶ܴˡСھhΪ׶̨߶ȣRΪԲ뾶bΪĺȡҪd1>d2>0h>0R>=hb>0ɲȷ룬ϹҪ밴ʾµĲ
    3չͼֱӸڰϣɲչʾͼ·
 ⶨһԭoԭΪԲģRs1Rs2Ϊ뾶ֱ𻭻Rs1Ļȡ㣬һػȡS1ȡҳLx1ҲչǶasȷԲнǡȷ󣬽ֱߵԭoRs1RS2ֱΧΪ׶չͼ
    4׶չͼȡҳLxȷʱעaֵСa<=180a>180ͬչʾͼ



#25                   ƽϿǲ弰Բܹ˵

    1ΪĽϿǵĲ弰ԲܵĹ壬ϲϿͬ뾶ͬԲĵԲӷڹɣ²ΪȫյԲڣΪһߡ
    2ʾͼеR1ΪԲڵڰ뾶R2R3R4ΪϿǽߵڰ뾶LwΪϿǲͬԲĵˮƽʹֱƫL1ΪǰԲܵĿȣL2ΪϿǷڵֱ峤ȣpΪϿǽR4Բƫľ룬h1ΪϿǲܸ߶ȣh2Ϊĸ߶ȣbΪĺȡҪR1h2b>0LWL2>=00=<L1<r10=<p<r1h1>h2L=0ĽߵϿǣw=0ǰԲ뽥ߵϿǡɲ߸ͼֽйȷ롣ʾͼеR2R3R4û룬R1LwpԶ
    3ܳnȷʵnֵ4ɲ߸ֱҪȷnֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    4չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һˮƽ߶Σ䳤ΪLphp1LeֱΪ뾶߶˵ΪԲĻཻ
    (2)߶߶˵ΪԲģmΪ뾶ԲԽΪԲģpa(1)Ϊ뾶ཻȻ½ΪԲģLa(1)Ϊ뾶ǰ潻ΪԲģm1Ϊ뾶ཻ
    (3)ͼ߶˳򻭳La(1)La(n/4)mpa(1)pa(n/4)m1߶ν㣻ٽ˳򻭳Lb(1)Lb(n/4)mpb(1)pb(n/4)m2ԼLc(1)Lc(n/4)mpc(1)pc(n/4)m3߶ν㡣
    (4)ͼ߽Lc(1)p+L2LxL2LeΪ뾶㡣
    (5)ͼֱ߻⻬Ӹ㣬ɵõԲܹչͼ
    չͼ
    (1)һˮƽ߶Σ䳤ΪL2+Ls1߶˻Ϊh1-h2ĴֱߣӸ߶ε˵㣬ΪϿǲչͼ    



