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#1                   ƽԲ·ӹܷ˵

    1ΪϿԲΣ¿ڷΣԲںͷͬģԲֱͷεı߳ȡֵӹܹ
    2ʾͼdΪԲֱLΪڱ߳ȣ hΪӹܸ߶, bΪĺȡҪdLhb>0
    3Բܳnȷߵʵnֵ4ɲ߸ֱҪȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    4չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(2)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(2)~Ld(n/4+1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(n/4+1)ΪԲģLb(1)Lc(n/4+1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(n/4+1)Ld(n/4+1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(n/4)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(n/4+1)~Lc(1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    5չͼͼλģھӹ㣬ʱΪ˽ԼϣҲhp߲ÿֳϣٴ⴦ÿֳɿϡ


$1


#2                   Բ¾ƽƫӹܷ˵

    1ΪϿԲΣ¿ھΣԲֱ;εĳȡֵƫĵӹܹpxpyΪ0ʱΪ˫ƫĵԲӹܡpxpyһΪ0ʱΪƫԲӹܡpxpyΪ0ʱΪԲӹܡ
    2ʾͼdΪԲֱLΪڱ߳ȣwΪڱ߿ȣhΪӹܸ߶, pxpyΪԲxyƫľ,bΪĺȡҪdLwhb>0pxpyȡʵ
    3pxpyֵҪԾΪo㣬ֱɵֱϵȷԲoҷʱpxΪֵʱpxΪֵԲoϷʱpyΪֵo·ʱpyΪֵoغΪ0pxpyرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵ4ɲ߸ֱҪȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(2)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(2)~Ld(n/4+1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(n/4+1)ΪԲģLb(1)Lc(n/4+1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(n/4+1)Ld(n/4+1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(n/4)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(n/4+1)~Lc(1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$2


#3                   ϾԲƽƫӹܷ˵

    1ΪϿھΣ¿ԲΣεĳԲֱȡֵƫĵӹܹpxpyΪ0ʱΪ˫ƫĵľԲӹܡpxpyһΪ0ʱΪƫľԲӹܡpxpyΪ0ʱΪľԲӹܡ
    2ʾͼdΪԲֱLΪڱ߳ȣwΪڱ߿ȣhΪӹܸ߶, pxpyΪԲxyƫľ룬bΪĺȡҪdLwhb>0pxpyȡʵ
    3pxpyֵҪԲɵֱϵȷԲΪo㡣oҷʱpxΪֵʱpxΪֵoϷʱpyΪֵo·ʱpyΪֵoغΪ0pxpyرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵ4ɲ߸ֱҪȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(2)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(2)~Ld(n/4+1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(n/4+1)ΪԲģLb(1)Lc(n/4+1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(n/4+1)Ld(n/4+1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(n/4)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(n/4+1)~Lc(1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$3


#4                   Բб¾ƽƫӹܷ˵

    1ΪϿΪԲΣ¿ΪΣԲֱ;εĳȡֵԲһΧڿбƫĵӹܹpxpyΪ0ʱΪ˫ƫбԲ¾ƽӹܡpxpyһΪ0ʱΪƫбԲӹܡpxpyΪ0ʱΪбԲӹܡ
    2ʾͼdΪԲֱLwΪεڱ߳ɻhΪӹߴֱ߶ȣaΪԲǣpxpyΪ¿xᡢyˮƽƫbΪĺȡҪdLwb>090>=a>=-90h>Abs(d*sin(a)/2)pxpyΪʵ
    3pxpyֵԾ߹ɵֱϵȷֵΪo㡣ԲoұʱpxΪֵoʱpxΪֵԲoϷʱpyΪֵo·ʱpyΪֵԲaͼʾȡֵ෴ȡֵpxpyaرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵɼ߸ֱСҪȷ4nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(2)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(2)~Ld(n/4+1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(n/4+1)ΪԲģLb(1)Lc(n/4+1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(n/4+1)Ld(n/4+1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(n/4)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(n/4)~Lc(1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$4


#5                   Բƽ¾бƫӹܷ˵

    1ΪϿΪԲΣ¿ΪΣԲֱ;εĳȡֵһΧڿбƫĵӹܹpxpyΪ0ʱΪ˫ƫԲƽ¾бӹܡpxpyһΪ0ʱΪƫбԲӹܡpxpyΪ0ʱΪбԲӹܡ
    2ʾͼdΪԲֱLwΪεڱ߳ɻhΪӹߴֱ߶ȣaΪǣpxpyΪ¿xᡢyˮƽƫbΪĺȡҪdLwb>090>=a>=-90h>Abs(L*sin(a)/2)pxpyΪʵ
    3pxpyֵԾΪo㣬ˮƽΪƽֱϵȷֵԲoұʱpxΪֵopxΪֵԲoϷpyΪֵo·pyΪֵԲaͼʾȡֵ෴ȡֵpxpyaرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵɼ߸ֱСҪȷ4nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(2)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(2)~Ld(n/4+1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(n/4+1)ΪԲģLb(1)Lc(n/4+1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(n/4+1)Ld(n/4+1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(n/4)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(n/4+1)~Lc(1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$5


#6                   ϾбԲƽƫӹܷ˵

    1ΪϿΪΣ¿ΪԲΣԲֱ;εĳȡֵһΧڿбƫĵӹܹpxpyΪ0ʱΪ˫ƫϾбԲƽӹܡpxpyһΪ0ʱΪƫбھԲӹܡpxpyΪ0ʱΪбھԲӹܡ
    2ʾͼdΪԲֱLwΪεڱ߳ɻhΪӹߴֱ߶ȣaΪǣpxpyΪ¿xᡢyˮƽƫbΪĺȡҪdLwb>090>=a>=-90h>Abs(L*sin(a)/2)pxpyΪʵ
    3pxpyֵԲΪo㣬Բ߹ɵֱϵȷֵoұʱpxΪֵoʱpxΪֵoϷʱpyΪֵo·ʱpyΪֵaͼʾȡֵ෴ȡֵpxpyaرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵɼ߸ֱСҪȷ4nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(2)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(2)~Ld(n/4+1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(n/4+1)ΪԲģLb(1)Lc(n/4+1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(n/4+1)Ld(n/4+1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(n/4)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(n/4+1)~Lc(1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$6


#7                   ϾƽԲбƫӹܷ˵

    1ΪϿھΣ¿ԲΣԲֱ;εĳȡֵԲһΧڿбڿƫĵӹܹpxpyΪ0ʱΪ˫ƫϾƽԲбӹܡpxpyһΪ0ʱΪƫϾƽԲбӹܡpxpyΪ0ʱΪϾƽԲбӹܡ
    2ʾͼdΪԲֱLwΪεڱ߳ɻhΪӹߴֱ߶ȣaΪԲǣpxpyΪ¿xᡢyˮƽƫbΪĺȡҪdLwhb>090>=a>=-90h>Abs(d*sin(a)/2)pxpyΪʵ
    3pxpyֵԲΪo㣬ˮƽΪƽֱϵȷֵoұʱpxΪֵopxΪֵoϷpyΪֵo·pyΪֵԲaͼʾȡֵ෴ȡֵpxpyaرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵɼ߸ֱСҪȷ4nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(2)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(2)~Ld(n/4+1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(n/4+1)ΪԲģLb(1)Lc(n/4+1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(n/4+1)Ld(n/4+1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(n/4)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(n/4)~Lc(1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλ,ʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$7


#8                   ¾ƽƫӹܷ˵

    1ΪϿԲΣ¿ھΣԲĳᡢ;εĳȡֵƫĵӹܹpxpyΪ0ʱΪ˫ƫĵ־ӹܡpxpyһΪ0ʱΪƫ־ӹܡpxpyΪ0ʱΪ־ӹܡ
    2ʾͼL1Ϊڱ߳ȣw1Ϊڱ߿ȣL2ΪԲᣬw2ΪԲᣬhΪӹܸ߶, pxpyΪԲxyƫľ, bΪĺȡҪL1w1L2w2hb>0pxpyȡʵ
    3pxpyֵҪԾΪo㣬ֱɵֱϵȷԲoҷʱpxΪֵʱpxΪֵԲoϷʱpyΪֵo·ʱpyΪֵoغΪ0pxpyرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵ4ɲ߸Բߴ缰Ҫȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL1˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(n/4+1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(n/4)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(n/4)~Ld(1)߶mĽ㡣
    (3)ͼֱADΪԲģw1Ϊ뾶La(1)Ld(1)ΪԲģLb(1)Lc(1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(1)Ld(1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(2)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(2)~Lc(n/4+1)߶mĽ㡣
    (5)ֱBCΪԲģLp1Ϊ뾶Lb(n/4+1)Lc(n/4+1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$8


#9                   Ͼƽƫӹܷ˵

    1ΪϿھΣ¿ԲΣεĳԲĳᡢȡֵƫĵӹܹpxpyΪ0ʱΪ˫ƫĵľӹܡpxpyһΪ0ʱΪƫľӹܡpxpyΪ0ʱΪľӹܡ
    2ʾͼL1ΪԲڳᣬw1ΪԲڶᣬL2Ϊڱ߳ȣw2Ϊڱ߿ȣhΪӹܸ߶, pxpyΪԲxyƫľ, bΪĺȡҪL1w1L2w2hb>0pxpyȡʵ
    3pxpyֵҪԲɵֱϵȷԲΪo㡣oҷʱpxΪֵʱpxΪֵoϷʱpyΪֵo·ʱpyΪֵoغΪ0pxpyرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵ4ɲ߸ݳἰҪȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL2˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(n/4+1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(n/4)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(n/4)~Ld(1)߶mĽ㡣
    (3)ͼֱADΪԲģw2Ϊ뾶La(1)Ld(1)ΪԲģLb(1)Lc(1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(1)Ld(1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(2)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(2)~Lc(n/4+1)߶mĽ㡣
    (5)ֱBCΪԲģLp2Ϊ뾶Lb(n/4+1)Lc(1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$9


#10                   Ͼбƽƫӹܷ˵

    1ΪϿΪԲΣ¿ΪΣԲĳᡢ;εĳȡֵԲһΧڿбƫĵӹܹpxpyΪ0ʱΪ˫ƫбԲ¾ƽӹܡpxpyһΪ0ʱΪƫб־ӹܡpxpyΪ0ʱΪб־ӹܡ
    2ʾͼL1w1ΪԲڱ߳ᡢᣨɻL2w2Ϊεڱ߳ɻhΪӹߴֱ߶ȣaΪԲǣpxpyΪ¿xᡢyˮƽƫbΪĺȡҪL1w1L2w2b>090>=a>=-90h>Abs(d*sin(a)/2)pxpyΪʵ
    3pxpyֵԾ߹ɵֱϵȷֵΪo㡣ԲoұʱpxΪֵoʱpxΪֵԲoϷʱpyΪֵo·ʱpyΪֵԲaͼʾȡֵ෴ȡֵpxpyaرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵɼ߸ݳСҪȷ4nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL2˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(n/4+1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(n/4)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(n/4)~Ld(1)߶mĽ㡣
    (3)ͼֱADΪԲģw2Ϊ뾶La(1)Ld(1)ΪԲģLb(1)Lc(1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(1)Ld(1)ֱΪԲģmΪ뾶ڽ໭BCΪԲģLb(2)Lc(2)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(2)~Lc(n/4+1)߶mĽ㡣
    (5)ֱBCΪԲģLp2Ϊ뾶Lb(n/4+1)Lc(n/4+1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$10


#11                   Ͼƽбƫӹܷ˵

    1ΪϿھΣ¿ԲΣԲĳᡢ;εĳȡֵԲһΧڿбڿƫĵӹܹpxpyΪ0ʱΪ˫ƫϾƽбӹܡpxpyһΪ0ʱΪƫϾƽбӹܡpxpyΪ0ʱΪϾƽбӹܡ
    2ʾͼL1w1ΪԲڳᡢᣨɻL2w2Ϊεڱ߳ɻhΪӹߴֱ߶ȣaΪԲǣpxpyΪ¿xᡢyˮƽƫbΪĺȡҪL1w1L2w2hb>090>=a>=-90h>Abs(d*sin(a)/2)pxpyΪʵ
    3pxpyֵԲΪo㣬ˮƽΪƽֱϵȷֵoұʱpxΪֵopxΪֵԲoϷpyΪֵo·pyΪֵԲaͼʾȡֵ෴ȡֵpxpyaֵرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵɼ߸ֱСҪȷ4nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL2˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(n/4+1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(n/4)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(n/4)~Ld(1)߶mĽ㡣
    (3)ͼֱADΪԲģw2Ϊ뾶La(1)Ld(1)ΪԲģLb(1)Lc(1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(1)Ld(1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(2)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(2)~Lc(n/4+1)߶mĽ㡣
    (5)ֱBCΪԲģLp2Ϊ뾶Lb(n/4+1)Lc(n/4+1)ΪԲģhpΪ뾶ཻõEF
    (6)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλ,ʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$11


#12                   Ͼ³Բƽƫӹܷ˵

    1ΪϿھΣ¿ڳԲΣεĳͳԲıⳤȡ뾶ȡֵƫĵӹܹpxpyΪ0ʱΪ˫ƫĵϾ³ԲӹܡpxpyһΪ0ʱΪƫϾ³ԲӹܡpxpyΪ0ʱΪϾ³Բӹܡ
    2ʾͼL1ΪԲڱ߳ȣw1ΪԲڱ߿ȣL2Ϊڱ߳ȣw2Ϊڱ߿ȣhΪӹܸ߶, pxpyΪ볤Բxyƫľ, bΪĺȡҪL1>w1>0L2w2hb>0pxpyȡʵ
    3pxpyֵҪԳԲɵֱϵȷԲΪo㡣oҷʱpxΪֵʱpxΪֵoϷʱpyΪֵo·ʱpyΪֵoغΪ0pxpyرעֵ󣬿ܻᵼ²ȷչͼ
    4ԲԲnȷߵʵnֵ4ɲ߸ݰ뾶Ҫȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģhpLd(n/4+1)Ϊ뾶һ㣬Խ㡢AΪԲģSLa(n/4+1)Ϊ뾶һ㡣ȻֱΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(n/4)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(n/4)~Ld(1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(1)ΪԲģLb(1)Lc(1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(1)Ld(1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(2)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(2)~Lc(n/4+1)߶mĽ㡣
    (5)BΪԲģhsΪ뾶Lb(n/4+1)ΪԲģSΪ뾶ཻõFBFֱΪԲģLLc(n/4+1)Ϊ뾶E㡣
    (6)ͼֱFEBAD C㣬ù⻬Ӹ㣬ɵõӹܵչͼٸλǷΪS1ϡ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲLa(n/4+1)߲ÿֳϣٴ⴦ÿֳɿϡ


$12


#13                   Բ³Բƽƫӹܷ˵

    1ΪϿԲΣ¿ڳԲΣԲֱͳԲıⳤȡ뾶ȡֵƫĵӹܹpxpyΪ0ʱΪ˫ƫĵԲ³ԲӹܡpxpyһΪ0ʱΪƫԲ³ԲӹܡpxpyΪ0ʱΪԲ³Բӹܡ
    2ʾͼLΪԲڱ߳ȣwΪԲڱ߿ȣdΪԲֱhΪӹܸ߶ȣ pxpyΪԲ볤Բxyƫľ, bΪĺȡҪL>w>0dhb>0pxpyȡʵ
    3pxpyֵҪԳԲɵֱϵȷԲΪo㡣ԲoҷʱpxΪֵʱpxΪֵԲoϷʱpyΪֵo·ʱpyΪֵoغΪ0pxpyرעֵ󣬿ܻᵼ²ȷչͼ
    4ԲܳԲԲnȷߵʵnֵ4ɲ߸ԲֱԲ뾶ߴ缰Ҫȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)ͼһֱ߶ΣȵS
    (2)߶˵ֱΪԲģLa(1)Lb(1)Ϊ뾶һ㣬ȻԽΪԲģm2Ϊ뾶ڽ໭߶˵ΪԲģLc(1)Ld(1)Ϊ뾶Բֱཻ߶˵ֱΪԲģm1Ϊ뾶ΪԲģLa(2)Lb(2)ֱΪ뾶µĽ㡣
    (3)˳λLa(2)~La(n/2+1)Lb(2)~Lb(n/2+1)߶m1Lc(2)~Lc(n/2)Ld(2)~Ld(n/2)߶m2Ľ㡣
    (4)ͼLa(n/2+1)߶˵ֱΪԲģSLb(n/2+1)ֱΪ뾶һ㡣
    (5)ͼֱߺ͹⻬Ӹ㣬ΪչͼٸλǷΪS1S2ϡ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲLa(1)߲ÿֳϣٴ⴦ÿֳɿϡ


$13


#14                   Բȿܷͨ˵

    1ϿֱͬԲΣ¿ͬߴΣȡͬƫԲӹཻɵԲ¾ؿͨ
    2 ʾͼdΪͨϲԲֱLwֱΪ²ؿڱߵĳhΪͨĸ߶ȣpx1px2ֱΪ12x᷽ƫľ룬pyΪؿy᷽ƫbΪĺȡҪdLwhb>0px1+px2>LpyȡʵΪ˼ͨܵh>px1px2
    3pyֵҪԲΪo㣬ֱɵֱϵȷoϷʱpyΪֵo·ʱpyΪֵoغΪ0pyرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵ4ɲ߸ֱҪȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·(Լ1Ϊ)
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(n/4+1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(n/4)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(n/4)~Ld(1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(1)ΪԲģLb(1)Lc(1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(1)Ld(1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(2)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(2)~Lc(n/4+1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(n/4+1)ΪԲģhp1Ϊ뾶ཻõEF
    (6)ͼֱClc(1)~lc(n/4+1)Dld(1)~ld(n/4+1)㣬ڸϷֱCDȡka(1)~ka(n/4)kb(1)~kb(n/4)ȡ
    (7)ͼֱEBAD CF㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    (8)21Ϸһֻȡֵ뷽һѣο1ϷԻչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs1hs2߲ÿֳϣٴ⴦ÿֳɿϡ


$14


#15                   Բȿܷͨ˵

    1ϿͬߴΣ¿ֱͬԲΣȡͬƫľԲӹཻɵϾԲͨ
    2 ʾͼdΪͨ²ԲֱLwֱΪϲؿڱߵĳhΪͨĸ߶ȣpx1px2ֱΪ12x᷽ƫľ룬pyΪؿy᷽ƫbΪĺȡҪdLwhb>0px1+px2>LpyȡʵΪ˼ͨܵh>px1px2
    3pyֵҪԾΪo㣬ֱɵֱϵȷԲoϷʱpyΪֵo·ʱpyΪֵoغΪ0pyرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵ4ɲ߸ֱҪȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·(Լ1Ϊ)
    (1)һֱ߶ΣȵL˵ֱΪAD
    (2)ͼֱADΪԲģLa(n/4+1)Ld(n/4+1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭ADΪԲģLa(n/4)Ld(n/4)Ϊ뾶Բֱཻ˳λLa(n/4)~La(1)Ld(n/4)~Ld(1)߶mĽ㡣
    (3)ͼֱADΪԲģwΪ뾶La(1)Ld(1)ΪԲģLb(1)Lc(1)Ϊ뾶ཻõµĽBC
    (4)Lb(1)La(1)㡢Lc(1)Ld(1)ֱΪԲģmΪ뾶ڽ໭ֱBCΪԲģLb(2)Lc(2)ֱΪ뾶ཻ˳λLb(2)~Lb(n/4+1)Lc(2)~Lc(n/4+1)߶mĽ㡣
    (5)ֱBCΪԲģLpΪ뾶Lb(n/4+1)Lc(n/4+1)ΪԲģhp1Ϊ뾶ཻõEF
    (6)ͼֱClc(1)~lc(n/4+1)Dld(1)~ld(n/4+1)㣬ڸϷֱlc(1)~lc(n/4+1)ld(1)~ld(n/4+1)ȡka(1)~ka(n/4)kb(1)~kb(n/4)ȡ
    (7)ͼֱEBAD CFԼFka(n/4+1)˵㡢ka(1)kb(1)kb(1)hs1hs1A㣬ù⻬Ӹ㣬ɵõӹܵչͼ
    (8)21Ϸһֻȡֵ뷽һѣο1ϷԻչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs1hs2߲ÿֳϣٴ⴦ÿֳɿϡ


$15


#16                   ƽԲԲǾӹܷ˵

    1ΪϿΪԲΣ¿ΪԲǾΣԲֱ;εĳȡֵԲһΧڿȡֵƫĵӹܹpxpyΪ0ʱΪ˫ƫƽԲԲǾӹܡpxpyһΪ0ʱΪƫƽԲԲǾӹܡpxpyΪ0ʱΪƽԲԲǾӹܡ
    2ʾͼdΪԲֱLwΪεڱ߳ɻhΪӹߴֱ߶ȣrΪԲǰ뾶pxpyΪ¿xᡢyˮƽƫbΪĺȡҪdLwhrb>0r<=W/2pxpyΪʵ
    3pxpyֵԾΪo㣬ˮƽΪƽֱϵȷֵԲoұʱpxΪֵopxΪֵԲoϷpyΪֵo·pyΪֵpxpyرעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵɼ߸ֱСҪȷ4ҲС12nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)һֱ߶ΣȵLp*2
    (2)ͼֱ߶˵ΪԲģLa(n/4+1)Ld(1)Ϊ뾶һ㡣ȻԽΪԲģm1Ϊ뾶ڽҲ໭߶Ҷ˵ΪԲģka(n/4)Ϊ뾶Բཻ߶˵ΪԲm2Ϊ뾶໭ԽΪԲģkd(1)Ϊ뾶ԲཻԸΪԲİ˳λLa(n/4)~La(1)Ld(2)~Ld(n/4+1)ka(n/4)~ka(1)kd(2)~kd(n/4)߶m1m2Ľ㡣
    (3)ͼֱLa(1)߶˵ΪԲģwpLb(1)Ϊ뾶ཻLd(n/4+1)߶˵ΪԲģwpLc(n/4+1)Ϊ뾶ཻõµĽ㡣
    (4)µĽΪԲģֱ𻭳Lb(2)~Lb(n/4+1)Lc(n/4)~Lc(1)kb(1)~kb(n/4)kc(n/4)~kc(1)߶m1m2Ľ㡣
    (5)ֱLb(n/4+1)Lc(1)߶ε˵ΪԲģLphpΪ뾶ཻõµĽ㡣
    (6)ͼֱߺ͹⻬Ӹ㣬ɵõӹܵչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhs߲ÿֳϣٴ⴦ÿֳɿϡ


$16


#17                   Բб³Բƽƫӹܷ˵

    1ϿΪԲΣˮƽǣ¿ΪˮƽԲΣԲֱͳԲıⳤȡ뾶ȡֵƫĵӹܹpxpyΪ0ʱΪ˫ƫĵԲб³ԲƽӹܡpxpyһΪ0ʱΪƫԲ³ԲӹܡpxpyΪ0ʱΪԲ³Բӹܡ
    2ʾͼLΪԲڱ߳ȣwΪԲڱ߿ȣdΪԲֱhΪӹܸ߶ȣ pxpyΪԲ볤Բxyƫľ, aΪԲбǶȣbΪĺȡҪL>w>0dhab>0pxpyȡʵ
    3pxpyֵҪԳԲɵֱϵȷԲΪo㡣ԲoҷʱpxΪֵʱpxΪֵԲoϷʱpyΪֵo·ʱpyΪֵoغΪ0pxpyرעֵ󣬿ܻᵼ²ȷչͼ
    4ԲܳԲԲnȷߵʵnֵ4ɲ߸ԲֱԲ뾶ߴ缰Ҫȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·
    (1)ͼһֱ߶ΣȵS
    (2)߶˵ֱΪԲģLa(1)Lb(1)Ϊ뾶һ㣬ȻԽΪԲģm2Ϊ뾶ڽ໭߶˵ΪԲģLc(1)Ld(1)Ϊ뾶Բֱཻ߶˵ֱΪԲģm1Ϊ뾶ΪԲģLa(2)Lb(2)ֱΪ뾶µĽ㡣
    (3)˳λLa(2)~La(n/2+1)Lb(2)~Lb(n/2+1)߶m1Lc(2)~Lc(n/2)Ld(2)~Ld(n/2)߶m2Ľ㡣
    (4)ͼLa(n/2+1)߶˵ֱΪԲģSLb(n/2+1)ֱΪ뾶һ㡣
    (5)ͼֱߺ͹⻬Ӹ㣬ΪչͼٸλǷΪS1S2ϡ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲLa(1)߲ÿֳϣٴ⴦ÿֳɿϡ
 


$17


#18                   Բ¾ؿܷͨ˵

    1ΪϿԲΣ¿ͬߴΣȡͬƫԲ¾ؿͨ4-14ͬǱ൱ԲεӹƴӶɣؿڵxyƫĿ仯
    2 ʾͼdΪͨϲԲֱL1w1L2w2ֱΪ²ؿڱߵĳͿhΪͨĸ߶ȣpx1px2ֱΪ12x᷽ƫľ룬py1py2ֱΪؿy᷽ƫbΪĺȡҪdL1w1L2w2hb>0px1>=L1/2px2>L2/2py1py2ȡʵΪ˼ͨܵͱϣh>px1px2
    3py1py2ֵҪԲΪo㣬ֱɵֱϵȷoϷʱpy1py2Ϊֵo·ʱΪֵoغΪ0py1py2رעֵ󣬿ܻᵼ²ȷչͼ
    4Բܳnȷߵʵnֵ4ɲ߸ֱҪȷ룬nֵԽչͼľԽߣչͼĹӦӡ˹һȡn=16~36ѿɱȽ׼ȷϣиϻǿ̻1:1壬nֵȡһЩ
    5չͼηϣչͼֳɸνмֱӸڰϣɲչʾͼ·(Ұ벿Ϊ)
    (1)һֱ߶Σȵw1
    (2)ͼֱ߶˵ΪԲģLa(1)Lb(1)Ϊ뾶һ㡣ȻԽΪԲģmΪ뾶ڽ໭߶˵ΪԲģLa(2)Lb(2)Ϊ뾶Բֱཻ˳λLa(1)La(n/4+1)Lb(1)Lb(n/4+1)߶mĽ㡣
    (3)ͼ߶ҵΪԲģL1Ϊ뾶Lb(n/4+1)ΪԲģhs1Ϊ뾶ཻõµҽ㣻߶˵ΪԲģL1Ϊ뾶La(n/4+1)ΪԲģhp1Ϊ뾶ཻõµ󽻵㡣
    (4)ͬķLs1dw1hs1Ϊ뾶ֱ𻭳ߵ㡣
    (5)ͼù⻬SȲָ㣬ֱ㣬ɵõӹܵչͼ
    (6)벿Ұ벿ֵϷһֻȡֵ뷽һѣοҰ벿ֵϷԻչͼ
    6չͼھӹ㣬ͼλģʱΪ˽ԼϣҲhp1hp2߲ÿֳϣٴ⴦ÿֳɿϡ



$18


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