果树种植最优解精美图形作法探讨

wayne

这种方法致命的地方就是 随机生成转换矩阵。 要想做出楼上提到的 eyond 发现的完美对称的图案几乎是不可能的

wayne

换一种思路： 在原始数据中找出能构成平面的三个点 映射到等腰直角三角形，等边三角形。。。 这样就唯一确定了一个仿射变换矩阵，稍后呈现

wayne

太惊喜了 太有意思了

wayne

ADGJBEIJCDHKAFIKCEGLBFHLCJMODINODLMPAHNPGKOPBGMQFJNQAEOQEHMRBKNRCFPRILQRABCSDEFSGHITJKLTMNST： 该组数据可以对应有181种非奇异的转换矩阵。 挑选集中好看的如下： A {0,0} B {1/4 (1+Sqrt[5]),-(1/2)} C {1/2 (-1+Sqrt[5]),1/2 (-3+Sqrt[5])} D {1/2 (-1+Sqrt[5]),0} E {2/Sqrt[5],1/10 (-5+Sqrt[5])} F {Sqrt[5]/2,-(1/2)} G {1/2 (1+Sqrt[5]),0} H {1/2 (-1+Sqrt[5]),-(1/2)} I {1/2 (-5+3 Sqrt[5]),1/2 (-3+Sqrt[5])} J {1,0} K {1/2 (-1+Sqrt[5]),1/10 (-5+Sqrt[5])} L {1/4 (-1+Sqrt[5]),-(1/2)} M {0,-1} N {-1+Sqrt[5],-1} O {3-Sqrt[5],2-Sqrt[5]} P {1/3 (-1+Sqrt[5]),-(1/3)} Q {1/3 (1+Sqrt[5]),-(1/3)} R {4/19 (-1+2 Sqrt[5]),1/19 (-10+Sqrt[5])} S {1/2 (1+Sqrt[5]),-1} T {1/2 (-3+Sqrt[5]),-1} A {0,1} B {1/2,1/2} C {1/2 (3-Sqrt[5]),1/2 (Sqrt[5]-1)} D {1/4 (Sqrt[5]-1),1} E {1/2,1/10 (Sqrt[5]+5)} F {1/8 (Sqrt[5]+3),1/2} G {1/4 (Sqrt[5]+1),1} H {1/8 (Sqrt[5]+1),1/2} I {1/2,1/2 (Sqrt[5]-1)} J {1/2,1} K {1/20 (Sqrt[5]+5),1/10 (Sqrt[5]+5)} L {1/4,1/2} M {1/4 (3-Sqrt[5]),0} N {1/4 (Sqrt[5]+1),0} O {1/4 (3 Sqrt[5]-5),3-Sqrt[5]} P {1/12 (Sqrt[5]+1),2/3} Q {1/12 (Sqrt[5]+5),2/3} R {3/76 (Sqrt[5]+9),1/19 (Sqrt[5]+9)} S {1,0} T {0,0}

wayne

24# wayne A {1,0} B {1/2 (-1+Sqrt[5]),1/2 (1-Sqrt[5])} C {1/4 (5-Sqrt[5]),-(1/2)} D {1,-(1/2)} E {1/2 (-5+3 Sqrt[5]),1/2 (1-Sqrt[5])} F {1/10 (5+Sqrt[5]),1/10 (-5-Sqrt[5])} G {1,1/10 (-5-Sqrt[5])} H {1/2,-(1/2)} I {3-Sqrt[5],1/2 (1-Sqrt[5])} J {1,1/2 (1-Sqrt[5])} K {1/4 (1+Sqrt[5]),-(1/2)} L {0,0} M {2,-1} N {0,-1} O {1/11 (-2) (-7+Sqrt[5]),1/11 (-4-Sqrt[5])} P {2/3,-(1/3)} Q {1/11 (7+Sqrt[5]),1/11 (-3-2 Sqrt[5])} R {1/11 (1+3 Sqrt[5]),1/11 (-4-Sqrt[5])} S {1/2 (3-Sqrt[5]),-1} T {1/2 (1+Sqrt[5]),-1}

wayne

A {1/2,-1} B {1/10 (5+Sqrt[5]),-1-1/Sqrt[5]} C {0,0} D {1/2 (3-Sqrt[5]),-1} E {1/2 (3+Sqrt[5]),1/2 (-3-Sqrt[5])} F {2/3,1/6 (-5-Sqrt[5])} G {1,-1} H {1,1/2 (-3-Sqrt[5])} I {1,1/2 (-1-Sqrt[5])} J {0,-1} K {1/10 (5-Sqrt[5]),1/10 (-5-Sqrt[5])} L {1/2,-(1/2)} M {0,1/2 (-3-Sqrt[5])} N {1-1/Sqrt[5],1/10 (-5-3 Sqrt[5])} O {0,1/2 (1-Sqrt[5])} P {1/11 (7-Sqrt[5]),1/22 (-15-Sqrt[5])} Q {1/11 (7+Sqrt[5]),1/22 (-3) (7+Sqrt[5])} R {1+1/Sqrt[5],1/2 (-3-Sqrt[5])} S {1/11 (4+Sqrt[5]),1/11 (-2) (4+Sqrt[5])} T {1,0}

wayne

ACEFDFHJBCIJBEHKADIKBFGMEJLMBDLNCGNODEGPFKNPAJOPAGLQCKMQCHLRDMOREIQRAHNSFIOSBPQSGHITABRTCDST
该组数据有111组非奇异转换矩阵。


{A,{0,0}}        {B,{1/5,1/5}}        {C,{1/2,0}}        {D,{1/6,1/3}}
{E,{-(1/2),0}}        {F,{1,0}}        {G,{0,1/4}}        {H,{3/8,1/4}}
{I,{1/8,1/4}}        {J,{-(1/4),1/2}}        {K,{1/12,1/6}}        {L,{0,1}}
{M,{-(1/3),1/3}}        {N,{3/14,1/7}}        {O,{-(1/6),1/3}}        {P,{-(1/10),1/5}}
{Q,{0,1/5}}        {R,{1/3,1/3}}        {S,{3/10,1/5}}        {T,{1/4,1/4}}
稍稍变换，犹如火箭升空：

{A,{0,0}}        {B,{-(1/4),-(1/(4 Sqrt[3]))}}        {C,{-(1/4),0}}        {D,{-(1/8),Sqrt[3]/8}}
{E,{-(1/2),0}}        {F,{-(2/7),0}}        {G,{-(5/16),Sqrt[3]/16}}        {H,{-(7/20),-(Sqrt[3]/20)}}
{I,{-(1/4),Sqrt[3]/4}}        {J,{-(1/4),1/(12 Sqrt[3])}}        {K,{1/4,-(Sqrt[3]/4)}}        {L,{-(5/28),Sqrt[3]/28}}
{M,{-(13/44),Sqrt[3]/44}}        {N,{-(7/32),-(Sqrt[3]/32)}}        {O,{-(9/32),Sqrt[3]/32}}        {P,{-(3/8),1/(8 Sqrt[3])}}
{Q,{-(5/12),1/(4 Sqrt[3])}}        {R,{-(3/4),-(Sqrt[3]/4)}}        {S,{-(7/24),-(1/(8 Sqrt[3]))}}        {T,{-(3/8),-(Sqrt[3]/8)}}


{A,{0,0}}        {B,{1/2,-1}}        {C,{1,-1}}        {D,{0,-(1/2)}}
{E,{1/3,-(1/3)}}        {F,{2/3,-(2/3)}}        {G,{1,0}}        {H,{2/5,-(3/5)}}
{I,{0,-1}}        {J,{2,-1}}        {K,{0,1}}        {L,{-(1/2),0}}
{M,{3/4,-(1/2)}}        {N,{1,-(3/2)}}        {O,{1,-(1/2)}}        {P,{1/2,-(1/4)}}
{Q,{1/2,0}}        {R,{1/4,-(1/2)}}        {S,{1/2,-(3/4)}}        {T,{1/3,-(2/3)}}

该图的形状比较有趣，
稍加变换，巧夺天工！
我要盛赞这幅图！

{A,{-2 Sqrt[3],-(1/2)}}        {B,{-(Sqrt[3]/2),0}}        {C,{0,-(1/2)}}        {D,{-((3 Sqrt[3])/2),0}}
{E,{-(4/Sqrt[3]),-(1/2)}}        {F,{-(2/Sqrt[3]),-(1/2)}}        {G,{-Sqrt[3],-(3/2)}}        {H,{-Sqrt[3],-(3/10)}}
{I,{-Sqrt[3],1/2}}        {J,{Sqrt[3],-(3/2)}}        {K,{-3 Sqrt[3],-(3/2)}}        {L,{-((5 Sqrt[3])/2),0}}
{M,{-((3 Sqrt[3])/4),-(3/4)}}        {N,{Sqrt[3]/2,0}}        {O,{-(Sqrt[3]/2),-1}}        {P,{-((5 Sqrt[3])/4),-(3/4)}}
{Q,{-((3 Sqrt[3])/2),-1}}        {R,{-((5 Sqrt[3])/4),-(1/4)}}        {S,{-((3 Sqrt[3])/4),-(1/4)}}        {T,{-Sqrt[3],-(1/6)}}

或者：

{{A,{-120,-50}},{B,{-30,40}},{C,{0,-50}},{D,{-90,40}}},
{{E,{-80,-50}},{F,{-40,-50}},{G,{-60,-230}},{H,{-60,-14}}},
{{I,{-60,130}},{J,{60,-230}},{K,{-180,-230}},{L,{-150,40}}},
{{M,{-45,-95}},{N,{30,40}},{O,{-30,-140}},{P,{-75,-95}}},
{{Q,{-90,-140}},{R,{-75,-5}},{S,{-45,-5}},{T,{-60,10}}}}

wayne

{A,{0,0}} {B,{1/7,-(3/7)}} {C,{-(1/5),-(1/5)}} {D,{-1,1}} {E,{1/3,1/3}} {F,{-(1/3),-(1/3)}} {G,{3,-1}} {H,{0,-1}} {I,{1,-1}} {J,{-(1/2),0}} {K,{1/5,-(1/5)}} {L,{-(3/11),1/11}} {M,{-1,-(1/5)}} {N,{0,-(1/4)}} {O,{-1,0}} {P,{1,0}} {Q,{3/5,-(1/5)}} {R,{-1,3}} {S,{0,-(1/2)}} {T,{1/3,-1}}

wayne

{A,{2/9,1}} {B,{1,0}} {C,{4/9,1}} {D,{0,3/2}} {E,{0,1}} {F,{2/3,1}} {G,{0,3}} {H,{-2,3}} {I,{-(2/3),3}} {J,{2/7,9/7}} {K,{2/5,3/5}} {L,{1/5,6/5}} {M,{1/2,3/2}} {N,{1/2,3/4}} {O,{1/3,3/2}} {P,{0,0}} {Q,{1/3,0}} {R,{-(1/6),3/2}} {S,{4/3,0}} {T,{-(4/3),3}} {A,{1/3,1}} {B,{1,0}} {C,{2/3,1}} {D,{1/4,3/2}} {E,{0,1}} {F,{1,1}} {G,{1,3}} {H,{-2,3}} {I,{0,3}} {J,{4/7,9/7}} {K,{2/5,3/5}} {L,{2/5,6/5}} {M,{1,3/2}} {N,{5/8,3/4}} {O,{3/4,3/2}} {P,{-(1/2),0}} {Q,{0,0}} {R,{0,3/2}} {S,{3/2,0}} {T,{-1,3}}

wayne

像蝴蝶啊，花点时间琢磨的话，绝对可以更像！ {A,{0,1/4}} {B,{3/2,1}} {C,{0,4/7}} {D,{-(6/11),2/11}} {E,{0,0}} {F,{0,1}} {G,{-3,1}} {H,{-(6/5),-(4/5)}} {I,{-2,0}} {J,{-(6/17),8/17}} {K,{6/13,4/13}} {L,{-(3/13),4/13}} {M,{-(3/4),1}} {N,{6/19,10/19}} {O,{-(2/3),2/3}} {P,{6/7,-(2/7)}} {Q,{1,0}} {R,{-(1/2),0}} {S,{2,2}} {T,{-(3/2),-(1/2)}}