果树种植最优解精美图形作法探讨

wayne · 发表于 2012-1-16 12:47:37

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 · 发表于 2012-1-16 12:54:26

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 · 发表于 2012-1-16 14:10:39

太惊喜了
太有意思了

wayne · 发表于 2012-1-16 21:38:11

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 · 发表于 2012-1-16 21:41:54

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 · 发表于 2012-1-16 21:50:58

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 · 发表于 2012-1-16 22:14:08

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 · 发表于 2012-1-16 22:17:06

{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 · 发表于 2012-1-16 22:19:33

{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 · 发表于 2012-1-16 22:25:16

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)}}

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[讨论] 果树种植最优解精美图形作法探讨