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编程模拟自然(一)：如何画一颗静态树

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万物初始之前，宇宙是无边无际混沌的黑暗，只有元之灵穿行其间。元对这无边的黑暗十分不满，就轻轻一敲键盘，说：“要有光”，于是世间就有了光。元称“光”为“昼”，称“黑暗”为“夜”。亮光隐去，黑暗重临，从此，世间就有了昼与夜的交替。这是元创世的第一天。

这个二次元世界诞生之初伴有一只程序猿，Ta的名字叫元。

第一章二叉树必须是最好的树!

元就是这样想的，为了表达对这种数据结构的崇拜之情，决定在这个世界造出一颗真实的树，一开始的构想是这样的

编程模拟自然(一)：如何画一颗静态树

“正所谓树极生三干，三干生六枝，六枝生十二叶。” 然而这并不是一颗二叉树。

第二章黄金分割現れる

树每递归一层需要按一定比例缩放，元苦苦冥想良久，终于找到了一个无限不循环小数，它的小数点后64位是这样的

0.6180339887 4989484820 4586834365 6381177203 0917980576 2862135448 6227...

[从左至右，比例系数依次是0.618, 0.5, 1, 1.6]

编程模拟自然(一)：如何画一颗静态树

当然树干的粗细也得缩放，元是想将这东西种在伊甸园的土地上的，那就再截去下方的子树

编程模拟自然(一)：如何画一颗静态树

“啊哈，这下叫二叉树没错了吧。”

“既然配图这么暗黄，就称这个无理数为黄金分割比例吧!”元心里想了想。

第三章不对称与伪随机

不对称才是美？不对称才是美？！所以元就在树的节点位置加入了伪随机扰动。

编程模拟自然(一)：如何画一颗静态树

“说点什么好呢？”

第四章更多的子树

元一直认为这个世界有时候是需要偏见的，二叉树肯定是最好的树。

虽然现在不止两个子树。

编程模拟自然(一)：如何画一颗静态树

“高清大图才能欣赏的过瘾。”你可以尝试目标另存为。

第五章绿叶与果实

在树的末梢长出叶子和果实，一颗树终于成型了。

编程模拟自然(一)：如何画一颗静态树

“对暗黄系简直审美疲劳，画风是该换一换了。”

“结束了，据说第六天还要加班造人？！”

后记

-- 亚，我饿了

-- 夏，我去给你摘果子

...

-- 亚，那个猿又在树上看着我们

-- 别管Ta，吃果子咯

-- 嗯哪

...

-- 夏，我一直以为那是只狗呢

...

Dim ph As Graphics Dim PaintBoard As Bitmap Dim centerX, centerY As Long Dim modeSequence() As Integer = {4, 5, 4, 6, 5, 6, 1, 2, 1, 3, 2, 3} Dim rnd As New Random Public Function Calculator(ByVal x As Double, ByVal y As Double, ByVal mode As Integer, ByVal r As Double, ByVal depth As Integer, ByVal radio As Double) As Double()  Dim R2 As Double  r = r * radio  R2 = Math.Sqrt(3) * (r / 2)  Dim Position(2) As Double  Dim tempRnd As Double = 1 '* rnd.Next(depth, 20) / 10  If mode = 1 Then   x = 0 : y = -r * tempRnd  ElseIf mode = 2 Then   x = -R2 * tempRnd : y = (r / 2) * tempRnd  ElseIf mode = 3 Then   x = R2 * tempRnd : y = (r / 2) * tempRnd  ElseIf mode = 4 Then   x = -R2 * tempRnd : y = -(r / 2) * tempRnd  ElseIf mode = 5 Then   x = R2 * tempRnd : y = -(r / 2) * tempRnd  ElseIf mode = 6 Then   x = 0 : y = r * tempRnd  End If  Position(0) = x  Position(1) = y  Position(2) = r  Return Position End Function Public Sub PaintLine(ByVal x As Double, ByVal y As Double, ByVal mode As Integer, ByVal r As Double, ByVal depth As Integer, ByVal radio As Double)  Dim position() As Double  Dim tempR As Double  Dim tempWidth As Double  Dim tempColor As Color  Dim tempRnd As Integer = rnd.Next(1, 3)  Dim tempAlpha As Integer  For j = 0 To 1   For pff = 0 To tempRnd    position = Calculator(x, y, modeSequence((mode - 1) * 2 + j), r, depth, radio)    Dim LineVector As New Vector2D(position(0), position(1))    LineVector.x *= rnd.NextDouble    LineVector.y *= rnd.NextDouble    LineVector.SetMag(IIf(depth <= 1, 20, position(2)))    position(0) = LineVector.x    position(1) = LineVector.y    Dim tempMag As Double = LineVector.Magnitude    Dim PointList As New List(Of PointF)    For m = 1 To tempMag     LineVector.SetMag(m)     PointList.Add(New PointF(x + LineVector.x, y + LineVector.y))    Next    If PointList.Count >= 2 Then     Dim tempNext As Double = rnd.NextDouble     tempAlpha = rnd.Next(20, 100)     For p = 0 To PointList.Count - 2      tempR = r * 0.015 * depth      tempWidth = IIf(depth <= 1, Math.Sin(p / 6) * 10, tempR - p / PointList.Count * (tempR - tempR * radio + r * 0.015 * radio))      tempColor = IIf(depth <= 1, Color.FromArgb(tempAlpha, Color.Green), Color.Black)      If depth <= 1 Then       If tempNext < 0.01 Then        tempWidth = Math.Sin(p / 6) * 20        tempColor = Color.FromArgb(rnd.Next(200, 255), Color.Red)       End If      End If      ph.DrawLine(New Pen(tempColor, tempWidth), PointList(p), PointList(p + 1))     Next    End If    PaintHexgon(position(0) + x, position(1) + y, modeSequence((mode - 1) * 2 + j), tempMag, depth - 1, radio)   Next  Next End Sub Public Sub PaintHexgon(ByVal x As Double, ByVal y As Double, ByVal mode As Integer, ByVal r As Double, ByVal depth As Integer, ByVal radio As Double)  If depth > 0 Then   If mode = 0 Then    ph.DrawLine(New Pen(Brushes.Black, r * 0.02 * depth), New PointF(x, y), New PointF(x, y + r))    PaintLine(x, y, 1, r, depth, radio)   Else    PaintLine(x, y, mode, r, depth, radio)   End If  End If End Sub '画树 Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click  PaintBoard = New Bitmap(PictureBox1.Width, PictureBox1.Height)  ph = Graphics.FromImage(PaintBoard)  ph.SmoothingMode = Drawing2D.SmoothingMode.AntiAlias  centerX = PictureBox1.Width / 2 : centerY = PictureBox1.Height / 2  PaintHexgon(centerX, centerY, 0, 200, 5, 0.6180339887)  ' PaintHexgon(centerX, centerY, 0, 20, 5, 1.61812)  PictureBox1.Image = PaintBoard End Sub