什么是数学背后的颜色轮

https://stackoverflow.com/questions/4235072

26-09-2019
|

题

我想创建一个馅饼12片，与每个片段不同的颜色。

几乎每一种颜色轮似乎遵循同样的格式；例如： http://www.tigercolor.com/color-lab/color-theory/color-theory-intro.htm .

但是，算法是否有用于产生颜色？什么是数学后RGB(theta)?当然，必须有一些建立科学关于这一点，但是不给我任何线索。

解决方案

看一看 http://www.easyrgb.com 它具有背后许多颜色转换的算法。这里的RGB - > HSV一个

var_R = ( R / 255 )                     //RGB from 0 to 255
var_G = ( G / 255 )
var_B = ( B / 255 )

var_Min = min( var_R, var_G, var_B )    //Min. value of RGB
var_Max = max( var_R, var_G, var_B )    //Max. value of RGB
del_Max = var_Max - var_Min             //Delta RGB value 

V = var_Max

if ( del_Max == 0 )                     //This is a gray, no chroma...
{
   H = 0                                //HSV results from 0 to 1
   S = 0
}
else                                    //Chromatic data...
{
   S = del_Max / var_Max

   del_R = ( ( ( var_Max - var_R ) / 6 ) + ( del_Max / 2 ) ) / del_Max
   del_G = ( ( ( var_Max - var_G ) / 6 ) + ( del_Max / 2 ) ) / del_Max
   del_B = ( ( ( var_Max - var_B ) / 6 ) + ( del_Max / 2 ) ) / del_Max

   if      ( var_R == var_Max ) H = del_B - del_G
   else if ( var_G == var_Max ) H = ( 1 / 3 ) + del_R - del_B
   else if ( var_B == var_Max ) H = ( 2 / 3 ) + del_G - del_R

   if ( H < 0 ) H += 1
   if ( H > 1 ) H -= 1
}

其他提示

颜色轮(如Mac OS X颜色选择器，如下图)显示色调和 饱和度 (两个三个组成部分，从单纯疱疹病毒的颜色空间).色调不同角度，并饱和而不同的半径。通常有一个单独的滑的值 (又名亮度)。

Mac OS X colour picker

维基百科上看到的对于如何来回转换之间的单纯疱疹病毒和RGB。或者有可能是一个API for编程语言的选择。例如，蟒蛇的 colorsys 图书馆.

我是玩弄使赫尔辛基公共基颜色轮在Excel VBA，使用微小的细胞为"象素"，它原来很好，所以我想我会分享。

这表明之间的转换 赫尔辛基公共和RGB 以及如何通过程序 画线/圈上的任何网 —即使是电子表格的单元。

代码是准备运行为-是：

Option Explicit

Const colorSheetName = "COLORS"
Const pi = 3.14159265358979
Const squareSize = 3.75             'cell square size (pts)
Const cDiameter = 80#               'circle diameter (cells)
Const numAngles = 360#              'number of angles (lines to draw)

Sub CalculateColorWheel()
  Dim ws As Worksheet, radsPerAngle As Double, radius As Long, xStop As Double, _
      yStop As Double, z As Integer, xyLength As Double, lineDot As Long, _ 
      lineLength As Long, h As Byte, s As Byte, v As Byte, r As Byte, g As Byte, b As Byte

    Set ws = ThisWorkbook.Sheets.Add                        'create new worksheet
    On Error Resume Next                                    'ignore error 
    Application.DisplayAlerts = False                       'ignore warning
    ThisWorkbook.Sheets(colorSheetName).Delete              'delete worksheet (if exists)
    Application.DisplayAlerts = True                        'stop ignoring warnings
    On Error GoTo 0                                         'stop ignoring errors

    With ws
        .Name = colorSheetName                              'name the new sheet
        .Rows.RowHeight = squareSize                        'set rowheight 
        .Columns.ColumnWidth=widthToColumnWidth(squareSize) 'match columnwidth to row
        ActiveWindow.DisplayGridlines = False               'hide gridlines
        ActiveWindow.DisplayHeadings = False                'hide row/col headings
        radius = cDiameter / 2                              'centre point
        lineLength = radius * 1.5                           'dots per angle (line)
        radsPerAngle = (360 / numAngles) * pi / 180         'radians=a(degrees)×pi÷180°

        Debug.Print "Grid size=" & .[a1].Height & "×" & .[a1].Width _
                & ", Diameter:" & cDiameter _
                & ", Area=" & Round(pi * radius ^ 2, 0) _
                & ", Circumference=" & Round(2 * pi * radius, 0) _
                & ", Radians per Angle=" & Round(radsPerAngle, 3) _
                & " × " & numAngles & " angles"                 'stats

        For z = 0 To numAngles - 1  'loop through each angle
            For lineDot = 1 To lineLength   'loop thru length of line
                xyLength = radius * (lineDot / lineLength)  'calc dot xy& offset top-left
                xStop = Int(Cos(radsPerAngle * z) * xyLength) + radius + 2 'x (column)
                yStop = Int(Sin(radsPerAngle * z) * xyLength) + radius + 2 'y (row)

                If .Cells(yStop, xStop).Interior.Pattern=xlNone Then 'skip colored cells
                    h = ((z + 1) / numAngles) * 255                'hue=angle
                    s = (lineDot / lineLength) * 255                    'saturation=radius
                    v = 255                    'maximum brightness. (Adjustable)
                    HSVtoRGB h, s, v, r, g, b                      'convert HSV to RGB
                    .Cells(yStop, xStop).Interior.Color=rgb(r,g,b) 'color the cell
                    dots = dots + 1
                End If
            Next lineDot
            Application.StatusBar = Format(z / (numAngles - 1), "0%") 
            DoEvents    'don't lag
        Next z
    End With
    Beep
    Application.StatusBar = "Finished drawing color circle (" & dots & " colors)"
End Sub

Public Function widthToColumnWidth(pts As Double) As Double
'convert desired column width (points) to Excel "ColWidthUnits"
'12pts and under is a 1:12 ratio of (colWidthUnits:Pts).
' Over 12pts: 1:12 for 1st unit, then 1:(75/11) for remainder
    Select Case pts
        Case Is <= 0:  widthToColumnWidth = 0
        Case Is <= 12: widthToColumnWidth = pts / 12
        Case Else:     widthToColumnWidth = 1 + (pts - 12) / (75 / 11) '
    End Select
End Function

Public Sub HSVtoRGB(h As Byte, s As Byte, v As Byte, r As Byte, g As Byte, b As Byte)
    Dim minV As Byte, maxV As Byte, Chroma As Byte, tempH As Double

    If v = 0 Then
        r = 0: g = 0: b = 0
    Else
        If s = 0 Then
            r = v: g = v: b = v:
        Else
            maxV = v: Chroma = s / 255 * maxV: minV = maxV - Chroma
            Select Case h
                Case Is >= 170: tempH = (h - 170) / 43: g = 0
                                If tempH < 1 Then
                                    b = maxV: r = maxV * tempH
                                Else: r = maxV: b = maxV * (2 - tempH): End If
                Case Is >= 85:  tempH = (h - 85) / 43: r = 0
                                If tempH < 1 Then
                                    g = maxV: b = maxV * tempH
                                Else: b = maxV: g = maxV * (2 - tempH): End If
                Case Else:      tempH = h / 43: b = 0
                                If tempH < 1 Then
                                    r = maxV: g = maxV * tempH
                                Else: g = maxV: r = maxV * (2 - tempH): End If
            End Select
            r = r / maxV * (maxV - minV) + minV
            g = g / maxV * (maxV - minV) + minV
            b = b / maxV * (maxV - minV) + minV
        End If
    End If
End Sub

怎么跑这个在Excel中： 贴上述代码贴到一个经常模块.(选择的代码， Ctrl+C 复制，然后在Excel中，保持住 Alt 打 F11+我+M 然后 Ctrl+V 贴，和 F5 运行。) 🤓

什么是数学背后的颜色轮

更多信息：