色轮背后的数学是啥
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【中文标题】色轮背后的数学是啥【英文标题】：What is the math behind the Colour Wheel色轮背后的数学是什么 【发布时间】：2011-05-13 05:07:55 【问题描述】：我想创建一个有 12 片的馅饼，每片都有不同的颜色。
几乎每个色轮都遵循相同的格式；例如：http://www.tigercolor.com/color-lab/color-theory/color-theory-intro.htm .
但是有什么算法可以生成颜色呢？ RGB(theta) 背后的数学原理是什么？当然，这方面肯定有一些既定的科学，但谷歌没有给我任何线索。
【问题讨论】：
不就是color(angle) = HSV(angle, 1, 1)吗？
好的...但是这背后的数学原理是什么？
你看过***.com/questions/180/…上的答案了吗？
请考虑支持/关注 StackExchange Color Theory 网站：area51.stackexchange.com/proposals/110687/color-theory
【参考方案1】：
看看http://www.easyrgb.com，它拥有许多颜色转换背后的算法。这是 RGB -> HSV 之一。
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
【讨论】：
【参考方案2】：色轮（例如 Mac OS X 颜色选择器，如下图所示）显示 hue 和 saturation（来自HSV colour space 的三个组件中的两个）。色调随角度变化，饱和度随半径变化。通常，值（又名亮度）有一个单独的滑块。
See Wikipedia 了解如何在 HSV 和 RGB 之间来回转换。或者，您选择的编程语言可能有一个 API。例如，Python 有colorsys library。
【讨论】：
【参考方案3】：我正在尝试在 Excel VBA 中制作一个基于 HSL 的色轮，使用微小的单元格作为“像素”，结果非常好，所以我想我会分享。
这演示了 HSL 和 RGB 之间的转换，以及如何以编程方式在任何网格上绘制线条/圆——甚至是电子表格单元格。
代码已准备好按原样运行：
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
如何在 Excel 中运行： 将上面的代码粘贴到regular module 中。 （选择代码，Ctrl+C复制，然后在Excel中，按住Alt并点击F11+I+M 然后 Ctrl+V 粘贴，F5 运行。） ?
更多信息：
***：HSL and HSV ***：Color Wheel - HSL colormatters.com：Basic Color Theory ***：Midpoint circle algorithm【讨论】：
【参考方案4】：如果您想要一个像您提供的示例一样的色轮（并且像大多数色轮一样，您会在工艺品商店的油漆区找到），其中红色与绿色相对，蓝色与黄橙色相对，紫色与黄色相对等.，您可以简单地进行以下数学运算来修改 HSL 或 HSV 的色调以获得旧色调...
double ToLegacyHue(double modernHue)
modernHue = ((modernHue % 360) + 360) % 360; // normalize 360 > modernHue >= 0
double ret = 0;
if(modernHue < 60)
ret = modernHue * 2;
else if(modernHue < 120)
ret = modernHue + 60;
else
ret = (modernHue - 120) * 0.75 + 180;
return ret;
double FromLegacyHue(double legacyHue)
legacyHue = ((legacyHue % 360) + 360) % 360; // normalize 360 > legacyHue >= 0
double ret = 0;
if(legacyHue < 120)
ret = legacyHue / 2;
else if(legacyHue < 180)
ret = legacyHue - 60;
else
ret = (legacyHue - 180) / 0.75 + 120;
return ret;
【讨论】：
【参考方案5】：绘制色轮的步骤
用笛卡尔坐标取一点：(x,y) 将笛卡尔坐标转换为极坐标：(x,y) -> (r,theta) 将坐标转换为颜色 = 极坐标为 hsv : (r,theta) -> (h,s,v)在哪里：
theta = 色相 半径 r = 饱和度 值为常量这是tool 和nice examples
【讨论】：
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