Mathematica渲染并输出为不同颜色的RGB颜色值的最小差异是什么? [英] What is the minimal difference in RGB color values which Mathematica renders and exports as different colors?

问题描述

我很惊讶发现，其中 Mathematica 为以下代码提供了True(在具有 Mathematica 8.0.1的32位Windows XP上):

I was amazed when I found that Mathematica gives True for the following code (on 32 bit Windows XP with Mathematica 8.0.1):

Rasterize[Graphics[{RGBColor[0, 0, 0], Disk[]}]] === 
 Rasterize[Graphics[{RGBColor[0, 0, 1/257], Disk[]}]]

Mathematica渲染并导出为不同颜色的RGB颜色值的最小差异是什么?是机器相关的吗?

What is the minimal difference in RGB color values which Mathematica renders and exports as different colors? Is it machine-dependent?

推荐答案

我相信此行为与计算机有关，但是我不知道它与操作系统之间的依赖程度.在我的机器上，仅当分母为511时，它的计算结果才为True.

I believe this behaviour is machine dependent, but I do not know how exactly it depends on the OS. On my machine, it evaluates to True only when the denominator is 511.

n = 257; 
While[(Rasterize[Graphics[{RGBColor[0, 0, 0], Disk[]}]] === 
    Rasterize[Graphics[{RGBColor[0, 0, 1/n], Disk[]}]]) != True, 
 n++]; 
Print@n

Out[1]=511

n<511

p1 = ImageData@Rasterize[Graphics[{RGBColor[0, 0, 0], Disk[]}]];
p2 = ImageData@Rasterize[Graphics[{RGBColor[0, 0, 1/257], Disk[]}]];
ArrayPlot[p1 - p2]

该差在整个n=510期间都是恒定的，并且等于1/255.

This difference is constant all the way through n=510 and is equal to 1/255.

Max[p2 - p1] === N[1/255]
Out[1]=True

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