bmp纵横比问题
bmp aspect ratio issue
我一直在尝试了解 bmp 文件的工作原理，以便我可以渲染一些 Mandelbrot 集图片并将它们输出为 bmp 文件，因为这似乎是最简单的方法之一，但由于某些原因，当我使用纵横比时那不是 1:1，即使它是 4 的幂（所以不需要填充）我得到像这些奇怪的人工制品 200:100 48:100 what I'm trying to do is turning an array of pixels that has white for even numbers and black for odd numbers into a bmp, this (100:100) 是 1:1 宽高比的样子。
我已经尝试阅读维基百科文章，看看我是否能弄清楚我做错了什么，但我仍然不明白我错过了什么。
这是我目前在 Lua 中编写的脚本：
ResolutionX = 100
ResolutionY = 100
local cos, atan, sin, atan2, sqrt, floor = math.cos, math.atan, math.sin, math.atan2, math.sqrt, math.floor
local insert, concat = table.insert, table.concat
local sub, char, rep = string.sub, string.char, string.rep
io.output("Test.bmp")
function Basen(n,b)
n = floor(n)
if not b or b == 10 then return tostring(n) end
local digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
local t = {}
repeat
local d = (n % b) + 1
n = floor(n / b)
insert(t, 1, digits:sub(d,d))
until n == 0
return rep("0",32-#t)..concat(t,"")
end
FileSize = Basen(ResolutionY*ResolutionX*3 + 54,2)
FileSize4 = tonumber(sub(FileSize,1,8),2) or 0
FileSize3 = tonumber(sub(FileSize,9,16),2) or 0
FileSize2 = tonumber(sub(FileSize,17,24),2) or 0
FileSize1 = tonumber(sub(FileSize,25,32),2) or 0
Width = Basen(ResolutionX,2)
print("Width: ",Width)
Width4 = tonumber(sub(Width,1,8),2) or 0
Width3 = tonumber(sub(Width,9,16),2) or 0
Width2 = tonumber(sub(Width,17,24),2) or 0
Width1 = tonumber(sub(Width,25,32),2) or 0
Height = Basen(ResolutionY,2)
print("Height: ",Height)
Height4 = tonumber(sub(Height,1,8),2) or 0
Height3 = tonumber(sub(Height,9,16),2) or 0
Height2 = tonumber(sub(Height,17,24),2) or 0
Height1 = tonumber(sub(Height,25,32),2) or 0
BMPSize = Basen(ResolutionY*ResolutionX*3,2)
BMPSize4 = tonumber(sub(BMPSize,1,8),2) or 0
BMPSize3 = tonumber(sub(BMPSize,9,16),2) or 0
BMPSize2 = tonumber(sub(BMPSize,17,24),2) or 0
BMPSize1 = tonumber(sub(BMPSize,25,32),2) or 0
print("TotalSize: ",FileSize1,FileSize2,FileSize3,FileSize4,"\nWidth: ",Width1,Width2,Width3,Width4,"\nHeight: ",Height1,Height2,Height3,Height4,"\nImage data: ",BMPSize1,BMPSize2,BMPSize3,BMPSize4)
Result = {"BM"..char( --File type
FileSize1,FileSize2,FileSize3,FileSize4,--File size
0,0,0,0, --Reserved
54,0,0,0, --Where the pixel data starts
40,0,0,0, --DIB header
Width1,Width2,Width3,Width4, --Width
Height1,Height2,Height3,Height4, --Height
1,0, --Color planes
24,00, --Bit depth
0,0,0,0, --Compression
BMPSize1,BMPSize2,BMPSize3,BMPSize4, --The amount of bytes pixel data will consume
Width1,Width2,Width3,Width4,
Height1,Height2,Height3,Height4,
0,0,0,0, --Number of colors in palatte
0,0,0,0
)}
for X = 0, ResolutionX - 1 do
for Y = 0, ResolutionY - 1 do
insert(Result,rep(char(255 * ((X + 1) % 2) * ((Y + 1) % 2)),3))
end
end
io.write(table.concat(Result))
欢迎使用 Stack Exchange :)
我建议看一下 PPM 文件，它们很简单。可以使用其他工具将它们转换为 png 或 bmp。
这是一个 PPM 解决方案：
ResolutionX = 48
ResolutionY = 100
local cos, atan, sin, atan2, sqrt, floor = math.cos, math.atan, math.sin, math.atan2, math.sqrt, math.floor
local insert, concat = table.insert, table.concat
local sub, char, rep = string.sub, string.char, string.rep
local file = io.open("Test.ppm","w")
-- PPM File headers
local Output = { }
Output[1] = "P3"
Output[2] = tostring(ResolutionX) .. " " .. tostring(ResolutionY)
Output[3] = "255"
-- Image body
for Y = 0, ResolutionY - 1 do
for X = 0, ResolutionX - 1 do
local value = 255 * ((X + 1) % 2) * ((Y + 1) % 2)
Output[#Output+1] = rep(tostring(floor(value)),3," ")
end
end
-- Join lines together
local Result = table.concat(Output,"\n")
file:write(Result)
注意： 我无法让您的代码写入文件（请参阅我对 file 的用法）。如果写入顺序为英文阅读顺序（左-右下-上），内循环必须是X（列），外循环必须是Y（行）。
好的，这是 BMP 版本。我已经把东西放在一个模块中，所以它可能更容易使用。
local writeBMP = {}
local floor = math.floor
local insert, concat = table.insert, table.concat
local sub, char, rep = string.sub, string.char, string.rep
local function Basen(n,b)
n = floor(n)
if not b or b == 10 then return tostring(n) end
local digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
local t = {}
repeat
local d = (n % b) + 1
n = floor(n / b)
insert(t, 1, digits:sub(d,d))
until n == 0
return rep("0",32-#t)..concat(t,"")
end
local function nextMul4(x)
if ( x % 4 == 0 ) then
return x
else
return x+4-(x%4)
end
end
local function clamp(x)
local y = x
if ( x > 255 ) then
y = 255
elseif ( x < 0 ) then
y = 0
end
return floor(y)
end
-- Accepts array of type pixelsXYC[X][Y][C] of numbers 0-255
-- C=1,2,3 are the red, green and blue channels respectively
-- X increases left to right, and Y increases top to bottom
function writeBMP.data(pixelsXYC, resolutionX, resolutionY)
local Pixels = pixelsXYC
local ResolutionX = resolutionX
local ResolutionY = resolutionY
assert(#Pixels == ResolutionX, "Table size and X resolution mismatch")
assert(#Pixels[1] == ResolutionY, "Table size and Y resolution mismatch")
local FileSize = Basen(ResolutionY*nextMul4(3*ResolutionX) + 54,2)
local FileSize4 = tonumber(sub(FileSize,1,8),2) or 0
local FileSize3 = tonumber(sub(FileSize,9,16),2) or 0
local FileSize2 = tonumber(sub(FileSize,17,24),2) or 0
local FileSize1 = tonumber(sub(FileSize,25,32),2) or 0
local Width = Basen(ResolutionX,2)
local Width4 = tonumber(sub(Width,1,8),2) or 0
local Width3 = tonumber(sub(Width,9,16),2) or 0
local Width2 = tonumber(sub(Width,17,24),2) or 0
local Width1 = tonumber(sub(Width,25,32),2) or 0
local Height = Basen(ResolutionY,2)
local Height4 = tonumber(sub(Height,1,8),2) or 0
local Height3 = tonumber(sub(Height,9,16),2) or 0
local Height2 = tonumber(sub(Height,17,24),2) or 0
local Height1 = tonumber(sub(Height,25,32),2) or 0
local BMPSize = Basen(ResolutionY*nextMul4(3*ResolutionX),2)
local BMPSize4 = tonumber(sub(BMPSize,1,8),2) or 0
local BMPSize3 = tonumber(sub(BMPSize,9,16),2) or 0
local BMPSize2 = tonumber(sub(BMPSize,17,24),2) or 0
local BMPSize1 = tonumber(sub(BMPSize,25,32),2) or 0
local Result = {}
Result[1] = "BM" .. char( --File type
FileSize1,FileSize2,FileSize3,FileSize4,--File size
0,0, --Reserved
0,0, --Reserved
54,0,0,0, --Where the pixel data starts
40,0,0,0, --DIB header
Width1,Width2,Width3,Width4, --Width
Height1,Height2,Height3,Height4, --Height
1,0, --Color planes
24,0, --Bit depth
0,0,0,0, --Compression
BMPSize1,BMPSize2,BMPSize3,BMPSize4, --The amount of bytes pixel data will consume
37,22,0,0, --Pixels per meter horizontal
37,22,0,0, --Pixels per meter vertical
0,0,0,0, --Number of colors in palatte
0,0,0,0
)
local Y = ResolutionY
while( Y >= 1 ) do
for X = 1, ResolutionX do
local r = clamp( Pixels[X][Y][1] )
local g = clamp( Pixels[X][Y][2] )
local b = clamp( Pixels[X][Y][3] )
Result[#Result+1] = char(b)
Result[#Result+1] = char(g)
Result[#Result+1] = char(r)
end
-- byte alignment
if ( ( (3*ResolutionX) % 4 ) ~= 0 ) then
local Padding = 4 - ((3*ResolutionX) % 4)
Result[#Result+1] = rep(char(0),Padding)
end
Y = Y - 1
end
return table.concat(Result)
end
function writeBMP.write(pixelsXYC, resolutionX, resolutionY, filename)
local file = io.open(filename,"wb")
local data = writeBMP.data(pixelsXYC, resolutionX, resolutionY)
file:write(data)
end
return writeBMP
一个简单的测试：
-- writeBMP example
local writeBMP = require "writeBMP"
local resolutionX = 100
local resolutionY = 100
-- Pixel data
local pixels = {}
for x=1,resolutionX do
pixels[x] = {}
for y=1, resolutionY do
pixels[x][y] = {}
local red = 255*(resolutionX-x+resolutionY-y)/(resolutionX+resolutionY)
local green = 255*y/resolutionY
local blue = 255*x/resolutionX
pixels[x][y][1] = red
pixels[x][y][2] = green
pixels[x][y][3] = blue
end
end
writeBMP.write(pixels,resolutionX,resolutionY,"testwritebmp.bmp")
return
注意：在BMP中，Y轴从底部开始。我比较习惯计算机图形中的Y轴从上到下（所以我这样写）。
感谢 HAX 提供代码。
我一直在尝试了解 bmp 文件的工作原理，以便我可以渲染一些 Mandelbrot 集图片并将它们输出为 bmp 文件，因为这似乎是最简单的方法之一，但由于某些原因，当我使用纵横比时那不是 1:1，即使它是 4 的幂（所以不需要填充）我得到像这些奇怪的人工制品 200:100 48:100 what I'm trying to do is turning an array of pixels that has white for even numbers and black for odd numbers into a bmp, this (100:100) 是 1:1 宽高比的样子。 我已经尝试阅读维基百科文章，看看我是否能弄清楚我做错了什么，但我仍然不明白我错过了什么。
这是我目前在 Lua 中编写的脚本：
ResolutionX = 100
ResolutionY = 100
local cos, atan, sin, atan2, sqrt, floor = math.cos, math.atan, math.sin, math.atan2, math.sqrt, math.floor
local insert, concat = table.insert, table.concat
local sub, char, rep = string.sub, string.char, string.rep
io.output("Test.bmp")
function Basen(n,b)
n = floor(n)
if not b or b == 10 then return tostring(n) end
local digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
local t = {}
repeat
local d = (n % b) + 1
n = floor(n / b)
insert(t, 1, digits:sub(d,d))
until n == 0
return rep("0",32-#t)..concat(t,"")
end
FileSize = Basen(ResolutionY*ResolutionX*3 + 54,2)
FileSize4 = tonumber(sub(FileSize,1,8),2) or 0
FileSize3 = tonumber(sub(FileSize,9,16),2) or 0
FileSize2 = tonumber(sub(FileSize,17,24),2) or 0
FileSize1 = tonumber(sub(FileSize,25,32),2) or 0
Width = Basen(ResolutionX,2)
print("Width: ",Width)
Width4 = tonumber(sub(Width,1,8),2) or 0
Width3 = tonumber(sub(Width,9,16),2) or 0
Width2 = tonumber(sub(Width,17,24),2) or 0
Width1 = tonumber(sub(Width,25,32),2) or 0
Height = Basen(ResolutionY,2)
print("Height: ",Height)
Height4 = tonumber(sub(Height,1,8),2) or 0
Height3 = tonumber(sub(Height,9,16),2) or 0
Height2 = tonumber(sub(Height,17,24),2) or 0
Height1 = tonumber(sub(Height,25,32),2) or 0
BMPSize = Basen(ResolutionY*ResolutionX*3,2)
BMPSize4 = tonumber(sub(BMPSize,1,8),2) or 0
BMPSize3 = tonumber(sub(BMPSize,9,16),2) or 0
BMPSize2 = tonumber(sub(BMPSize,17,24),2) or 0
BMPSize1 = tonumber(sub(BMPSize,25,32),2) or 0
print("TotalSize: ",FileSize1,FileSize2,FileSize3,FileSize4,"\nWidth: ",Width1,Width2,Width3,Width4,"\nHeight: ",Height1,Height2,Height3,Height4,"\nImage data: ",BMPSize1,BMPSize2,BMPSize3,BMPSize4)
Result = {"BM"..char( --File type
FileSize1,FileSize2,FileSize3,FileSize4,--File size
0,0,0,0, --Reserved
54,0,0,0, --Where the pixel data starts
40,0,0,0, --DIB header
Width1,Width2,Width3,Width4, --Width
Height1,Height2,Height3,Height4, --Height
1,0, --Color planes
24,00, --Bit depth
0,0,0,0, --Compression
BMPSize1,BMPSize2,BMPSize3,BMPSize4, --The amount of bytes pixel data will consume
Width1,Width2,Width3,Width4,
Height1,Height2,Height3,Height4,
0,0,0,0, --Number of colors in palatte
0,0,0,0
)}
for X = 0, ResolutionX - 1 do
for Y = 0, ResolutionY - 1 do
insert(Result,rep(char(255 * ((X + 1) % 2) * ((Y + 1) % 2)),3))
end
end
io.write(table.concat(Result))
欢迎使用 Stack Exchange :)
我建议看一下 PPM 文件，它们很简单。可以使用其他工具将它们转换为 png 或 bmp。
这是一个 PPM 解决方案：
ResolutionX = 48
ResolutionY = 100
local cos, atan, sin, atan2, sqrt, floor = math.cos, math.atan, math.sin, math.atan2, math.sqrt, math.floor
local insert, concat = table.insert, table.concat
local sub, char, rep = string.sub, string.char, string.rep
local file = io.open("Test.ppm","w")
-- PPM File headers
local Output = { }
Output[1] = "P3"
Output[2] = tostring(ResolutionX) .. " " .. tostring(ResolutionY)
Output[3] = "255"
-- Image body
for Y = 0, ResolutionY - 1 do
for X = 0, ResolutionX - 1 do
local value = 255 * ((X + 1) % 2) * ((Y + 1) % 2)
Output[#Output+1] = rep(tostring(floor(value)),3," ")
end
end
-- Join lines together
local Result = table.concat(Output,"\n")
file:write(Result)
注意： 我无法让您的代码写入文件（请参阅我对 file 的用法）。如果写入顺序为英文阅读顺序（左-右下-上），内循环必须是X（列），外循环必须是Y（行）。
好的，这是 BMP 版本。我已经把东西放在一个模块中，所以它可能更容易使用。
local writeBMP = {}
local floor = math.floor
local insert, concat = table.insert, table.concat
local sub, char, rep = string.sub, string.char, string.rep
local function Basen(n,b)
n = floor(n)
if not b or b == 10 then return tostring(n) end
local digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
local t = {}
repeat
local d = (n % b) + 1
n = floor(n / b)
insert(t, 1, digits:sub(d,d))
until n == 0
return rep("0",32-#t)..concat(t,"")
end
local function nextMul4(x)
if ( x % 4 == 0 ) then
return x
else
return x+4-(x%4)
end
end
local function clamp(x)
local y = x
if ( x > 255 ) then
y = 255
elseif ( x < 0 ) then
y = 0
end
return floor(y)
end
-- Accepts array of type pixelsXYC[X][Y][C] of numbers 0-255
-- C=1,2,3 are the red, green and blue channels respectively
-- X increases left to right, and Y increases top to bottom
function writeBMP.data(pixelsXYC, resolutionX, resolutionY)
local Pixels = pixelsXYC
local ResolutionX = resolutionX
local ResolutionY = resolutionY
assert(#Pixels == ResolutionX, "Table size and X resolution mismatch")
assert(#Pixels[1] == ResolutionY, "Table size and Y resolution mismatch")
local FileSize = Basen(ResolutionY*nextMul4(3*ResolutionX) + 54,2)
local FileSize4 = tonumber(sub(FileSize,1,8),2) or 0
local FileSize3 = tonumber(sub(FileSize,9,16),2) or 0
local FileSize2 = tonumber(sub(FileSize,17,24),2) or 0
local FileSize1 = tonumber(sub(FileSize,25,32),2) or 0
local Width = Basen(ResolutionX,2)
local Width4 = tonumber(sub(Width,1,8),2) or 0
local Width3 = tonumber(sub(Width,9,16),2) or 0
local Width2 = tonumber(sub(Width,17,24),2) or 0
local Width1 = tonumber(sub(Width,25,32),2) or 0
local Height = Basen(ResolutionY,2)
local Height4 = tonumber(sub(Height,1,8),2) or 0
local Height3 = tonumber(sub(Height,9,16),2) or 0
local Height2 = tonumber(sub(Height,17,24),2) or 0
local Height1 = tonumber(sub(Height,25,32),2) or 0
local BMPSize = Basen(ResolutionY*nextMul4(3*ResolutionX),2)
local BMPSize4 = tonumber(sub(BMPSize,1,8),2) or 0
local BMPSize3 = tonumber(sub(BMPSize,9,16),2) or 0
local BMPSize2 = tonumber(sub(BMPSize,17,24),2) or 0
local BMPSize1 = tonumber(sub(BMPSize,25,32),2) or 0
local Result = {}
Result[1] = "BM" .. char( --File type
FileSize1,FileSize2,FileSize3,FileSize4,--File size
0,0, --Reserved
0,0, --Reserved
54,0,0,0, --Where the pixel data starts
40,0,0,0, --DIB header
Width1,Width2,Width3,Width4, --Width
Height1,Height2,Height3,Height4, --Height
1,0, --Color planes
24,0, --Bit depth
0,0,0,0, --Compression
BMPSize1,BMPSize2,BMPSize3,BMPSize4, --The amount of bytes pixel data will consume
37,22,0,0, --Pixels per meter horizontal
37,22,0,0, --Pixels per meter vertical
0,0,0,0, --Number of colors in palatte
0,0,0,0
)
local Y = ResolutionY
while( Y >= 1 ) do
for X = 1, ResolutionX do
local r = clamp( Pixels[X][Y][1] )
local g = clamp( Pixels[X][Y][2] )
local b = clamp( Pixels[X][Y][3] )
Result[#Result+1] = char(b)
Result[#Result+1] = char(g)
Result[#Result+1] = char(r)
end
-- byte alignment
if ( ( (3*ResolutionX) % 4 ) ~= 0 ) then
local Padding = 4 - ((3*ResolutionX) % 4)
Result[#Result+1] = rep(char(0),Padding)
end
Y = Y - 1
end
return table.concat(Result)
end
function writeBMP.write(pixelsXYC, resolutionX, resolutionY, filename)
local file = io.open(filename,"wb")
local data = writeBMP.data(pixelsXYC, resolutionX, resolutionY)
file:write(data)
end
return writeBMP
一个简单的测试：
-- writeBMP example
local writeBMP = require "writeBMP"
local resolutionX = 100
local resolutionY = 100
-- Pixel data
local pixels = {}
for x=1,resolutionX do
pixels[x] = {}
for y=1, resolutionY do
pixels[x][y] = {}
local red = 255*(resolutionX-x+resolutionY-y)/(resolutionX+resolutionY)
local green = 255*y/resolutionY
local blue = 255*x/resolutionX
pixels[x][y][1] = red
pixels[x][y][2] = green
pixels[x][y][3] = blue
end
end
writeBMP.write(pixels,resolutionX,resolutionY,"testwritebmp.bmp")
return
注意：在BMP中，Y轴从底部开始。我比较习惯计算机图形中的Y轴从上到下（所以我这样写）。
感谢 HAX 提供代码。