snibgo's ImageMagick pages

Cylinders

We can displace a rectangular image to it apears to be on the face of a cylinder, or go in the opposite direction.

See cylPlane2.bat.

Suppose we have an image and we want to distort it so it appears to be on the surface of a cylinder. Or we have a photograph of a cylinder and want to project an image on to it. Or we want to unroll the photographed cylinder, manipulate it, and replace it.

We assume the camera is infinitely far from the cylinder (parallel projection). This removes the complication of more distant objects appearing smaller. Lines that are parallel in a scene will be parallel in the image.

For example, if we have a cylinder radius 100 pixels, diameter 200, semi-circumference = pi * r = 314, we can make two absolute displacement maps. One is for mapping from the cylinder to the plane, and the other is from the plane to the cylinder.

The maths

If:

x = r.sin(α)
x' = r.α

Thus:

x = r.sin (x'/r)
x' = r.asin (x/r)

When the camera is tilted up or down by angle (τ), we have two effects:

  1. The vertical dimension is shrunk, by multiplying by cos(τ).
  2. The front of the cylinder is raised or lowered with respect to the sides. At angle (α), the cylinder is at distance r.cos(α) from the centre line. This is multiplied by sin(τ). When the camera is above the horizontal, looking downwards, τ>0 and the centre of the cylinder is lower than the edges.

From a photograph we can measure the tilt by measuring the apparent width and height of a circle. τ = arcsin(mH/mW).

By default we map an entire rectangular image to 180° of a cylinder, and vice versa. If a plane is to be mapped to more or less than 180°, it could be cropped or extended first. For mapping to less than 180°, we can specify the start and end angles. (But we need a facility to readily rotate, so the image might be two appended crops from a single source.)

The image starts at pcStartAng and ends at pcEndAng. -90 <= pcStartAng < pcEndAng <= +90. 0° is the centre of the cylinder, at the front.

The width of the resulting segment of the cylinder, cylWW, will be the cylinder radius (cylRad) multiplied by sin(-pcStartAng)+sin(pcEndAng).

cylWW = cylRad * (sin(-pcStartAng)+sin(pcEndAng)).

Inverse: cylRad = cylWW / (sin(-pcStartAng)+sin(pcEndAng)).

The cylinder diameter is plWW * 180/(pcEndAng-pcStartAng) * 2/pi where plWW is the width of the plane image. So cylRad = plWW * 180/(pcEndAng-pcStartAng) / pi.

Inverse: plWW = cylRad * pi * (pcEndAng-pcStartAng)/180.

Special case when pcEndAng==pcStartAng: cylWW = plWW.

farZy = cylRad*cos(α)*cos(τ)

Plane to cylinder Cylinder to plane
plWW = image width cylWW = image width
plHH = image height extendV = image height
cylHH = h - w.abs(sinT)
tiltFact = -sinT/2 tiltFact = sinT/2
plHH = (h - abs(w/2*sinT))/cosT
cylRad = plWW * 180/pi / (EndAng - StartAng)
farZAng =
farZy = cylRad.abs(sin(farZAng)).sinT
cylWW = cylRad * (sinEndAng - sinStartAng) cylRad = cylWW / (sinEndAng - sinStartAng)
plWW = cylRad * pi/180 * (EndAng - StartAng)
cylHH = plHH.cosT
extendV = plHH.cosT + cylRad.abs(sinT)/2
Resize to cylWW x cylHH Apply displacement maps, 0 x cylWW/2 then cylWW/2 x 0
Extend to extendV high Crop to cylWW x cylHH
Apply displacement map, cylWW/2 x cylWW/2 Resize to plWW x plHH

Create a demonstration input file

%IM%convert ^
  -size 600x240 ^
  -background yellow -fill Blue ^
  label:snibgo -trim +repage ^
  cp_plane.png

FOR /F "usebackq" %%L ^
IN (`%IM%identify -format "WW=%%w\nHH=%%h\ncylWW=%%[fx:int(w*2/pi+0.5)]\nWW_2=%%[fx:int(w/2+0.5)]" cp_plane.png`) ^
DO set %%L

call %PICTBAT%grid %WW% %HH% 8 4 1 Black None

%IM%convert cp_plane.png grid.png -composite cp_plane.png

del grid.png
cp_plane.png

Transform plane to cylinder

We find the dimensions of the plane, and easily calculate those of the cylinder.

An input parameter is the tilt angle, or the required dip in the centre of the cylinder.

The script does the following:

  1. creates the displacement map (asin);
  2. resizes to the smaller dimensions;
  3. extends the image verically;
  4. applies the displacement map.
set pcDebug=1
set pcStartAng=-60
set pcEndAng=30
set pcStartAng=-90
set pcEndAng=0
set pcBackCol=Khaki
set cp_TiltAng=45
set cp_TiltAng=20

timec call %PICTBAT%plane2cyl cp_plane.png %cp_TiltAng% 2>&1>p2c.lis
rem @p2c.lis

The horizontal and vertical displacements both vary across the image, but each line has the same displacements. Hence the displacement maps can be represented by an image with a single row.

Horizontal displacement, cp_asin:

cp_asin_g1d.png

Vertical displacement, cp_v:

cp_v_g1d.png

Combined map, cp_map_p2c.png (red is horizontal displacement, green is vertical, blue is irrelevant):

cp_map_p2c_glc.png

The result, cp_plane_p2c.png, is:

cp_plane_p2c.png

Transform cylinder to plane

We assume the image is the smallest size that contains the image of the cylinder. Hence we know the width (cylinder diameter) and extended height. An input parameter is the tilt angle, or the measured dip in the centre of the cylinder, so we then calculate the cylinder height. From the cylinder width and height we calculate the plane width and height.

The script does the following:

  1. creates the displacement map (sinus);
  2. applies the displacement map;
  3. crops to the correct dimensions;
  4. resizes to the larger dimensions.
timec call %PICTBAT%cyl2plane cp_plane_p2c.png %cp_TiltAng% 2>&1>c2p.lis
rem @c2p.lis

Horizontal displacement, cp_sinus.png:

cp_sinus_g1d.png

The vertical displacement is the same as for the plane-to-cylinder transformation, but in the opposite direction. cp_v_c2p.png:

cp_v_c2p_g1d.png

The result, cp_plane_p2c_c2p.png, is:

cp_plane_p2c_c2p.png

How different is this from the original?

%IM%compare -metric RMSE cp_plane.png cp_plane_p2c_c2p.png NULL: 
echo.
%IM%identify cp_plane.png
%IM%identify cp_plane_p2c_c2p.png
10003.4 (0.152641)
cp_plane.png PNG 592x191 592x191+0+0 8-bit sRGB 20.2KB 0.000u 0:00.000
cp_plane_p2c_c2p.png PNG 592x191 592x191+0+0 8-bit sRGB 61.5KB 0.000u 0:00.000

However ...

For animation, we want to slowly roll a plane into a cylinder. So we need to specify small angles without needing to create large files.

To do this: "+level" the gradients that are the foundations of the displacement maps, and adjust the extendV calculations, and plWW <-> cylWW.

Hmm, not so easy. Maybe we need: "given a clut, find the difference between it and a straight line drawn through first and last points". See clutDiffEnds.bat

And it would be neat to easily get the reverse, ie the bit at the back. But this is fairly trivial: reverse the image left-to-right and negate the tilt.

Wrap cylinders

We might want to take a rectangular image and wrap it around a cylinder, in a way that facilitates animation. The script wrapCylinder.bat does the job. It takes parameters:

wrapCylinder.bat makes an appended image of two copies of the source, with a transparent gap between them and at the end. This is cropped to form the sources for the front and rear.

It calls plane2cyl.bat twice: once for the front and once for the rear. An optional effect can be applied to the rear portion, before composition.

set wcRearEffect=-modulate 75,80,100 -blur 0x1
call %PICTBAT%wrapCylinder cp_plane.png 20 -50 200
%IM%convert cp_plane_wc.png cp_plane_wc0.png
cp_plane_wc0.png

We can animate this:

rem goto skipLoop

set TEMPDIR=%TEMP%

del /q %TEMPDIR%\snibRot_*.png

set wcRearEffect=-modulate 75,80,100 -blur 0x1
set wcBackCol=White

set N=0
for /L %%i in (355,-5,0) do (
  set sN=00000!N!
  set sN=!sN:~-6!
  set /A endAng=%%i+250

  call %PICTBAT%wrapCylinder cp_plane.png 20 %%i !endAng!
  copy cp_plane_wc.png %TEMPDIR%\snibRot_!sN!.png

  set /A N+=1
)

%IM%convert ^
  -dispose Background ^
  %TEMPDIR%\snibRot_*.png ^
  -loop 0 -delay 3 -layers optimize ^
  cp_snibRot.gif

:skipLoop
cp_snibRot.gif

Beyond the simple

We can generalise this to a cone. For some purposes, a cone may be unrolled to a plane where the top and bottom are circular arcs. For other purposes, the narrow end can be widened to the same width as the wide end, unrolled as a cylinder, and one end narrowed again. However, tilt then probably needs to be treated separately.

From a photographed cylinder, we can derive a lighting map. Unroll the cylinder and find the difference at each pixel from the mean. For some purposes, a difference in lightness will be sufficient, or it could be a difference in each of the RGB channels.

We could simulate perspective, 3-D lighting, shadows and so on. But there comes a time when it is easier to use a 3-D tool such as POV-Ray. See below for the POV-Ray scene files.

For the command-line options, see POV-Ray help, Reference, Command Line.

-D turn off graphic display
+A anti-alias threshold
+W pixels width
+H pixels height
+FN output bit depth
+UA alpha output
+I input POV script filename
+O output image filename

Examples:

Make a png file with transparent piece, for subsequent POV operations.

%IM%convert ^
  cp_plane.png ^
  -background None -extent 144x100%% ^
  cp_plane_ext.png

Start with a single object. No background or sky sphere.

%POV% ^
  -D +A0.01 +W400 +H300 +FN16 +UA ^
  +IsnibCylT.pov +Ocp_snibCylT_pov.png

The shape and gradation of the shadow would be difficult using IM.

cp_snibCylT_pov.png

Add a floor.

%POV% ^
  -D +A0.01 +W400 +H300 +FN16 ^
  +IsnibCyl.pov +Ocp_snibCyl_pov.png
cp_snibCyl_pov.png

A different object, using "sor" (surface of revolution).

%POV% ^
  -D +A0.01 +W400 +H300 +FN16 ^
  +IsnibSor.pov +Ocp_snibSor_pov.png
cp_snibSor_pov.png

A different object, using "lathe".

%POV% ^
  -D +A0.01 +W400 +H300 +FN16 ^
  +IsnibLathe.pov +Ocp_snibLathe_pov.png
cp_snibLathe_pov.png

For a more complex example that uses POV-Ray to distort a displacement map, see my page Coffee mug.

For other uses of POV-Ray, see my page Knots: Ray-tracing.

Scripts

For convenience, .bat scripts are also available in a single zip file. See Zipped BAT files.

plane2cyl.bat

rem Transforms from plane to cylinder.
rem %1 is image.
rem %2 is tilt angle, degrees. Default=0=no tilt. Positive is with camera above cylinder, looking down.
@rem
@rem Also uses:
@rem   pcStartAng. Default -90.
@rem   pcEndAng. Default 90.
@rem   pcDebug. Default 0.
@rem   pcBackCol. Default None.


@setlocal enabledelayedexpansion

@call echoOffSave

@call %PICTBAT%setInOut %1 p2c


set tiltAng=%2
if "%tiltAng%"=="" set tiltAng=0

call %PICTBAT%planeCylSetup

if %pcForceRecalc%==1 (
  del %fP2C_HORIZ%
  del %fP2C_VERT%
  del %fP2C_COMB%
)

if "%pcDebug%"=="1" echo farZAng=%farZAng%

rem plWW = width
rem plWW_2 = half width
rem cylWWxX = w*2/pi = required width of cylinder, assuming we go all the way from -90 to +90.
FOR /F "usebackq" %%L ^
IN (`%CALC% "plWW=%%w\nplWW_2=%%[fx:int(w/2+0.5)]\nplHH=%%h\ncylWWxX=%%[fx:int(w*2/pi+0.5)]" %INFILE%`) ^
DO set %%L

if %ZeroAng%==1 (
  set cylRad=0
  set cylWW=%plWW%
) else (
  FOR /F "usebackq" %%L ^
IN (`%CALC% "cylRad=%%[fx:%plWW%*180/((%pcEndAng%)-(%pcStartAng%))/pi]" xc:`) ^
DO set %%L

  FOR /F "usebackq" %%L ^
IN (`%CALC% "cylWW=%%[fx:!cylRad!*(sin(-(%pcStartAng%*pi/180))+sin(%pcEndAng%*pi/180))]\nfarZy=%%[fx:!cylRad!*abs(sin(%farZAng%*pi/180))*%sinT%]" xc:`) ^
DO set %%L
)

echo cylRad=%cylRad%  cylWWxX=%cylWWxX%  cylWW=%cylWW%  farZy=%farZy%

rem cylHH = plHH * cosT
rem tiltFact = -sinT/2
FOR /F "usebackq" %%L ^
IN (`%CALC% "cylWW_2=%%[fx:int(%cylWW%/2+0.5)]\ncylHH=%%[fx:int(%plHH%*%cosT%+0.5)]\ntiltFact=%%[fx:-%sinT%/2]" xc:`) ^
DO set %%L

@rem extendV = plHH.cosT + plWW.2/pi.abs(sinT)/2
@rem FOR /F "usebackq" %%L ^
@rem IN (`%CALC% "extendV=%%[fx:int(%plHH%*%cosT%+%plWW%*2/pi*abs(%sinT%)/2+0.5)]" xc:`) ^
@rem DO set %%L

rem extendV = plHH.cosT + cylRad.abs(sinT)/2  But not /2??
FOR /F "usebackq" %%L ^
IN (`%CALC% "extraV=%%[fx:int(%cylWW%/2*abs(%sinT%)+0.5)]" xc:`) ^
DO set %%L

FOR /F "usebackq" %%L ^
IN (`%CALC% "extendV=%%[fx:int(%plHH%*%cosT%+%cylWW%/2*abs(%sinT%)+0.5)]\nIsSouth=%%[fx:%tiltAng%<0?1:0]" xc:`) ^
DO set %%L

if "%pcDebug%"=="1" echo extendV=%extendV%

if %IsSouth%==1 (
  set GRAV=South
) else (
  set GRAV=North
)

if %tiltAng%==0 (
  set EXTEND=
) else (
  set EXTEND=-gravity %GRAV% -background %pcBackCol% -extent %cylWW%x%extendV%
)

if "%pcDebug%"=="1" echo plWW=%plWW% plHH=%plHH% cylWW=%cylWW% cylHH=%cylHH% plWW_2=%WW_2% cylWW_2=%cylWW_2% extendV=%extendV% tiltFact=%tiltFact%

@rem %IM%convert ^
@rem   -size 1x%cylWW% gradient:gray(%pc180end%%%)-gray(%pc180start%%%) -rotate 90 ^
@rem   ( +clone -function arcsin 1,0.5,1,0.5 ) ^
@rem   -evaluate Divide 2 ^
@rem   -compose ModulusSubtract -composite ^
@rem   -evaluate AddModulus 50%% ^
@rem   cp_asin.png


if exist %fP2C_COMB% goto skipComb

call %PICTBAT%p2cHoriz.bat


%IM%convert ^
  -size 1x%cylWW% ^
  gradient:gray(%pc180end%%%)-gray(%pc180start%%%) -rotate 90 ^
  -function Polynomial -4,4,0 -evaluate Pow 0.5 ^
  -function Polynomial %tiltFact%,0.5 ^
  %fP2C_VERT%

rem Combine the displacement maps
%IM%convert ^
  %fP2C_HORIZ% ^
  %fP2C_VERT% ^
  -size %cylWW%x1 xc:gray50 ^
  -combine -set colorspace sRGB ^
  %fP2C_COMB%

if "%pcDebug%"=="1" (
  %IM%convert %fP2C_HORIZ% cp_asin.png
  %IM%convert %fP2C_VERT% cp_v.png
  %IM%convert %fP2C_COMB% cp_map_p2c.png
  call %PICTBAT%graph1d cp_asin.png
  call %PICTBAT%graph1d cp_v.png
  call %PICTBAT%graphLineCol cp_map_p2c.png Black 0 0
)

:skipComb

if %pcBackCol%==None (
  set VIRT_PIX=-virtual-pixel None
) else (
  set VIRT_PIX=-background %pcBackCol% -virtual-pixel background
)

%IM%convert ^
  %INFILE% ^
  -resize "%cylWW%x%cylHH%^!" ^
  %EXTEND% ^
  ( %fP2C_COMB% -scale "%cylWW%x%extendV%^!" ) ^
  %VIRT_PIX% ^
  -interpolate bicubic ^
  -compose displace -set option:compose:args %cylWW_2%x%cylWW_2% -composite ^
  %OUTFILE%

call echoRestore

endlocal & set p2cExtraV=%extraV%& set pcOUTFILE=%OUTFILE%

cyl2plane.bat

rem Transforms from cylinder to plane.
rem %1 is image.
rem %2 is tilt angle, degrees. Default=0=no tilt. Positive is with camera above cylinder, looking down.
@rem
@rem Also uses:
@rem   pcStartAng. Default -90.
@rem   pcEndAng. Default 90.
@rem   pcDebug. Default 0.
@rem   pcBackCol. Default None.

@setlocal enabledelayedexpansion

@call echoOffSave

call %PICTBAT%setInOut %1 c2p


set tiltAng=%2
if "%tiltAng%"=="" set tiltAng=0

call %PICTBAT%planeCylSetup

if %pcForceRecalc%==1 (
  del %fC2P_HORIZ%
  del %fC2P_VERT%
  del %fC2P_COMB%
)


if "%pcDebug%"=="1" echo farZAng=%farZAng%

rem plHH=%%[fx:int((h-w*%sinT%/2)/%cosT%+0.5)]
rem tiltFact: opposite sign to Plane2Cylinder.
FOR /F "usebackq" %%L ^
IN (`%CALC% "cylWW=%%w\nextendV=%%h\ncylHH=%%[fx:int(h-w*abs(%sinT%)/2+0.5)]\nplWWxX=%%[fx:int(w*pi/2+0.5)]\ncylWW_2=%%[fx:int(w/2+0.5)]\ntiltFact=%%[fx:%sinT%/2]\nplHH=%%[fx:int((h-abs(w/2*%sinT%))/%cosT%+0.5)]" %INFILE%`) ^
DO set %%L

if "%pcDebug%"=="1" echo extendV=%extendV%

if %ZeroAng%==1 (
  set cylRad=0
  set plWW=%cylWW%
) else (
  FOR /F "usebackq" %%L ^
IN (`%CALC% "cylRad=%%[fx:%cylWW%/(sin(-(%pcStartAng%*pi/180))+sin(%pcEndAng%*pi/180))]" xc:`) ^
DO set %%L

  FOR /F "usebackq" %%L ^
IN (`%CALC% "plWW=%%[fx:!cylRad!*pi*(%pcEndAng%-(%pcStartAng%))/180]\nIsSouth=%%[fx:%tiltAng%<0?1:0]" xc:`) ^
DO set %%L
)

if %IsSouth%==1 (
  set GRAV=South
) else (
  set GRAV=North
)

if "%pcDebug%"=="1" echo extendV=%extendV% cylWW=%cylWW% cylHH=%cylHH% plWW=%plWW% plHH=%plHH% cylWW_2=%cylWW_2%

goto skipSelfSinus
@rem %IM%convert ^
@rem   -size 1x%cylWW% gradient:gray(%pc180end%%%)-gray(%pc180start%%%) -rotate 90 ^
@rem   ( +clone -function sinusoid 0.5,-90,0.5,0.5 ) ^
@rem   -evaluate Divide 2 ^
@rem   -compose ModulusSubtract -composite ^
@rem   -evaluate AddModulus 50%% ^
@rem   cp_sinus.png

%IM%convert ^
  -size 1x%cylWW% gradient:gray(%pc180end%%%)-gray(%pc180start%%%) -rotate 90 ^
  -function sinusoid 0.5,-90,0.5,0.5 ^
  cp_sinus.png

FOR /F "usebackq" %%L ^
IN (`%IM%convert cp_sinus.png -format "COL_0=%%[pixel:p{0,0}]\nCOL_1=%%[pixel:p{w-1,h-1}]" info:`) ^
DO set %%L

%IM%convert ^
  ( -size 1x%cylWW% gradient:%COL_1%-%COL_0% -rotate 90 ) ^
  cp_sinus.png ^
  -evaluate Divide 2 ^
  -compose ModulusSubtract -composite ^
  -evaluate AddModulus 50%% ^
  cp_sinus.png

:skipSelfSinus

rem Forget what we've just done. Invert the plane2cyl version.

if not exist %fC2P_HORIZ% (
  if not exist %fP2C_HORIZ% call %PICTBAT%p2cHoriz.bat

  call %PICTBAT%invRelClut %fP2C_HORIZ%
  rem %IM%convert cp_asin_irc.png cp_sinus.png
)

if "%pcDebug%"=="1" (
  %IM%convert %fC2P_HORIZ% cp_sinus.png
  call %PICTBAT%graph1d cp_sinus.png
)

if not exist %fC2P_VERT% %IM%convert ^
  -size 1x%cylWW% ^
  gradient:gray(%pc180end%%%)-gray(%pc180start%%%) -rotate 90 ^
  -function Polynomial -4,4,0 -evaluate Pow 0.5 ^
  -function Polynomial %tiltFact%,0.5 ^
  %fC2P_VERT%

if "%pcDebug%"=="1" (
  %IM%convert %fC2P_VERT% cp_v_c2p.png
  call %PICTBAT%graph1d cp_v_c2p.png
)


goto skipJunk

goto skipComb
rem Combine the displacement maps
%IM%convert ^
  %fC2P_HORIZ% ^
  %fC2P_VERT% ^
  -size %cylWW%x1 xc:gray50 ^
  -combine -set colorspace sRGB ^
  cp_map_c2p.png


%IM%convert ^
  %INFILE% ^
  ( cp_map_c2p.png -scale "%cylWW%x%extendV%^!" ) ^
  -background lightgreen -virtual-pixel background ^
  -interpolate bicubic ^
  -compose displace -set option:compose:args %cylWW%x%cylWW_2% -composite ^
  %OUTFILE%
:skipComb

%IM%convert ^
  %INFILE% ^
  ( cp_v_c2p.png -scale "%cylWW%x%extendV%^!" ) ^
  -background lightgreen -virtual-pixel background ^
  -interpolate bicubic ^
  -compose displace -set option:compose:args 0x%cylWW_2% -composite ^
  ( %fC2P_HORIZ% -scale "%cylWW%x%extendV%^!" ) ^
  -compose displace -set option:compose:args %cylWW%x0 -composite ^
  -crop %cylWW%x%cylHH%+0+0 +repage ^
  -resize "%plWW%x%plHH%^!" ^
  %OUTFILE%

:skipJunk

if %pcBackCol%==None (
  set VIRT_PIX=-virtual-pixel None
) else (
  set VIRT_PIX=-background %pcBackCol% -virtual-pixel background
)

rem Width was cylWW
%IM%convert ^
  %INFILE% ^
  %VIRT_PIX% ^
  -interpolate bicubic ^
  ( cp_v_c2p.png -scale "%cylWW%x%extendV%^!" ) ^
  -compose displace -set option:compose:args 0x%cylWW_2% -composite ^
  ( cp_sinus.png -scale "%cylWW%x%extendV%^!" ) ^
  -compose displace -set option:compose:args %cylWW_2%x0 -composite ^
  -gravity %GRAV% ^
  -crop %cylWW%x%cylHH%+0+0 +repage ^
  -resize "%plWW%x%plHH%^!" ^
  %OUTFILE%


rem First disp args: 0x%cylWW_2%

call echoRestore

planeCylSetup.bat

rem Called by plane2cy and cyl2plane.

if "%pcStartAng%"=="" set pcStartAng=-90
if "%pcEndAng%"=="" set pcEndAng=90

if "%pcBackCol%"=="" set pcBackCol=None

if "%pcForceRecalc%"=="" set pcForceRecalc=0


set PCDIR=%TEMP%

rem FIXME: suffix also needs file dims.
rem
set SUFF=%tiltAng%_%pcStartAng%_%pcEndAng%
set fP2C_HORIZ=%PCDIR%\p2c_h_%SUFF%.miff
set fP2C_VERT=%PCDIR%\p2c_v_%SUFF%.miff
set fP2C_COMB=%PCDIR%\p2c_c_%SUFF%.miff
set fC2P_HORIZ=%PCDIR%\p2c_h_%SUFF%_irc.miff
set fC2P_VERT=%PCDIR%\c2p_v_%SUFF%.miff
set fC2P_COMB=%PCDIR%\c2p_c_%SUFF%.miff

echo Files: %fP2C_HORIZ% %fP2C_VERT% %fP2C_COMB%

set CALC=%IM%identify -precision 9 -format

rem Start and end, as percentages. Zero is far left; 100 is far right.
rem ZeroAng is whether the difference between start and end is effectively zero.
rem farZAng is the angle that is most towards the back; used to calc farZy, which isn't used.
rem
FOR /F "usebackq" %%L ^
IN (`%CALC% ^
  "pc180start=%%[fx:(%pcStartAng%+90)/1.80]\npc180end=%%[fx:(%pcEndAng%+90)/1.80]\nZeroAng=%%[fx:abs(%pcStartAng%-(%pcEndAng%))<0.01]\nfarZAng=%%[fx:abs(%pcStartAng%)>abs(%pcEndAng%))?%pcStartAng%:%pcEndAng%]" ^
  xc:`) ^
DO set %%L

FOR /F "usebackq" %%L ^
IN (`%CALC% "sinT=%%[fx:sin(%tiltAng%*pi/180)]\ncosT=%%[fx:cos(%tiltAng%*pi/180)]" xc:`) ^
DO set %%L

p2cHoriz.bat

rem Called by plane2cy and cyl2plane.

%IM%convert ^
  -size 1x%cylWW% gradient:gray(%pc180end%%%)-gray(%pc180start%%%) -rotate 90 ^
  -function arcsin 1,0.5,1,0.5 ^
  -depth 16 ^
  %fP2C_HORIZ%


rem FIXME: don't bother with next two if doing from -90 to +90.

FOR /F "usebackq" %%L ^
IN (`%IM%convert %fP2C_HORIZ% -format "COL_0=%%[pixel:p{0,0}]\nCOL_1=%%[pixel:p{w-1,h-1}]" info:`) ^
DO set %%L

%IM%convert ^
  ( -size 1x%cylWW% gradient:%COL_1%-%COL_0% -rotate 90 ) ^
  %fP2C_HORIZ% ^
  -compose Mathematics -define compose:args=0,0.5,-0.5,0.5 -composite ^
  %fP2C_HORIZ%

wrapCylinder.bat

rem From image %1, wraps it into a cylinder.
rem
rem %2 is tilt angle, degrees. Default=0=no tilt. Positive is with camera above cylinder, looking down.
rem %3 is start angle, degrees. Default = -90.
rem %4 is end angle, degrees. Default = 90.


@if "%1"=="" findstr /B "rem @rem" %~f0 & exit /B 1

@setlocal

@call echoOffSave

call %PICTBAT%setInOut %1 wc

set CALC=%IM%identify -precision 9 -format

set tiltAng=%2
if "%tiltAng%"=="" set tiltAng=0

set startAng=%3
if "%startAng%"=="" set startAng=-90

set endAng=%4
if "%endAng%"=="" set endAng=90

if "%wcBackCol%"=="" set wcBackCol=None

rem for /F "usebackq" %%L ^
rem in (`%CALC% "ANG=%startAng%;startAng=%%[fx:while(ANG>180,ANG-=360)]" xc:`) ^
rem do set %%L

for /F "usebackq" %%L ^
in (`%CALC% "startAng=%%[fx:%startAng%<=180?%startAng%:%startAng%-360]" xc:`) ^
do set %%L

echo startAng=%startAng%


rem transAng = (startAng - endAng) mod 360.

for /F "usebackq" %%L ^
in (`%CALC% "negTiltAng=%%[fx:-%tiltAng%]\ntransAng=%%[fx:ta=(%startAng%-%endAng%)%% 360;ta<0?ta+360:ta]" xc:`) ^
do set %%L

for /F "usebackq" %%L ^
in (`%CALC% "imgAng=%%[fx:360-%transAng%]\nbadAng=%%[fx:%transAng%<360?0:1]" xc:`) ^
do set %%L

if %badAng%==1 (
  echo Bad angle
  exit /B 1
)

echo imgAng=%imgAng% transAng=%transAng%

FOR /F "usebackq" %%L ^
IN (`%CALC% "WW=%%w\nHH=%%h\ntransPix=%%[fx:w*%transAng%/%imgAng%]" %INFILE%`) ^
DO set %%L

rem So we have pix/degree = (WW + transPix) / 360

FOR /F "usebackq" %%L ^
IN (`%CALC% ^
  "pixPerDeg=%%[fx:(%WW%+w*%transAng%/%imgAng%)/360]\npix360=%%[fx:%WW%+%transPix%]\npix180=%%[fx:(%WW%+%transPix%)/2]" ^
  %INFILE%`) ^
DO set %%L

rem In the appended image, what are the pixel coords of -90 and +90?
rem Image starts (pix=0) at startAng and ends (pix=WW) at endAng.
rem -90 is at (-90-startAng)*pixPerDegree ??
rem +90 is at ( 90-startAng)*pixPerDegree ??

FOR /F "usebackq" %%L ^
IN (`%CALC% "pm90=%%[fx:(-90-(%startAng%))*%pixPerDeg%]" xc:`) ^
DO set %%L

FOR /F "usebackq" %%L ^
IN (`%CALC% "pp90=%%[fx:(90-(%startAng%))*%pixPerDeg%]\npmNeg=%%[fx:%pm90%<0?1:0]" xc:`) ^
DO set %%L

FOR /F "usebackq" %%L ^
IN (`%CALC% "ppNeg=%%[fx:%pp90%<0?1:0]" xc:`) ^
DO set %%L

set pixFL=%pm90%
set pixFR=%pp90%
set pixRR=%pp90%

if %pmNeg%==1 FOR /F "usebackq" %%L ^
IN (`%CALC% "pixFL=%%[fx:%pm90%+%pix360%]\npixFR=%%[fx:%pp90%+%pix360%]" xc:`) ^
DO set %%L

if %ppNeg%==1 FOR /F "usebackq" %%L ^
IN (`%CALC% "pixRR=%%[fx:%pp90%+%pix360%]" xc:`) ^
DO set %%L

FOR /F "usebackq" %%L ^
IN (`%CALC% "pixRL=%%[fx:%pixRR%+%pix360%/2]" xc:`) ^
DO set %%L

rem ccalc = %pix360% * 2 = exit

%IM%convert ^
  %INFILE% ^
  -size %transPix%x%HH% xc:None ^
  +append ^
  +clone ^
  +append ^
  -write wc_img.png ^
  ( +clone -crop %pix180%x%HH%+%pixFL%+0 +repage -write wc_front.png +delete ) ^
  ( +clone -crop %pix180%x%HH%+%pixRR%+0 +repage -flop -write wc_rear.png +delete ) ^
  NULL:

rem Verify:
if "%wcDEBUG%"=="1" %IM%convert ^
  wc_front.png ^
  wc_rear.png ^
  -append ^
  -bordercolor black -border 1 ^
  wc_comp.png

set pcStartAng=-90
set pcEndAng=90
rem set pcForceRecalc=1
set pcBackCol=None
call %PICTBAT%plane2cyl wc_rear.png %negTiltAng%
call %PICTBAT%plane2cyl wc_front.png %tiltAng%

%IM%convert ^
  wc_rear_p2c.png ^
  %wcRearEffect% ^
  ( wc_front_p2c.png -repage +0+%p2cExtraV% ) ^
  -background %wcBackCol% ^
  -layers merge ^
  +repage ^
  %OUTFILE%

grid.bat

rem Makes a grid with specified number of intervals.
rem %1,%2 are width and height.
rem %3 and %4 are number of gaps between horizontal and vertical grid lines, >=1 (default 4)
rem %5 is whether to draw diagonal (default 0)
rem %6 is grid colour (default white)
rem %7 is background colour, can be "none" (default black)
rem %8 is colour for boundary
rem %9 is output file (default grid.png)
@rem
@rem Also uses:
@rem   gridSTROKE_WIDTH default 1
@rem

rem No required arguments.
rem @if "%2"=="" findstr /B "rem @rem" %~f0 & exit /B 1

@setlocal enabledelayedexpansion

@call echoOffSave

set WW=%1
if "%WW%"=="." set WW=
if "%WW%"=="" set WW=150
set HH=%2
if "%HH%"=="." set HH=
if "%HH%"=="" set HH=100

set nX=%3
if "%nX%"=="." set nX=
if "%nX%"=="" set nX=4
set nY=%4
if "%nY%"=="." set nY=
if "%nY%"=="" set nY=4

set DO_DIAG=%5
if "%DO_DIAG%"=="." set DO_DIAG=
if "%DO_DIAG%"=="" set DO_DIAG=0

set GRID_COL=%6
if "%GRID_COL%"=="." set GRID_COL=
if "%GRID_COL%"=="" set GRID_COL=White

set BACK_COL=%7
if "%BACK_COL%"=="." set BACK_COL=
if "%BACK_COL%"=="" set BACK_COL=Black

set BOUND_COL=%8
if "%BOUND_COL%"=="." set BOUND_COL=

set OUTFILE=%9
if "%OUTFILE%"=="." set OUTFILE=
if "%OUTFILE%"=="" set OUTFILE=grid.png

if "%gridSTROKE_WIDTH%"=="" set gridSTROKE_WIDTH=0


FOR /F "usebackq" %%L ^
IN (`%IM%identify ^
  -ping ^
  -format ^
Wm1^=%%[fx:%WW%-1]\n^
Hm1^=%%[fx:%HH%-1]\n^
dX^=%%[fx:%WW%/%nX%]\n^
dY^=%%[fx:%HH%/%nY%]\n^
nXm1^=%%[fx:%nX%-1]\n^
nYm1^=%%[fx:%nY%-1] ^
  xc:`) ^
DO set %%L

set LINESFILE=%TEMP%\gridlines.txt
del %LINESFILE% 2>nul

if %nXm1% GTR 0 for /L %%i in (1, 1, %nXm1%) do (
  FOR /F %%L IN ('%IM%identify ^
    -ping -format "v=%%[fx:int(%dX%*%%i+0.5)]" xc:') DO @set %%L
  echo line !v!,0 !v!,%Hm1% >>%LINESFILE%
)

if %nYm1% GTR 0 for /L %%i in (1, 1, %nYm1%) do (
  FOR /F %%L IN ('%IM%identify ^
    -ping -format "v=%%[fx:int(%dY%*%%i+0.5)]" xc:') DO @set %%L
  echo line 0,!v! %Wm1%,!v! >>%LINESFILE%
)

if %DO_DIAG%==1 (
  echo line %Wm1%,0 0,%Hm1% >>%LINESFILE%
  echo line 0,0 %Wm1%,%Hm1% >>%LINESFILE%
)

if not "%BOUND_COL%"=="" (
  echo fill %BOUND_COL% >>%LINESFILE%
  echo line 0,0 %Wm1%,0 >>%LINESFILE%
  echo line 0,0 0,%Hm1% >>%LINESFILE%
  echo line %Wm1%,0 %Wm1%,%Hm1% >>%LINESFILE%
  echo line 0,%Hm1% %Wm1%,%Hm1% >>%LINESFILE%
)

if %gridSTROKE_WIDTH%==1 (
  set sSTROKEW=
) else (
  set sSTROKEW=-strokewidth %gridSTROKE_WIDTH%
)


%IM%convert ^
  -size %WW%x%HH% ^
  xc:%BACK_COL% ^
  -fill None ^
  -stroke %GRID_COL% ^
  %sSTROKEW% ^
  -draw "@%LINESFILE%" ^
  %OUTFILE%

call echoRestore

POV-Ray files

snibCylT.pov

#include "cylPov.inc"

object { SnibCyl }

snibCyl.pov

#include "cylPov.inc"

union {
  object { Floor }
  object { SnibCyl }
}

snibSor.pov

#include "cylPov.inc"

union {
  object { Floor }
  object { SnibSor }
}

snibLathe.pov

#include "cylPov.inc"

union {
  object { Floor }
  object { SnibLathe }
}

cylPov.inc

#version 3.7;
global_settings { assumed_gamma 1.0 } 

#include "colors.inc"
#include "textures.inc"
#include "shapes.inc"
#include "metals.inc"
#include "glass.inc"
#include "woods.inc"         

camera {
   location <-5, 10, -15>
   angle 45 // direction <0, 0,  1.7>
   right x*image_width/image_height
   look_at <0,0,0>
}

// Uncomment the area lights only if you've got lots of time.
#declare Dist=80.0;

light_source {< -50, 25, -50> color White
     fade_distance Dist fade_power 2
//   area_light <-40, 0, -40>, <40, 0, 40>, 3, 3
//   adaptive 1
//   jitter
}
light_source {< 50, 10,  -4> color Gray30
     fade_distance Dist fade_power 2
     area_light <-20, 0, -20>, <20, 0, 20>, 3, 3
     adaptive 1
     jitter
}
light_source {< 0, 100,  0> color Gray30
     fade_distance Dist fade_power 2
//   area_light <-30, 0, -30>, <30, 0, 30>, 3, 3
//   adaptive 1
//   jitter
}

//sky_sphere {
//    pigment {
//        gradient y
//        color_map {
//            [0, 1  color Gray50 color Gray80]
//        }
//    }
//}

#declare M_Wood18B =
colour_map {
    [0.00 0.25   color rgbf < 0.50, 0.26, 0.12, 0.10>
                 color rgbf < 0.54, 0.29, 0.13, 0.20>]
    [0.25 0.40   color rgbf < 0.54, 0.29, 0.13, 0.20>
                 color rgbf < 0.55, 0.28, 0.10, 0.70>]
    [0.40 0.50   color rgbf < 0.55, 0.28, 0.10, 0.70>
                 color rgbf < 0.50, 0.23, 0.15, 0.95>]
    [0.50 0.70   color rgbf < 0.50, 0.23, 0.15, 0.95>
                 color rgbf < 0.56, 0.29, 0.17, 0.70>]
    [0.70 0.98   color rgbf < 0.56, 0.29, 0.17, 0.70>
                 color rgbf < 0.54, 0.29, 0.13, 0.20>]
    [0.98 1.00   color rgbf < 0.54, 0.29, 0.13, 0.20>
                 color rgbf < 0.50, 0.26, 0.12, 0.10>]
}


#declare Floor_Texture =
    texture { pigment { P_WoodGrain18A color_map { M_Wood18A }}}
    texture { pigment { P_WoodGrain12A color_map { M_Wood18B }}}
    texture {
        pigment { P_WoodGrain12B color_map { M_Wood18B }}
        finish { reflection 0.25 }
    }

#declare Floor =
plane { y,0
    texture { Floor_Texture
        scale 0.5
        rotate y*90
        rotate <10, 0, 15>
        translate z*4
    }
}



#declare SnibCylPig =
  pigment {
    image_map {
      "cp_plane_ext.png"
      map_type 2
    }       
  }


#declare SnibCyl =
cylinder {
  <0, 0.00,  0.0>,
  <0, 1.00,  0.0>, 1 
  open
  pigment { SnibCylPig }
  finish { phong 1 }
  scale 4.0
}


#declare SnibSor =
sor{
  7,
  <0.000, 0.000>,
  <0.800, 0.000>,
  <0.900, 0.300>,
  <0.600, 0.500>,
  <0.800, 0.800>,
  <1.000, 1.000>,
  <1.200, 1.200>
  open
  pigment { SnibCylPig }
  scale 4.0  rotate<0,0,0> translate<0,0,0>
}


#declare SnibLathe =
lathe {
  linear_spline
  5,
  <0.8, 0>, <1, 0>, <1, 1>, <0.8, 1>, <0.8, 0>
  pigment { SnibCylPig }
  scale 4.0  rotate<0,0,0> translate<0,0,0>
}

All images on this page were created by the commands shown, using:

%IM%identify -version
Version: ImageMagick 6.9.2-5 Q16 x64 2015-10-31 http://www.imagemagick.org
Copyright: Copyright (C) 1999-2015 ImageMagick Studio LLC
License: http://www.imagemagick.org/script/license.php
Visual C++: 180031101
Features: Cipher DPC Modules OpenMP 
Delegates (built-in): bzlib cairo freetype jng jp2 jpeg lcms lqr openexr pangocairo png ps rsvg tiff webp xml zlib

... and POV-Ray 3.7, with "Render, On completion, Exit POV-Ray for Windows" ticked.

"POV-Ray" is a trademark of Persistence of Vision Raytracer Pty Ltd.

Source file for this web page is clinder.h1. To re-create this web page, run "procH1 cylinder".


This page, including the images, is my copyright. Anyone is permitted to use or adapt any of the code, scripts or images for any purpose, including commercial use.

Anyone is permitted to re-publish this page, but only for non-commercial use.

Anyone is permitted to link to this page, including for commercial use.


Page version v2.1 27-Dec-2013.

Page created 05-Jun-2016 07:20:13.

Copyright © 2016 Alan Gibson.