3D Plot - Optical Transfer Function

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
2
down vote

favorite
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For my Thesis i would like to replot the image shown above. unfortunately i have absolutly no idea how to do that. my skills in tikz are not that bad, however, this exceeds my abilities.
two dimensional convolution of line source



hopefully someone can help, thanks a lot guys :)



i started with something like that:



documentclassstandalone

usepackagetikz
usepackagetikz-3dplot

usepackageamsmath
usepackageamsfonts
usepackageamstext

tdplotsetmaincoords70150

begindocument
begintikzpicture[scale = 1,
 >=stealth,
 lens/.style = black,
 parameter/.style = thick,->,
 rounded corners = 1pt,
 opticalaxis/.style = dashdotted,
 tdplot_main_coords
 ]
draw[parameter] (0,0,0) coordinate(zero) --++ (-1,0,0); 
draw[thick] (zero) --++ (1,0,0);
draw[thick,->] (zero) --++ (0,2,0) node[below] $y$;
draw[thick] (zero) --++ (0,-2,0);
draw[parameter] (zero) --++ (0,0,1) node[above]$delta(x) 1(y)$;

foreach y in -1.8,-1.7,...,1.8 
 draw[->, >=latex] (0,y,0) -- (0,y,0.6);
 

endtikzpicture
enddocument





tikz-pgf







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Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.



















  • Welcome to TeX.SE! What have you tried? The first and last plots can be done with tikz-3dplot or pgfplots, the middle plot also but requires some more effort than the other two.
    – marmot
    6 hours ago










  • i thought the last one would be the hardest..
    – Bakira
    6 hours ago














up vote
2
down vote

favorite
1












For my Thesis i would like to replot the image shown above. unfortunately i have absolutly no idea how to do that. my skills in tikz are not that bad, however, this exceeds my abilities.
two dimensional convolution of line source



hopefully someone can help, thanks a lot guys :)



i started with something like that:



documentclassstandalone

usepackagetikz
usepackagetikz-3dplot

usepackageamsmath
usepackageamsfonts
usepackageamstext

tdplotsetmaincoords70150

begindocument
begintikzpicture[scale = 1,
 >=stealth,
 lens/.style = black,
 parameter/.style = thick,->,
 rounded corners = 1pt,
 opticalaxis/.style = dashdotted,
 tdplot_main_coords
 ]
draw[parameter] (0,0,0) coordinate(zero) --++ (-1,0,0); 
draw[thick] (zero) --++ (1,0,0);
draw[thick,->] (zero) --++ (0,2,0) node[below] $y$;
draw[thick] (zero) --++ (0,-2,0);
draw[parameter] (zero) --++ (0,0,1) node[above]$delta(x) 1(y)$;

foreach y in -1.8,-1.7,...,1.8 
 draw[->, >=latex] (0,y,0) -- (0,y,0.6);
 

endtikzpicture
enddocument





tikz-pgf







share|improve this question









New contributor




Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.



















  • Welcome to TeX.SE! What have you tried? The first and last plots can be done with tikz-3dplot or pgfplots, the middle plot also but requires some more effort than the other two.
    – marmot
    6 hours ago










  • i thought the last one would be the hardest..
    – Bakira
    6 hours ago












up vote
2
down vote

favorite
1









up vote
2
down vote

favorite
1






1





For my Thesis i would like to replot the image shown above. unfortunately i have absolutly no idea how to do that. my skills in tikz are not that bad, however, this exceeds my abilities.
two dimensional convolution of line source



hopefully someone can help, thanks a lot guys :)



i started with something like that:



documentclassstandalone

usepackagetikz
usepackagetikz-3dplot

usepackageamsmath
usepackageamsfonts
usepackageamstext

tdplotsetmaincoords70150

begindocument
begintikzpicture[scale = 1,
 >=stealth,
 lens/.style = black,
 parameter/.style = thick,->,
 rounded corners = 1pt,
 opticalaxis/.style = dashdotted,
 tdplot_main_coords
 ]
draw[parameter] (0,0,0) coordinate(zero) --++ (-1,0,0); 
draw[thick] (zero) --++ (1,0,0);
draw[thick,->] (zero) --++ (0,2,0) node[below] $y$;
draw[thick] (zero) --++ (0,-2,0);
draw[parameter] (zero) --++ (0,0,1) node[above]$delta(x) 1(y)$;

foreach y in -1.8,-1.7,...,1.8 
 draw[->, >=latex] (0,y,0) -- (0,y,0.6);
 

endtikzpicture
enddocument





tikz-pgf







share|improve this question









New contributor




Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











For my Thesis i would like to replot the image shown above. unfortunately i have absolutly no idea how to do that. my skills in tikz are not that bad, however, this exceeds my abilities.
two dimensional convolution of line source



hopefully someone can help, thanks a lot guys :)



i started with something like that:



documentclassstandalone

usepackagetikz
usepackagetikz-3dplot

usepackageamsmath
usepackageamsfonts
usepackageamstext

tdplotsetmaincoords70150

begindocument
begintikzpicture[scale = 1,
 >=stealth,
 lens/.style = black,
 parameter/.style = thick,->,
 rounded corners = 1pt,
 opticalaxis/.style = dashdotted,
 tdplot_main_coords
 ]
draw[parameter] (0,0,0) coordinate(zero) --++ (-1,0,0); 
draw[thick] (zero) --++ (1,0,0);
draw[thick,->] (zero) --++ (0,2,0) node[below] $y$;
draw[thick] (zero) --++ (0,-2,0);
draw[parameter] (zero) --++ (0,0,1) node[above]$delta(x) 1(y)$;

foreach y in -1.8,-1.7,...,1.8 
 draw[->, >=latex] (0,y,0) -- (0,y,0.6);
 

endtikzpicture
enddocument





tikz-pgf




tikz-pgf






share|improve this question









New contributor




Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 6 hours ago





















New contributor




Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 6 hours ago









Bakira

113




113




New contributor




Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Bakira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











  • Welcome to TeX.SE! What have you tried? The first and last plots can be done with tikz-3dplot or pgfplots, the middle plot also but requires some more effort than the other two.
    – marmot
    6 hours ago










  • i thought the last one would be the hardest..
    – Bakira
    6 hours ago
















  • Welcome to TeX.SE! What have you tried? The first and last plots can be done with tikz-3dplot or pgfplots, the middle plot also but requires some more effort than the other two.
    – marmot
    6 hours ago










  • i thought the last one would be the hardest..
    – Bakira
    6 hours ago















Welcome to TeX.SE! What have you tried? The first and last plots can be done with tikz-3dplot or pgfplots, the middle plot also but requires some more effort than the other two.
– marmot
6 hours ago




Welcome to TeX.SE! What have you tried? The first and last plots can be done with tikz-3dplot or pgfplots, the middle plot also but requires some more effort than the other two.
– marmot
6 hours ago












i thought the last one would be the hardest..
– Bakira
6 hours ago




i thought the last one would be the hardest..
– Bakira
6 hours ago










1 Answer
1






active

oldest

votes

















up vote
3
down vote













You seem to already have done the first plot. (Notice, however, that you are loading tikz-3dplot, even set the view but never implement it. You need to put tdplot_main_coords somewhere.) Here is a pgfplots alternative. I guessed functions that look somewhat like what you plot on your screen shot. 



documentclass[border=3.14mm,tikz]standalone
usetikzlibrarypositioning
usepackageamsmath
DeclareMathOperatorPSFPSF
DeclareMathOperatorLSFLSF

usepackagepgfplots
pgfplotssetcompat=1.16,width=12cm,view=-4545
begindocument
 begintikzpicture[declare function=f(r)=cos(r*48)/(11+r*r);
 g(r)=0.05+cos(r*48)/(11+1.5*r*r);]
 % https://tex.stackexchange.com/a/275668/121799
 beginaxis[name=plot1,xshift=-6cm,axis lines = center,
 ticks=none,
 every axis z label/.append style=name=zlabel-1,
 at=(ticklabel* cs:1.15), 
 data cs=polar,
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $delta(x)cdot 1(y)$,
 ticks=none,samples y=1,ymin=-12,ymax=12,
 enlargelimits=0.3]
 addplot3[draw=none] (0,x,f(x));
 pgfplotsinvokeforeach-12,...,12
 draw[-latex] (0,#1,0) -- (0,#1,0.07);
 endaxis

 % https://tex.stackexchange.com/a/124936/121799
 beginaxis[name=plot2,axis lines = center,
 ticks=none, 
 data cs=polar,
 every axis z label/.append style=name=zlabel-2,
 at=(ticklabel* cs:1.15),
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $PSF(x,y)$,
 enlargelimits=0.3,
 samples=30,
 domain=0:360, 
 y domain=0:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] f(y);
 endaxis
 beginaxis[xshift=6cm,yshift=0.5cm,view=-4545,
 samples=30,shader=interp,axis lines = center,
 ticks=none, 
 domain=-12:12,
 every axis z label/.append style=name=zlabel-3,
 at=(ticklabel* cs:1.05),
 xlabel = $x$,
 ylabel = $y$, 
 zlabel = $LSF(x)$,
 enlargelimits=0.6,
 y domain=-12:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] 
 g(x);
 draw[fill=gray] plot[variable=x,smooth,samples=30,domain=-12:12] 
 (x,-12,g(x)) --(12,-12,0) -- (-12,-12,0) -- 
 (-12,12,0) -- (-12,12,g(12)) -- cycle;
 endaxis
 path (zlabel-1) -- node[midway]$times$ (zlabel-2)
 -- node[midway]$=$ (zlabel-3);
 endtikzpicture
enddocument


enter image description here






share|improve this answer






















  • One way to get a mesh is to remove shader=interp and add draw=black,thin, to the respective plots.
    – marmot
    5 hours ago










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
3
down vote













You seem to already have done the first plot. (Notice, however, that you are loading tikz-3dplot, even set the view but never implement it. You need to put tdplot_main_coords somewhere.) Here is a pgfplots alternative. I guessed functions that look somewhat like what you plot on your screen shot. 



documentclass[border=3.14mm,tikz]standalone
usetikzlibrarypositioning
usepackageamsmath
DeclareMathOperatorPSFPSF
DeclareMathOperatorLSFLSF

usepackagepgfplots
pgfplotssetcompat=1.16,width=12cm,view=-4545
begindocument
 begintikzpicture[declare function=f(r)=cos(r*48)/(11+r*r);
 g(r)=0.05+cos(r*48)/(11+1.5*r*r);]
 % https://tex.stackexchange.com/a/275668/121799
 beginaxis[name=plot1,xshift=-6cm,axis lines = center,
 ticks=none,
 every axis z label/.append style=name=zlabel-1,
 at=(ticklabel* cs:1.15), 
 data cs=polar,
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $delta(x)cdot 1(y)$,
 ticks=none,samples y=1,ymin=-12,ymax=12,
 enlargelimits=0.3]
 addplot3[draw=none] (0,x,f(x));
 pgfplotsinvokeforeach-12,...,12
 draw[-latex] (0,#1,0) -- (0,#1,0.07);
 endaxis

 % https://tex.stackexchange.com/a/124936/121799
 beginaxis[name=plot2,axis lines = center,
 ticks=none, 
 data cs=polar,
 every axis z label/.append style=name=zlabel-2,
 at=(ticklabel* cs:1.15),
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $PSF(x,y)$,
 enlargelimits=0.3,
 samples=30,
 domain=0:360, 
 y domain=0:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] f(y);
 endaxis
 beginaxis[xshift=6cm,yshift=0.5cm,view=-4545,
 samples=30,shader=interp,axis lines = center,
 ticks=none, 
 domain=-12:12,
 every axis z label/.append style=name=zlabel-3,
 at=(ticklabel* cs:1.05),
 xlabel = $x$,
 ylabel = $y$, 
 zlabel = $LSF(x)$,
 enlargelimits=0.6,
 y domain=-12:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] 
 g(x);
 draw[fill=gray] plot[variable=x,smooth,samples=30,domain=-12:12] 
 (x,-12,g(x)) --(12,-12,0) -- (-12,-12,0) -- 
 (-12,12,0) -- (-12,12,g(12)) -- cycle;
 endaxis
 path (zlabel-1) -- node[midway]$times$ (zlabel-2)
 -- node[midway]$=$ (zlabel-3);
 endtikzpicture
enddocument


enter image description here






share|improve this answer






















  • One way to get a mesh is to remove shader=interp and add draw=black,thin, to the respective plots.
    – marmot
    5 hours ago














up vote
3
down vote













You seem to already have done the first plot. (Notice, however, that you are loading tikz-3dplot, even set the view but never implement it. You need to put tdplot_main_coords somewhere.) Here is a pgfplots alternative. I guessed functions that look somewhat like what you plot on your screen shot. 



documentclass[border=3.14mm,tikz]standalone
usetikzlibrarypositioning
usepackageamsmath
DeclareMathOperatorPSFPSF
DeclareMathOperatorLSFLSF

usepackagepgfplots
pgfplotssetcompat=1.16,width=12cm,view=-4545
begindocument
 begintikzpicture[declare function=f(r)=cos(r*48)/(11+r*r);
 g(r)=0.05+cos(r*48)/(11+1.5*r*r);]
 % https://tex.stackexchange.com/a/275668/121799
 beginaxis[name=plot1,xshift=-6cm,axis lines = center,
 ticks=none,
 every axis z label/.append style=name=zlabel-1,
 at=(ticklabel* cs:1.15), 
 data cs=polar,
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $delta(x)cdot 1(y)$,
 ticks=none,samples y=1,ymin=-12,ymax=12,
 enlargelimits=0.3]
 addplot3[draw=none] (0,x,f(x));
 pgfplotsinvokeforeach-12,...,12
 draw[-latex] (0,#1,0) -- (0,#1,0.07);
 endaxis

 % https://tex.stackexchange.com/a/124936/121799
 beginaxis[name=plot2,axis lines = center,
 ticks=none, 
 data cs=polar,
 every axis z label/.append style=name=zlabel-2,
 at=(ticklabel* cs:1.15),
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $PSF(x,y)$,
 enlargelimits=0.3,
 samples=30,
 domain=0:360, 
 y domain=0:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] f(y);
 endaxis
 beginaxis[xshift=6cm,yshift=0.5cm,view=-4545,
 samples=30,shader=interp,axis lines = center,
 ticks=none, 
 domain=-12:12,
 every axis z label/.append style=name=zlabel-3,
 at=(ticklabel* cs:1.05),
 xlabel = $x$,
 ylabel = $y$, 
 zlabel = $LSF(x)$,
 enlargelimits=0.6,
 y domain=-12:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] 
 g(x);
 draw[fill=gray] plot[variable=x,smooth,samples=30,domain=-12:12] 
 (x,-12,g(x)) --(12,-12,0) -- (-12,-12,0) -- 
 (-12,12,0) -- (-12,12,g(12)) -- cycle;
 endaxis
 path (zlabel-1) -- node[midway]$times$ (zlabel-2)
 -- node[midway]$=$ (zlabel-3);
 endtikzpicture
enddocument


enter image description here






share|improve this answer






















  • One way to get a mesh is to remove shader=interp and add draw=black,thin, to the respective plots.
    – marmot
    5 hours ago












up vote
3
down vote










up vote
3
down vote









You seem to already have done the first plot. (Notice, however, that you are loading tikz-3dplot, even set the view but never implement it. You need to put tdplot_main_coords somewhere.) Here is a pgfplots alternative. I guessed functions that look somewhat like what you plot on your screen shot. 



documentclass[border=3.14mm,tikz]standalone
usetikzlibrarypositioning
usepackageamsmath
DeclareMathOperatorPSFPSF
DeclareMathOperatorLSFLSF

usepackagepgfplots
pgfplotssetcompat=1.16,width=12cm,view=-4545
begindocument
 begintikzpicture[declare function=f(r)=cos(r*48)/(11+r*r);
 g(r)=0.05+cos(r*48)/(11+1.5*r*r);]
 % https://tex.stackexchange.com/a/275668/121799
 beginaxis[name=plot1,xshift=-6cm,axis lines = center,
 ticks=none,
 every axis z label/.append style=name=zlabel-1,
 at=(ticklabel* cs:1.15), 
 data cs=polar,
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $delta(x)cdot 1(y)$,
 ticks=none,samples y=1,ymin=-12,ymax=12,
 enlargelimits=0.3]
 addplot3[draw=none] (0,x,f(x));
 pgfplotsinvokeforeach-12,...,12
 draw[-latex] (0,#1,0) -- (0,#1,0.07);
 endaxis

 % https://tex.stackexchange.com/a/124936/121799
 beginaxis[name=plot2,axis lines = center,
 ticks=none, 
 data cs=polar,
 every axis z label/.append style=name=zlabel-2,
 at=(ticklabel* cs:1.15),
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $PSF(x,y)$,
 enlargelimits=0.3,
 samples=30,
 domain=0:360, 
 y domain=0:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] f(y);
 endaxis
 beginaxis[xshift=6cm,yshift=0.5cm,view=-4545,
 samples=30,shader=interp,axis lines = center,
 ticks=none, 
 domain=-12:12,
 every axis z label/.append style=name=zlabel-3,
 at=(ticklabel* cs:1.05),
 xlabel = $x$,
 ylabel = $y$, 
 zlabel = $LSF(x)$,
 enlargelimits=0.6,
 y domain=-12:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] 
 g(x);
 draw[fill=gray] plot[variable=x,smooth,samples=30,domain=-12:12] 
 (x,-12,g(x)) --(12,-12,0) -- (-12,-12,0) -- 
 (-12,12,0) -- (-12,12,g(12)) -- cycle;
 endaxis
 path (zlabel-1) -- node[midway]$times$ (zlabel-2)
 -- node[midway]$=$ (zlabel-3);
 endtikzpicture
enddocument


enter image description here






share|improve this answer














You seem to already have done the first plot. (Notice, however, that you are loading tikz-3dplot, even set the view but never implement it. You need to put tdplot_main_coords somewhere.) Here is a pgfplots alternative. I guessed functions that look somewhat like what you plot on your screen shot. 



documentclass[border=3.14mm,tikz]standalone
usetikzlibrarypositioning
usepackageamsmath
DeclareMathOperatorPSFPSF
DeclareMathOperatorLSFLSF

usepackagepgfplots
pgfplotssetcompat=1.16,width=12cm,view=-4545
begindocument
 begintikzpicture[declare function=f(r)=cos(r*48)/(11+r*r);
 g(r)=0.05+cos(r*48)/(11+1.5*r*r);]
 % https://tex.stackexchange.com/a/275668/121799
 beginaxis[name=plot1,xshift=-6cm,axis lines = center,
 ticks=none,
 every axis z label/.append style=name=zlabel-1,
 at=(ticklabel* cs:1.15), 
 data cs=polar,
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $delta(x)cdot 1(y)$,
 ticks=none,samples y=1,ymin=-12,ymax=12,
 enlargelimits=0.3]
 addplot3[draw=none] (0,x,f(x));
 pgfplotsinvokeforeach-12,...,12
 draw[-latex] (0,#1,0) -- (0,#1,0.07);
 endaxis

 % https://tex.stackexchange.com/a/124936/121799
 beginaxis[name=plot2,axis lines = center,
 ticks=none, 
 data cs=polar,
 every axis z label/.append style=name=zlabel-2,
 at=(ticklabel* cs:1.15),
 xlabel = $x$,
 ylabel = $y$,
 zlabel = $PSF(x,y)$,
 enlargelimits=0.3,
 samples=30,
 domain=0:360, 
 y domain=0:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] f(y);
 endaxis
 beginaxis[xshift=6cm,yshift=0.5cm,view=-4545,
 samples=30,shader=interp,axis lines = center,
 ticks=none, 
 domain=-12:12,
 every axis z label/.append style=name=zlabel-3,
 at=(ticklabel* cs:1.05),
 xlabel = $x$,
 ylabel = $y$, 
 zlabel = $LSF(x)$,
 enlargelimits=0.6,
 y domain=-12:12,samples y=72]
 addplot3 [surf,mesh/ordering=y varies,shader=interp,z buffer=sort] 
 g(x);
 draw[fill=gray] plot[variable=x,smooth,samples=30,domain=-12:12] 
 (x,-12,g(x)) --(12,-12,0) -- (-12,-12,0) -- 
 (-12,12,0) -- (-12,12,g(12)) -- cycle;
 endaxis
 path (zlabel-1) -- node[midway]$times$ (zlabel-2)
 -- node[midway]$=$ (zlabel-3);
 endtikzpicture
enddocument


enter image description here







share|improve this answer














share|improve this answer



share|improve this answer








edited 5 hours ago

























answered 6 hours ago









marmot

57.6k462124




57.6k462124











  • One way to get a mesh is to remove shader=interp and add draw=black,thin, to the respective plots.
    – marmot
    5 hours ago
















  • One way to get a mesh is to remove shader=interp and add draw=black,thin, to the respective plots.
    – marmot
    5 hours ago















One way to get a mesh is to remove shader=interp and add draw=black,thin, to the respective plots.
– marmot
5 hours ago




One way to get a mesh is to remove shader=interp and add draw=black,thin, to the respective plots.
– marmot
5 hours ago










Bakira is a new contributor. Be nice, and check out our Code of Conduct.









 

draft saved


draft discarded


















Bakira is a new contributor. Be nice, and check out our Code of Conduct.












Bakira is a new contributor. Be nice, and check out our Code of Conduct.











Bakira is a new contributor. Be nice, and check out our Code of Conduct.













 


draft saved


draft discarded














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Long meetings (6-7 hours a day): Being “babysat” by supervisor

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Prepared foods made with a lot of sugar or other cabohydrates "Sweetmeat" redirects here. For the racehorse, see Sweetmeat (horse). Not to be confused with Sweetbread. This Kransekake is a traditional Scandinavian baker's confection. Confectionery is the art of making confections , which are food items that are rich in sugar and carbohydrates. Exact definitions are difficult. [1] In general, though, confectionery is divided into two broad and somewhat overlapping categories, bakers' confections and sugar confections. [2] Bakers' confectionery, also called flour confections , includes principally sweet pastries, cakes, and similar baked goods. Sugar confectionery includes candies ( sweets in British English), candied nuts, chocolates, chewing gum, bubble gum, pastillage, and other confections that are made primarily of sugar. In some cases, chocolate confections (confections made of chocolate) are treated as a separate category, as are sugar-free versions of
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