How to draw a coffee cup

Question

Topologists need to explain that coffee cups are homeomorphic to donuts. There are nice ways to draw donuts. So far, my best attempt is

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{shadings}
\begin{document}
\begin{tikzpicture}
\shade[ball color=gray!10] (-2,0) arc (180:360:2cm);
\shade[left color=gray!10, right color=gray!80] (-2,0) arc (180:540:2cm and 1cm);
\fill[top color=gray!50,bottom color=gray!80] (1.8,-.45) arc (135:225:.35cm) arc (45:-150:.35cm) arc (90:270:.25cm) arc (-90:45:.85cm) -- cycle;
\end{tikzpicture}
\end{document}

Answer 1

Just a small addition to the growing number of cups on this page:

\documentclass[border=0.125cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{fadings}

\tikzfading[name=fade out, inner color=transparent!0, outer color=transparent!100]

\begin{document}

\begin{tikzpicture}

% Saucer
\begin{scope}[shift={(0,-1)}]
    \fill [black!87.5, path fading=fade out] 
      (0,-2/8) ellipse [x radius=6/4, y radius=3/4];
    \shade [left color=gray!20, right color=gray!80] 
      (0,0) ++(180:1.25) arc (180:360:5/4 and 5/8+1/16);
    \shade [left color=gray!40, right color=gray!20] 
      (0,0) ellipse [x radius=5/4, y radius=5/8];
    \shade [right color=gray!40, left color=gray!20] 
      (0,0) ellipse [x radius=5/4/2, y radius=5/8/2];
    \shade [left color=gray!40, right color=gray!20] 
      (0,-1/16) ellipse [x radius=5/4/2-1/16, y radius=5/8/2-1/16];
\end{scope} 

% Handle
\begin{scope}[shift=(10:7/8), rotate=-30, yslant=1/2, xslant=-1/8]
  \shade [top color=gray!80, bottom color=gray!30] 
    (0,0) arc (130:-100:3/8 and 1/2) -- ++(0,1/4) arc (-100:130:1/8 and 1/4) -- cycle;
  \shade [top color=gray!10, bottom color=gray!60] 
    (0,0) arc (130:-100:3/8 and 1/2) -- ++(0,1/32) arc (-100:130:1/4 and 1/3) -- cycle;
\end{scope}

% Cup
\fill [black!75, path fading=fade out] 
    (0,-1) ellipse [x radius=3/4, y radius=1/2];
\shade [left color=gray!60, right color=gray!30] 
  (-1,0) arc (180:360:1 and 5/4);
\shade [bottom color=gray, top color=gray!30, opacity=1/2]
  (-1,0) arc (180:360:1 and 5/4);
\shade [left color=gray!20, right color=gray!40] 
  (0,0) ellipse [x radius=1, y radius=1/2];
\shade [left color=gray!40, right color=gray!20] 
  (0,0) ellipse [x radius=1-1/16, y radius=1/2-1/16];
\shade [bottom color=gray, top color=gray!10, opacity=1/2] 
  (0,0) ellipse [x radius=1-1/16, y radius=1/2-1/16];

% Coffee
\begin{scope}
\clip ellipse [x radius=1-1/16, y radius=1/2-1/16];
\fill [brown!25!black] 
  (0,-1/4) ellipse [x radius=3/4, y radius=3/8];
\fill [brown!50!black, path fading=fade out] 
  (0,-1/4) ellipse [x radius=3/4, y radius=3/8];
\end{scope}

\end{tikzpicture}

\end{document}

And clearly I've given up on doing any "proper" work today:

\documentclass[border=0.125cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{fadings}

\tikzfading[name=fade out, inner color=transparent!0, outer color=transparent!100]


\begin{document}

\begin{tikzpicture}
\foreach \c [count=\i from 0] in {white,gray,red!75!black,blue!25, purple,orange}{

\tikzset{xshift={mod(\i,2)*3cm}, yshift=-floor(\i/2)*3cm}
\colorlet{cup}{\c}

% Saucer
\begin{scope}[shift={(0,-1-1/16)}]
    \fill [black!87.5, path fading=fade out] 
      (0,-2/8) ellipse [x radius=6/4, y radius=3/4];
    \fill [cup, postaction={left color=black, right color=white, opacity=1/3}] 
      (0,0) ++(180:5/4) arc (180:360:5/4 and 5/8+1/16);
    \fill [cup, postaction={left color=black!50, right color=white, opacity=1/3}] 
      (0,0) ellipse [x radius=5/4, y radius=5/8];
    \fill [cup, postaction={left color=white, right color=black, opacity=1/3}]
      (0,1/16) ellipse [x radius=5/4/2, y radius=5/8/2];
    \fill [cup, postaction={left color=black, right color=white, opacity=1/3}] 
      (0,0) ellipse [x radius=5/4/2-1/16, y radius=5/8/2-1/16];
\end{scope} 

% Handle
\begin{scope}[shift=(10:7/8), rotate=-30, yslant=1/2, xslant=-1/8]
  \fill [cup, postaction={top color=black, bottom color=white, opacity=1/3}] 
    (0,0) arc (130:-100:3/8 and 1/2) -- ++(0,1/4) arc (-100:130:1/8 and 1/4) -- cycle;
  \fill [cup, postaction={top color=white, bottom color=black, opacity=1/3}] 
    (0,0) arc (130:-100:3/8 and 1/2) -- ++(0,1/32) arc (-100:130:1/4 and 1/3) -- cycle;
\end{scope}

% Cup
\fill [cup!25!black, path fading=fade out] 
    (0,-1-1/16) ellipse [x radius=3/4, y radius=1/3];
\fill [cup, postaction={left color=black, right color=white, opacity=1/3/2},
  postaction={bottom color=black, top color=white, opacity=1/3/2}] 
    (-1,0) arc (180:360:1 and 5/4);
\fill [cup, postaction={left color=white, right color=black, opacity=1/3}] 
  (0,0) ellipse [x radius=1, y radius=1/2];
\fill [cup, postaction={left color=black, right color=white, opacity=1/3/2},
  postaction={bottom color=black, top color=white, opacity=1/3/2}] 
    (0,0) ellipse [x radius=1-1/16, y radius=1/2-1/16];

% Coffee
\begin{scope}
\clip ellipse [x radius=1-1/16, y radius=1/2-1/16];
\fill [brown!25!black] 
  (0,-1/4) ellipse [x radius=3/4, y radius=3/8];
\fill [brown!50!black, path fading=fade out] 
  (0,-1/4) ellipse [x radius=3/4, y radius=3/8];
\end{scope}
}
\end{tikzpicture}

\end{document}

Answer 2

In my opinion, it's really not worth it re-inventing the wheel when there's a bounty of coffee cups already out there:

All of the above images are open-source and can be opened/edited in Inkscape. Furthermore, if needed, it can be exported as-is in a variety of vectorized formats (if not downloaded in PDF from the source), or exported to TikZ using inkscape2tikz (never tried it though).

Answer 3

How about a cut that actually transforms into a donut (more or less smoothely)?

Code

\documentclass[tikz, border=2mm]{standalone}
\usetikzlibrary{shadings}

\begin{document}

\foreach \x in {0,...,10}
{   \begin{tikzpicture}
        \shade[left color=gray!80, right color=gray!30] (-2,0-\x*0.04) -- (-2,-4+\x*0.04) arc (180:360:2 and 0.5) -- (2,0-\x*0.04) arc (360:180:2 and 0.5);
        \shade[left color=gray!60, right color=gray!20,even odd rule] (0,0-\x*0.04) circle (2 and 0.5) (0,0-\x*0.04) circle (1.8+\x*0.02 and 0.45+\x*0.005);
        \shade[left color=gray!30, right color=gray!80] (0,0-\x*0.04) circle (1.8+\x*0.02 and 0.45+\x*0.005);
        \begin{scope}
            \clip (2,-0.4) arc (90:270:0.05-\x*0.005 and 0.2) arc (90:-90:0.6 and 1.2) arc (90:270:0.05-\x*0.005 and 0.2) arc (-90:90:0.8 and 1.6);
            \fill[inner color=white, outer color=gray!60] (2,-2) circle (0.8 and 1.6);
        \end{scope}
        \draw (-2.1,-4.6) rectangle (2.9,0.6);
    \end{tikzpicture}
}

\foreach \x in {0,...,10}
{   \begin{tikzpicture}
        \shade[left color=gray!80, right color=gray!30] (-2+\x*0.36,-0.4) -- (-2+\x*0.36,-3.6) arc (180:360:2-\x*0.18 and 0.5-\x*0.05) -- (2,-0.4) arc (360:180:2-\x*0.18 and 0.5-\x*0.05);
        \shade[left color=gray!30, right color=gray!80] (0+\x*0.18,-0.4) circle (2-\x*0.18 and 0.5-\x*0.05);
        \begin{scope}
            \clip (2,-0.4) -- ++(0,-0.4) arc (90:-90:0.6 and 1.2) -- ++(0,-0.4) arc (-90:90:0.8 and 1.6);
            \fill[inner color=white, outer color=gray!60] (2,-2) circle (0.8 and 1.6);
        \end{scope}
        \draw (-2.1,-4.6) rectangle (2.9,0.6);
    \end{tikzpicture}
}

\foreach \x in {0,...,10}
{   \begin{tikzpicture}
        \begin{scope}
            \clip (2,-0.4) -- ++(-0.4+\x*0.04,0) arc (90:270:\x*0.08 and 1.6) -| ++(0.4-\x*0.04,0.4) arc (270:90:\x*0.06 and 1.2);
            \fill[inner color=white, outer color=gray!60] (1.2,-0.4) rectangle ++(1.6,-3.2);
        \end{scope}
        \begin{scope}
            \clip (2,-0.4) -- ++(0,-0.4) arc (90:-90:0.6 and 1.2) -- ++(0,-0.4) arc (-90:90:0.8 and 1.6);
            \fill[inner color=white, outer color=gray!60] (2,-2) circle (0.8 and 1.6);
        \end{scope}
        \draw (-2.1,-4.6) rectangle (2.9,0.6);
    \end{tikzpicture}
}

\foreach \x in {0,...,10}
{   \begin{tikzpicture}
        \fill[inner color=white, outer color=gray!60,even odd rule] (2-\x*0.16,-2) circle (0.8+\x*0.16 and 1.6) (2-\x*0.16,-2) circle (0.6+\x*0.09 and 1.2-\x*0.02);
        \draw (-2.1,-4.6) rectangle (2.9,0.6);
    \end{tikzpicture}
}

\end{document}

Output

Answer 4

This is really expanding on Werner's answer.

\documentclass[tikz, border=4pt]{standalone}

\begin{document}

\definecolor{cC6C5C4}{RGB}{198,197,196}
\definecolor{c9B9999}{RGB}{155,153,153}
\definecolor{cEBEBEB}{RGB}{235,235,235}
\definecolor{cE2E1E1}{RGB}{226,225,225}
\definecolor{cC37660}{RGB}{195,118,96}


\begin{tikzpicture}[y=0.80pt,x=0.80pt,yscale=-1, inner sep=0pt, outer sep=0pt]
\path[fill=cC6C5C4] (434.7610,355.3470) .. controls (434.8330,355.1840) and
  (434.9160,355.0280) .. (435.0060,354.8760) .. controls (430.1610,355.7890) and
  (419.1950,356.2480) .. (419.1950,356.2480) .. controls (419.1950,356.2480) and
  (359.8720,367.7830) .. (359.0480,369.7050) .. controls (358.2240,371.6270) and
  (362.8930,376.8460) .. (369.7590,379.0430) .. controls (371.7360,379.6760) and
  (375.8590,381.0100) .. (381.4600,382.1710) .. controls (382.2580,381.3470) and
  (383.4360,380.8590) .. (385.0000,381.0010) .. controls (393.6770,381.7930) and
  (402.7990,381.9730) .. (411.3610,380.1380) .. controls (415.4250,379.2670) and
  (419.5480,378.7220) .. (423.6640,378.1630) .. controls (423.9010,377.5740) and
  (424.2730,377.0450) .. (424.7990,376.6330) .. controls (426.7260,375.1190) and
  (429.2370,374.1350) .. (430.4720,371.9760) .. controls (431.6770,369.8710) and
  (432.7150,367.6620) .. (433.9490,365.5770) .. controls (433.9980,365.4950) and
  (434.0510,365.4230) .. (434.1000,365.3420) .. controls (428.4430,365.0610) and
  (428.7070,355.9080) .. (434.7610,355.3470) -- cycle;
\path[fill=c9B9999] (439.8940,313.0410) .. controls (439.4410,316.1700) and
  (437.8830,327.5880) .. (435.6440,338.7910) .. controls (438.5020,338.1150) and
  (442.3000,335.1050) .. (444.6440,329.0410) .. controls (448.8940,318.0410) and
  (446.3940,310.2910) .. (444.8940,311.2910) .. controls (444.1440,311.7910) and
  (441.8320,311.8520) .. (439.8940,313.0410) -- (439.8940,313.0410) --
  cycle(394.1430,280.5400) .. controls (402.8930,281.0400) and
  (404.8790,280.1140) .. (424.6430,284.2900) .. controls (442.3930,288.0400) and
  (441.8930,297.0400) .. (441.8930,297.0400) -- (441.8930,299.7900) .. controls
  (444.8290,298.8320) and (448.2350,299.1590) .. (450.1430,299.5400) .. controls
  (452.6430,300.0400) and (463.1430,308.7910) .. (457.3930,325.7910) .. controls
  (451.6430,342.7910) and (444.1430,349.7910) .. (436.6430,354.7910) .. controls
  (434.3390,356.3260) and (432.5070,357.5780) .. (431.0750,358.5780) .. controls
  (430.2000,362.6210) and (429.5680,365.3080) .. (429.3930,365.5410) .. controls
  (428.6430,366.5410) and (424.1430,375.0410) .. (396.8930,376.0410) .. controls
  (369.6430,377.0410) and (358.8930,371.0410) .. (355.3930,366.7910) .. controls
  (351.8930,362.5410) and (340.6430,302.0400) .. (340.8930,297.0400) .. controls
  (341.1430,292.0400) and (347.8930,287.0400) .. (358.3930,283.7900) .. controls
  (367.5340,280.9610) and (385.3930,280.0400) .. (394.1430,280.5400) --
  (394.1430,280.5400) -- cycle;
\path[fill=cEBEBEB] (370.3090,309.2830) .. controls (353.7600,307.1420) and
  (346.5490,302.1870) .. (343.4390,297.9180) .. controls (342.9600,291.7080) and
  (353.7490,286.0490) .. (366.8760,284.2900) .. controls (369.4630,283.9430) and
  (374.3920,283.3960) .. (374.3920,283.3960) -- (388.0050,282.5240) .. controls
  (388.0050,282.5240) and (393.1330,282.4410) .. (394.4630,282.5320) .. controls
  (395.7930,282.6230) and (399.6760,282.7570) .. (399.6760,282.7570) .. controls
  (399.6760,282.7570) and (415.3420,284.5460) .. (416.7500,284.7780) .. controls
  (431.0540,287.1390) and (439.0400,290.5350) .. (440.0560,297.4870) --
  (439.8670,298.8380) .. controls (437.9280,301.0720) and (435.6770,303.1010) ..
  (433.2030,304.3380) .. controls (424.9630,308.4590) and (405.4790,313.8300) ..
  (370.3090,309.2830) -- (370.3090,309.2830) -- cycle;
\path[fill=cC6C5C4] (343.4380,297.9180) .. controls (346.5480,302.1870) and
  (353.7590,307.1420) .. (370.3080,309.2830) .. controls (405.4780,313.8300) and
  (424.9620,308.4590) .. (433.2020,304.3390) .. controls (435.6760,303.1020) and
  (437.9270,301.0730) .. (439.8660,298.8390) .. controls (438.5560,308.0820) and
  (430.7960,361.7480) .. (426.6110,365.5860) .. controls (420.0190,371.6270) and
  (409.3080,374.1000) .. (388.9840,374.3730) .. controls (368.6600,374.6480) and
  (364.1210,370.3400) .. (357.4000,365.8590) .. controls (354.1050,363.6620) and
  (345.8640,316.5660) .. (343.4670,298.1920) -- (343.4380,297.9180) --
  (343.4380,297.9180) -- cycle;
\path[fill=cC6C5C4,even odd rule] (429.2200,290.6070) .. controls
  (425.8610,289.3550) and (417.8990,287.2900) .. (413.6920,286.8720) .. controls
  (411.6200,286.6650) and (402.2160,285.3330) .. (391.4220,285.2500) .. controls
  (380.3000,285.1650) and (367.7140,286.3620) .. (361.1080,288.4100) .. controls
  (354.6080,290.4250) and (344.3550,294.4520) .. (347.2380,298.4350) .. controls
  (347.6940,299.0640) and (348.6340,299.8310) .. (350.0340,300.6580) .. controls
  (353.0400,299.0340) and (358.4560,296.6780) .. (366.6230,295.0120) .. controls
  (367.1020,295.5020) and (367.7790,295.8270) .. (368.6660,295.8350) .. controls
  (373.8160,295.8780) and (380.9310,296.8800) .. (385.7810,294.1870) .. controls
  (386.0070,294.2790) and (386.2510,294.3550) .. (386.5350,294.3950) .. controls
  (389.6370,294.8240) and (392.6640,295.5840) .. (395.7740,295.9720) .. controls
  (399.0870,296.3860) and (401.5770,294.6470) .. (404.7350,294.3600) .. controls
  (405.3010,294.3080) and (405.8600,294.2900) .. (406.4160,294.2860) .. controls
  (408.3660,294.8480) and (410.2280,295.0640) .. (412.0880,294.9370) .. controls
  (416.2760,295.8640) and (420.3010,297.5530) .. (424.5350,298.5620) .. controls
  (425.5620,298.8070) and (426.4580,298.5410) .. (427.1180,298.0080) .. controls
  (427.1320,298.0130) and (427.1450,298.0190) .. (427.1590,298.0240) .. controls
  (429.4520,298.9060) and (431.3660,299.8630) .. (432.8070,300.6700) .. controls
  (438.7790,296.6600) and (434.2660,292.4890) .. (429.2200,290.6070) -- cycle;
\path[fill=cC6C5C4] (426.8860,307.9100) .. controls (426.8860,307.9100) and
  (440.7690,301.3120) .. (446.9350,301.0430) .. controls (453.2520,300.7690) and
  (457.3720,309.6950) .. (456.5470,318.4840) .. controls (455.8180,326.2610) and
  (451.3290,340.0430) .. (443.0900,347.4590) .. controls (436.6800,353.2290) and
  (422.2170,361.1910) .. (422.2170,361.1910) -- (426.6120,342.7890) .. controls
  (426.6120,342.7890) and (437.8290,343.2930) .. (442.2660,336.7480) .. controls
  (453.2520,320.5430) and (447.7590,311.4800) .. (446.3860,309.8320) .. controls
  (445.0120,308.1840) and (427.4350,316.1480) .. (427.4350,316.1480) --
  (426.8860,307.9100) -- (426.8860,307.9100) -- cycle;
\path[fill=cEBEBEB] (441.5790,303.1040) .. controls (445.8360,301.4560) and
  (447.7590,301.0440) .. (450.5050,302.6920) .. controls (453.2520,304.3400) and
  (454.9000,310.2450) .. (454.9000,310.2450) .. controls (454.9000,310.2450) and
  (451.7420,305.1640) .. (449.1320,304.3400) .. controls (446.5220,303.5160) and
  (437.3220,304.7510) .. (441.5790,303.1040) -- (441.5790,303.1040) -- cycle;
\path[fill=cEBEBEB,even odd rule] (434.4380,343.6130) .. controls
  (437.7340,341.9650) and (440.8920,339.9060) .. (443.5010,337.1600) .. controls
  (446.1100,334.4120) and (447.3460,329.3320) .. (447.3460,329.3320) .. controls
  (447.3460,329.3320) and (443.9130,340.4550) .. (440.4800,343.6130) .. controls
  (437.0470,346.7710) and (434.4380,349.6560) .. (434.0260,350.6170) .. controls
  (433.6140,351.5780) and (431.1430,345.2620) .. (434.4380,343.6130) --
  (434.4380,343.6130) -- cycle;
\path[fill=cE2E1E1] (374.1530,313.9510) .. controls (376.3500,313.9510) and
  (384.8640,313.6780) .. (393.1040,314.2260) .. controls (401.3440,314.7740) and
  (416.7240,312.0290) .. (416.7240,312.0290) .. controls (416.7240,312.0290) and
  (410.6820,334.0000) .. (410.6820,348.2830) .. controls (410.6820,362.5640) and
  (403.8160,371.6270) .. (401.6190,371.6270) .. controls (399.4220,371.6270) and
  (389.8090,374.1000) .. (387.6120,370.8030) .. controls (385.4150,367.5080) and
  (376.0770,345.5350) .. (375.5280,339.4940) .. controls (374.9770,333.4510) and
  (371.9560,313.9510) .. (374.1530,313.9510) -- (374.1530,313.9510) -- cycle;
\path[fill=c9B9999] (359.3230,374.9240) .. controls (370.5830,380.4160) and
  (404.2280,382.7500) .. (423.1780,375.1970) .. controls (433.2290,371.1910) and
  (431.4170,363.1130) .. (431.4170,363.1130) .. controls (431.4170,363.1130) and
  (434.2680,364.6930) .. (434.8510,367.0950) .. controls (435.9500,371.6260) and
  (426.1630,379.2140) .. (415.6250,380.9640) .. controls (367.6990,388.9300) and
  (348.0620,369.4300) .. (359.3230,374.9240) -- (359.3230,374.9240) -- cycle;
\path[fill=cC37660] (350.0350,300.6580) .. controls (353.2680,298.9110) and
  (359.7100,295.7890) .. (368.5220,294.6450) .. controls (377.3340,293.5010) and
  (381.6000,293.1490) .. (384.0970,293.0750) .. controls (386.5940,293.0010) and
  (388.1780,293.3240) .. (392.0060,293.0790) .. controls (395.8340,292.8340) and
  (410.6660,293.9330) .. (414.4520,294.5400) .. controls (418.2380,295.1470) and
  (423.9010,296.7690) .. (427.1610,298.0220) .. controls (429.4540,298.9040) and
  (431.3680,299.8610) .. (432.8090,300.6680) .. controls (429.1930,303.0950) and
  (421.7300,305.4620) .. (408.2100,307.2230) .. controls (378.0340,311.1540) and
  (357.4950,305.0590) .. (350.0350,300.6580) -- (350.0350,300.6580) -- cycle;

\end{tikzpicture}


\end{document}

I started with a free clip art coffee cup, edited it until I was happy with it (I felt the steam and saucer distracted from its topological properties), and used the inkscape plugin inkscape2tikz. The resulting code is pretty indecipherable, but you get a nice coffee cup!

Also: I think I might have a hardcore procrastination problem.

Answer 5

Just a little addition to make the border of the cup thicker and improving the lighting:

\usetikzlibrary{shadings}
\begin{tikzpicture}
\shade[ball color=gray!10] (-2,0) arc (180:360:2cm);
\shade[left color=gray!30, right color=gray!80] (-2,0) arc (180:540:2cm and 1cm);
\shade[left color=gray!80, right color= gray!10] (-1.8,0) arc (180:540:18mm and 8mm);
\fill[top color=gray!20,bottom color=gray!90] (1.8,-.45) arc (135:225:.35cm) arc (45:-150:.35cm) arc (90:270:.25cm) arc (-90:45:.85cm) -- cycle;
\end{tikzpicture}