Bézier

Frizzande's F

2025-03-26

I have had a request from Andre Compadre to produce an F for his site frizzande.io.

guess-work

/projects/typesetting/frizzande/
thick.svg — thick

/projects/typesetting/frizzande/
thin.svg — thin

\begin{tikzpicture}[line width=3pt,xscale=0.7,yscale=0.7,line cap=round, line join=round]
\coordinate (a) at (0,4);
\coordinate (z) at (3.7,6);
\coordinate (b) at (2.5,6);
\coordinate (c) at (3,0);
\coordinate (d) at (1,2.5);
\coordinate (e) at (5,4.25);
\coordinate (f) at (4.5,4.25);
\coordinate (g) at (4.75,4.25);
\coordinate (h) at (4.625,4.25);

\draw (a) parabola (z);
\draw (z) to[out=68, in=74] (b);
\draw[bend left] (b) to[out=-30, in=-90] (c);
\draw[bend left] (c) to[out=-120, in=0] (d) to[out=-90, in=-90] (e);
\draw (e) to[out=90,in=90] (f) to[out=-90, in=-90] (g) to[out=90,in=90] (h);
\end{tikzpicture}

thick

\begin{tikzpicture}[line cap=round, line join=round]
\coordinate (a) at (2,3);
\coordinate (b) at (3,6);
\coordinate (c) at (2,0);
\coordinate (d) at (1,2.5);
\coordinate (e) at (4,4.5);
\coordinate (f) at (3.5,4.5);
\coordinate (g) at (3.75,4.5);
\coordinate (h) at (3.625,4.5);

\draw[bend right] (a) to[out=0, in=-90] (b) to[out=90, in=90] (c);
\draw[bend right] (c) to[out=-90, in=0] (d) to[out=-90, in=-90] (e);
\draw (e) to[out=90,in=90] (f) to[out=-90, in=-90] (g) to[out=90,in=90] (h);
\end{tikzpicture}

thin

supervised learning

\begin{tikzpicture}[line width=3pt,xscale=0.7,yscale=0.7,line cap=round, line join=round]

\coordinate (o) at (0,0);
\coordinate (a) at (2,6);
\coordinate (b) at (-2,-6);
\coordinate (c) at (-2,1);
\coordinate (d) at (3,-1);
\coordinate (e) at (2,-2);
\coordinate (f) at (4,-2);
\coordinate (z) at (2,-1);

\draw[bend right] (o) to (a);
\draw (a) to (b);
\draw[bend right] (b) to (o);
\draw (o) ++(-1.3,0.66) circle [x radius=1.5cm, y radius=0.66cm, rotate=-30];
%\draw[bend right] (o) to (c) to (o);
\draw[bend left] (o) to (d) ++(-0.05,0);
%\draw[bend left] (d) to (e) to (d);
\draw (d) ++(-0.4,-0.15) circle [x radius=0.35cm, y radius=0.45cm, rotate=20];
\draw[bend right] (d) to (f);


\end{tikzpicture}

/projects/typesetting/frizzande/
two-ellipses.svg — thick

Producing the Omega symbol with Splines

2025-03-08 (updated: 2025-04-11)

b%C3%A9zier

“Sometimes science is more art than science, Morty. A lot of people don’t get that.”

— Rick Sanchez, “Anatomy Park” (Rick and Morty, Season 1, Episode 3)

img

code

\begin{tikzpicture}
  \node (a) at (3,3) {A};
  \node (b) at (3,1) {B};
  \node (c) at (0,1) {C};
  \node (d) at (0,3) {D};
  \node (e) at (2,3) {E};
  \node (f) at (4,7) {F};
  \node (g) at (6,3) {G};
  \node (h) at (8,3) {H};
  \node (i) at (8,1) {I};
  \node (j) at (5,1) {J};
  \node (k) at (5,3) {K};
  \node (l) at (4,6) {L};
  \node (z) at (2.5,2) {z};
  \node (y) at (1.5,2) {y};
  \node (x) at (6.5,2) {x};
  \node (w) at (5.5,2) {w};
  \node (v) at (8,4.5) {v};
  \node (u) at (6,4.5) {u};
  \node (t) at (2,4.5) {t};
  \node (s) at (0,4.5) {s};
  
  % backbone controls
  \draw[line width=5pt, color=gray] (a) -- (b) -- (c) -- (d) -- (e) -- (f)
  -- (g) -- (h) -- (i) -- (j) -- (k) -- (l) -- (a);
  % left leg
  \draw[blue] (a) .. controls (z) .. (b);
  \draw[blue] (b) .. controls (z) and (y) .. (c);
  \draw[blue] (c) .. controls (y) .. (d);
  \draw[blue] (d) .. controls (y) .. (e);
  % top arch
  \draw[blue] (e) .. controls (0,5) and (0,7) .. (f);
    \draw[blue] (g) .. controls (8,5) and (8,7) .. (f);
  %\draw[blue] (k) .. controls ($(u) + (0,1)$) and ($(u) - (0,1)$) .. (l);
  \draw[blue] (k) .. controls (6,4) and (6,6) .. (l);
  \draw[blue] (a) .. controls (2,4) and (2,6) .. (l);
  % right leg
  \draw[blue] (g) .. controls (x) .. (h);
  \draw[blue] (h) .. controls (x) .. (i);
  \draw[blue] (i) .. controls (x) and (w) .. (j);
  \draw[blue] (j) .. controls (w) .. (k);

  
  %\draw[line width=10pt] (0,0) .. controls (1,1) .. (4,0) .. controls (5,0) and (5,1) .. (4,1);
\end{tikzpicture}


\begin{tikzpicture}
    \draw[fill=blue!20] (-1,0) .. controls (-1,0.555) and (-0.555,1) .. (0,1)
    .. controls (0.555,1) and (1,0.555) .. (1,0) .. controls (1, 1.555) and (0.555, 2) .. (0, 2)
    .. controls (-0.555, 2) and (-1, 1.555) .. (-1, 0) -- cycle;

    \filldraw[gray] (-1,0.555) circle [radius=2pt]
    (-0.555,1) circle [radius=2pt]
    (0.555, 1) circle [radius=2pt]
    (1,0.555) circle [radius=2pt];
\end{tikzpicture}

\begin{tikzpicture}
  \coordinate (a) at (3,3) {};
  \coordinate (b) at (3,1) {};
  \coordinate (c) at (0,1) {};
  \coordinate (d) at (0,3) {};
  \coordinate (e) at (2,3) {};
  \coordinate (f) at (4,7) {};
  \coordinate (g) at (6,3) {};
  \coordinate (h) at (8,3) {};
  \coordinate (i) at (8,1) {};
  \coordinate (j) at (5,1) {};
  \coordinate (k) at (5,3) {};
  \coordinate (l) at (4,6) {};
  \coordinate (z) at (2.5,2) {};
  \coordinate (y) at (1.5,2) {};
  \coordinate (x) at (6.5,2) {};
  \coordinate (w) at (5.5,2) {};
  \coordinate (v) at (8,4.5) {};
  \coordinate (u) at (6,4.5) {};
  \coordinate (t) at (2,4.5) {};
  \coordinate (s) at (0,4.5) {};

  \draw[fill=blue!20] (a) .. controls (z) .. (b)
  .. controls (z) and (y) .. (c)
  .. controls (y) .. (d)
  .. controls (y) .. (e)
  .. controls (0,5) and (0,7) .. (f)
  .. controls (8,7) and (8,5) .. (g)
  .. controls (x) .. (h)
  .. controls (x) .. (i)
  .. controls (x) and (w) .. (j)
  .. controls (w) .. (k)
  .. controls (6,4) and (6,6) .. (l)
  .. controls (2,6) and (2,4) .. (a) -- cycle;
\end{tikzpicture}


\begin{tikzpicture}[relative=false]
  \coordinate (a) at (3,3) {};
  \coordinate (b) at (3,1) {};
  \coordinate (c) at (0,1) {};
  \coordinate (d) at (0,3) {};
  \coordinate (e) at (2,3) {};
  \coordinate (f) at (4,7) {};
  \coordinate (g) at (6,3) {};
  \coordinate (h) at (8,3) {};
  \coordinate (i) at (8,1) {};
  \coordinate (j) at (5,1) {};
  \coordinate (k) at (5,3) {};
  \coordinate (l) at (4,6) {};
  \coordinate (z) at (2.5,2) {};
  \coordinate (y) at (1.5,2) {};
  \coordinate (x) at (6.5,2) {};
  \coordinate (w) at (5.5,2) {};
  \coordinate (v) at (8,4.5) {};
  \coordinate (u) at (6,4.5) {};
  \coordinate (t) at (2,4.5) {};
  \coordinate (s) at (0,4.5) {};

  \draw[fill=blue!20] (a) to[out=270,in=90] (b)
  to[out=180,in=0] (c)
  to[out=90,in=270] (d)
  to[out=0,in=180] (e)
  .. controls (0,5) and (0,7) .. (f)
  .. controls (8,7) and (8,5) .. (g)
  to[out=0,in=180] (h)
  to[out=270,in=90] (i)
  to[out=180,in=0] (j)
  to[out=90, in=270] (k)
  .. controls (6,4) and (6,6) .. (l)
  .. controls (2,6) and (2,4) .. (a) -- cycle;
\end{tikzpicture}

\begin{tikzpicture}[out=180,in=135]
\draw (0,0) to (1,0)
to (2,1)
to (2,2);
\end{tikzpicture}


\begin{tikzpicture}[line width=3pt,xscale=0.7,yscale=0.7,line cap=round, line join=round]
  \draw[fill=red] (-0.1, 0) coordinate (a) arc [start angle=-60, end angle=240,
  x radius=0.75cm, y radius=0.66cm] coordinate (b);
  \draw (0.66, 0) coordinate (c) arc [start angle=-30, end angle=210,
  x radius=1.3cm, y radius=1cm] coordinate (d);
  \draw (c) to[out=0,in=225] ++(0.66,0) to[out=-105,in=105] ++(0,-0.66) to[out=165,in=15] ++(-1.5,0.1) to[out=75,in=-75] (a);
  \draw (d) to[out=180,in=-45] ++(-0.66,0) to[out=-75,in=75] ++(0,-0.66) to[out=15,in=165] ++(1.5,0.1) to[out=105,  in=-105] (b);

\end{tikzpicture}

\begin{tikzpicture}[line width=3pt,xscale=0.7,yscale=0.7,line cap=round, line join=round]
  \draw[fill=purple] (-0.1, 0) coordinate (a) arc [start angle=-60, end angle=240,
  x radius=0.75cm, y radius=0.66cm] coordinate (b) (0.66, 0) coordinate (c) arc [start angle=-30, end angle=210,
  x radius=1.3cm, y radius=1cm] coordinate (d) (c) to[out=0,in=225] ++(0.66,0) to[out=-105,in=105] ++(0,-0.66) to[out=165,in=15] ++(-1.5,0.1) to[out=75,in=-75] (a) (d) to[out=180,in=-45] ++(-0.66,0) to[out=-75,in=75] ++(0,-0.66) to[out=15,in=165] ++(1.5,0.1) to[out=105,  in=-105] (b);

\end{tikzpicture}



\begin{tikzpicture}
  % Use even odd rule to fill the outer arc minus the inner arc
  \path[fill=gray!30, even odd rule]
    % --- Outer arc (big ellipse) ---
    (0.66, 0) arc [
      start angle=-30, end angle=210,
      x radius=2cm, y radius=1.33cm
    ]
    -- cycle
    % --- Inner arc (smaller ellipse) ---
    (0, 0) arc [
      start angle=-45, end angle=225,
      x radius=1.5cm, y radius=1cm
    ]
    -- cycle;
\end{tikzpicture}


\begin{tikzpicture}[line width=3pt,xscale=0.6,yscale=0.7,line cap=round, line join=round]
\definecolor{bostonuniversityred}{rgb}{0.8, 0.0, 0.0}
  \coordinate (c) at (0.66,0);
  
  \path[
    fill=bostonuniversityred,            % Fill the interior in red
    draw=black]

    (c)
      arc [
        start angle=-30, end angle=210,
        x radius=1.3cm, y radius=1cm
      ] coordinate (d)

      to[out=180, in=-45] ++(-0.66,0)
      to[out=-75, in=75]  ++(0,-0.66)
      to[out=15,  in=165] ++(1.5,0.1)
      to[out=105, in=-105] coordinate (b) ++(0,0.5)

      arc [
        start angle=240, end angle=-60,
        x radius=0.75cm, y radius=0.66cm
      ] coordinate (a)

      to[out=-75,in=75] ++(0,-0.6)
      to[out=15, in=165] ++(1.33,0.1)
      to[out=105, in=-105] ++(0,0.66)
      to[out=225, in=0] (c) -- cycle;

\end{tikzpicture}

Convert Font files to Bezier Curves

2025-02-25

b%C3%A9zier mathjax fonts woff otf ttf python

Really the github repository is self-documenting.

Here are couple of SVG's though:

/projects/typesetting/font2splines/
o.svg — uppercase Computer Modern Omega

/projects/typesetting/font2splines/
o-bold.svg — uppercase **Bold** Computer Modern Omega