Skip to content
tikzfigure

Coordinates and Midpoints

tikzfigure can compute new node positions geometrically from existing ones. fig.midpoint(node_a, node_b) places a new node exactly halfway between two existing nodes. For a lighter alternative with no visible output, use fig.coordinate(label, x, y) to define a named invisible waypoint.

This tutorial covers: - basic midpoint usage - point/vector translations from node positions - using label strings as references - edge labels on a triangle - recursive bisection - computing a triangle’s centroid via iterated midpoints - named coordinates as invisible path waypoints - routing paths via intermediate coordinates - expression-based coordinates with the calc library

from tikzfigure import TikzFigure, TikzVector, arrows, styles
fig = TikzFigure()


A = fig.node(
    (0, 0),
    label="A",
    content="$A$",
    shape="circle",
    fill="blue!20",
    draw="blue",
)
B = fig.node(
    (6, 0),
    label="B",
    content="$B$",
    shape="circle",
    fill="blue!20",
    draw="blue",
)
C = fig.node(
    (2, 4),
    label="C",
    content="$C$",
    shape="circle",
    fill="blue!20",
    draw="blue",
)


fig.draw(
    [A.center, "B", "C"],
    center=True,
    cycle=True,
    color="blue",
    fill="blue!10",
    line_width="1.5pt",
)


fig.show()

Basic midpoint

Section titled “Basic midpoint”

Pass two nodes (or label strings) and any additional node kwargs. The returned node has .x and .y set to the computed midpoint.

fig = TikzFigure()


n1 = fig.node(
    (0, 0),
    label="A",
    content="A",
    shape="circle",
    fill="blue!30",
    draw="blue",
)
n2 = fig.node(
    (4, 0),
    label="B",
    content="B",
    shape="circle",
    fill="red!30",
    draw="red",
)


mid = fig.midpoint(
    n1,
    "B",
    label="M",
    content="M",
    shape="circle",
    fill="green!30",
    draw="green",
)


fig.draw([n1, n2], options=[styles.dashed], color="gray")


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=circle, fill=blue!30, draw=blue] (A) at ({0}, {0}) {A};
    \node[shape=circle, fill=red!30, draw=red] (B) at ({4}, {0}) {B};
    \node[shape=circle, fill=green!30, draw=green] (M) at ({2.0}, {0.0}) {M};
    \draw[dashed, color=gray] (A) to (B);
\end{tikzpicture}

Point and vector operations

Section titled “Point and vector operations”

Each positioned node exposes its point as node.position. Subtracting two points gives a TikzVector, and adding a vector to a point translates it to a new position. That lets you place derived geometry without retyping coordinates.

fig = TikzFigure()


A = fig.node(
    (0, 0),
    label="A",
    content="$A$",
    shape="circle",
    fill="blue!20",
    draw="blue",
)
B = fig.node(
    (4, 2),
    label="B",
    content="$B$",
    shape="circle",
    fill="orange!20",
    draw="orange",
)


AB = A.vector_to(B)
midpoint = A.position + 0.5 * AB
offset = TikzVector(-1, 2)


M = fig.node(
    midpoint,
    label="M",
    content="$M$",
    shape="circle",
    fill="yellow!40",
    draw="yellow!60!black",
)
A_shifted = fig.node(
    A.translate(offset),
    label="Ashift",
    content="$A+v$",
    shape="circle",
    fill="green!20",
    draw="green!60!black",
)


fig.draw([A, B], options=[styles.dashed], color="gray")
fig.draw([A, A_shifted], arrows=arrows.forward, color="green!60!black")
fig.draw([A, M, B], color="purple")
fig.node(
    (2, 3.3),
    content=rf"$\|AB\| = {A.distance_to(B):.2f}$",
    draw="none",
)


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=circle, fill=blue!20, draw=blue] (A) at ({0}, {0}) {$A$};
    \node[shape=circle, fill=orange!20, draw=orange] (B) at ({4}, {2}) {$B$};
    \node[shape=circle, fill=yellow!40, draw=yellow!60!black] (M) at ({2.0}, {1.0}) {$M$};
    \node[shape=circle, fill=green!20, draw=green!60!black] (Ashift) at ({-1.0}, {2.0}) {$A+v$};
    \draw[dashed, color=gray] (A) to (B);
    \draw[->, color=green!60!black] (A) to (Ashift);
    \draw[color=purple] (A) to (M) to (B);
    \node[draw=none] (node4) at ({2}, {3.3}) {$\|AB\| = 4.47$};
\end{tikzpicture}

Using label strings

Section titled “Using label strings”

You can refer to any node by its label string instead of keeping the Python object.

fig = TikzFigure()


fig.node(
    (0, 2),
    label="P",
    content="P",
    shape="circle",
    fill="orange!40",
    draw="orange",
)
fig.node(
    (6, 2),
    label="Q",
    content="Q",
    shape="circle",
    fill="orange!40",
    draw="orange",
)


fig.midpoint(
    "P",
    "Q",
    label="PQ",
    content="mid",
    shape="circle",
    fill="white",
    draw="black",
)


fig.draw(["P", "Q"], options=[styles.dashed], color="gray")


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=circle, fill=orange!40, draw=orange] (P) at ({0}, {2}) {P};
    \node[shape=circle, fill=orange!40, draw=orange] (Q) at ({6}, {2}) {Q};
    \node[shape=circle, fill=white, draw=black] (PQ) at ({3.0}, {2.0}) {mid};
    \draw[dashed, color=gray] (P) to (Q);
\end{tikzpicture}

Edge labels on a triangle

Section titled “Edge labels on a triangle”

A classic use case: place a label at the midpoint of each edge.

fig = TikzFigure(
    figure_setup="every node/.append style={draw, minimum size=0.7cm}",
)


fig.node(
    (0, 0),
    label="A",
    content="A",
    shape="circle",
    fill="blue!20",
)
fig.node(
    (4, 0),
    label="B",
    content="B",
    shape="circle",
    fill="blue!20",
)
fig.node(
    (2, 3),
    label="C",
    content="C",
    shape="circle",
    fill="blue!20",
)


fig.draw(["A", "B"], color="black")
fig.draw(["B", "C"], color="black")
fig.draw(["A", "C"], color="black")


fig.midpoint(
    "A",
    "B",
    label="AB",
    content="$c$",
    draw="none",
    fill="yellow!60",
)
fig.midpoint(
    "B",
    "C",
    label="BC",
    content="$a$",
    draw="none",
    fill="yellow!60",
)
fig.midpoint(
    "A",
    "C",
    label="AC",
    content="$b$",
    draw="none",
    fill="yellow!60",
)


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}[every node/.append style={draw, minimum size=0.7cm}]
    \node[shape=circle, fill=blue!20] (A) at ({0}, {0}) {A};
    \node[shape=circle, fill=blue!20] (B) at ({4}, {0}) {B};
    \node[shape=circle, fill=blue!20] (C) at ({2}, {3}) {C};
    \draw[color=black] (A) to (B);
    \draw[color=black] (B) to (C);
    \draw[color=black] (A) to (C);
    \node[fill=yellow!60, draw=none] (AB) at ({2.0}, {0.0}) {$c$};
    \node[fill=yellow!60, draw=none] (BC) at ({3.0}, {1.5}) {$a$};
    \node[fill=yellow!60, draw=none] (AC) at ({1.0}, {1.5}) {$b$};
\end{tikzpicture}

Recursive bisection

Section titled “Recursive bisection”

Repeatedly calling midpoint bisects a segment. Here we produce three levels of binary subdivision.

fig = TikzFigure()


dot = dict(
    shape="circle",
    minimum_size="6pt",
    fill="black",
    draw="black",
    inner_sep="0pt",
    content="",
)


left = fig.node(
    (0, 0),
    label="L",
    **dot,
)
right = fig.node(
    (8, 0),
    label="R",
    **dot,
)
fig.draw([left, right], color="gray")


m1 = fig.midpoint(
    left,
    right,
    label="M1",
    **dot,
)
m2a = fig.midpoint(
    left,
    m1,
    label="M2a",
    **dot,
)
m2b = fig.midpoint(
    m1,
    right,
    label="M2b",
    **dot,
)


fig.midpoint(
    left,
    m2a,
    label="M3a",
    **dot,
)
fig.midpoint(
    m2a,
    m1,
    label="M3b",
    **dot,
)
fig.midpoint(
    m1,
    m2b,
    label="M3c",
    **dot,
)
fig.midpoint(
    m2b,
    right,
    label="M3d",
    **dot,
)


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (L) at ({0}, {0}) {};
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (R) at ({8}, {0}) {};
    \draw[color=gray] (L) to (R);
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (M1) at ({4.0}, {0.0}) {};
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (M2a) at ({2.0}, {0.0}) {};
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (M2b) at ({6.0}, {0.0}) {};
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (M3a) at ({1.0}, {0.0}) {};
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (M3b) at ({3.0}, {0.0}) {};
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (M3c) at ({5.0}, {0.0}) {};
    \node[shape=circle, fill=black, draw=black, minimum size=6pt, inner sep=0pt] (M3d) at ({7.0}, {0.0}) {};
\end{tikzpicture}

Triangle centroid via iterated midpoints

Section titled “Triangle centroid via iterated midpoints”

The centroid GG of a triangle satisfies G=A+B+C3G = \frac{A+B+C}{3}. We can reach it with two midpoint calls: G=midpoint(midpoint(A,B),  C)G = \text{midpoint}(\text{midpoint}(A, B),\; C)

(This is equivalent to taking 2/3 along the median from CC to the midpoint of ABAB.)

fig = TikzFigure()


A = fig.node(
    (0, 0),
    label="A",
    content="$A$",
    shape="circle",
    fill="blue!20",
    draw="blue",
)
B = fig.node(
    (6, 0),
    label="B",
    content="$B$",
    shape="circle",
    fill="blue!20",
    draw="blue",
)
C = fig.node(
    (2, 4),
    label="C",
    content="$C$",
    shape="circle",
    fill="blue!20",
    draw="blue",
)


fig.draw(
    [A.center, "B", "C"],
    center=True,
    cycle=True,
    color="blue",
    fill="blue!10",
    line_width="1.5pt",
)


# Midpoint of BC - used to draw the median from A
mid_BC = fig.midpoint(
    B,
    C,
    label="MBC",
    content="",
    shape="circle",
    minimum_size="4pt",
    fill="gray",
    draw="gray",
    inner_sep="0pt",
)
fig.draw([A, mid_BC], options=[styles.dashed], color="gray")


# Centroid = midpoint(midpoint(A, B), C)
centroid = fig.midpoint(
    fig.midpoint(
        A,
        B,
        label="_MAB",
        content="",
    ),
    C,
    label="G",
    content="$G$",
    shape="circle",
    fill="red!60",
    draw="red",
)


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=circle, fill=blue!20, draw=blue] (A) at ({0}, {0}) {$A$};
    \node[shape=circle, fill=blue!20, draw=blue] (B) at ({6}, {0}) {$B$};
    \node[shape=circle, fill=blue!20, draw=blue] (C) at ({2}, {4}) {$C$};
    \draw[color=blue, fill=blue!10, line width=1.5pt] (A.center) to (B.center) to (C.center) -- cycle;
    \node[shape=circle, fill=gray, draw=gray, minimum size=4pt, inner sep=0pt] (MBC) at ({4.0}, {2.0}) {};
    \draw[dashed, color=gray] (A) to (MBC);
    \node (_MAB) at ({3.0}, {0.0}) {};
    \node[shape=circle, fill=red!60, draw=red] (G) at ({2.5}, {2.0}) {$G$};
\end{tikzpicture}

Named coordinates as path waypoints

Section titled “Named coordinates as path waypoints”

fig.coordinate(label, x, y) plants an invisible named point — no box, no content, no border. It emits \coordinate (label) at (x,y); in TikZ and can be referenced in any path list just like a node label.

This is lighter than fig.node() when you only need a reusable geometric anchor, not a visible element.

fig = TikzFigure()


# Four invisible corners of a diamond
fig.coordinate("top", x=3, y=4)
fig.coordinate("right", x=6, y=2)
fig.coordinate("bot", x=3, y=0)
fig.coordinate("left", x=0, y=2)


# Draw a diamond outline and its diagonals
fig.draw(
    ["top", "right", "bot", "left"],
    cycle=True,
    color="teal",
    line_width=2,
)
fig.draw(
    ["top", "bot"],
    options=[styles.dashed],
    color="gray",
)
fig.draw(
    ["left", "right"],
    options=[styles.dashed],
    color="gray",
)


# A visible centre node for reference
fig.node(
    (3, 2),
    content="centre",
    draw="none",
    font=r"\small",
)


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \coordinate (top) at ({3}, {4});
    \coordinate (right) at ({6}, {2});
    \coordinate (bot) at ({3}, {0});
    \coordinate (left) at ({0}, {2});
    \draw[color=teal, line width=2] (top)
        to
        (right)
        to
        (bot)
        to
        (left) -- cycle;
    \draw[dashed, color=gray] (top) to (bot);
    \draw[dashed, color=gray] (left) to (right);
    \node[draw=none, font=\small] (node0) at ({3}, {2}) {centre};
\end{tikzpicture}

Routing paths via intermediate coordinates

Section titled “Routing paths via intermediate coordinates”

A common TikZ pattern is bending a connection around an obstacle by routing it through an invisible corner coordinate. Here two nodes are connected with an L-shaped arrow: the path goes horizontally to a corner, then vertically up.

fig = TikzFigure()


fig.node(
    (0, 0),
    label="src",
    shape="rectangle",
    draw="blue!70",
    fill="blue!15",
    minimum_width="1.8cm",
    minimum_height="0.8cm",
    content="source",
)
fig.node(
    (5, 3),
    label="dst",
    shape="rectangle",
    draw="orange!80",
    fill="orange!15",
    minimum_width="1.8cm",
    minimum_height="0.8cm",
    content="dest",
)


# Corner at the same column as dst, same row as src
fig.coordinate("corner", x=5, y=0)


fig.draw(
    ["src.east", "corner", "dst.south"],
    arrows=arrows.forward,
    options=[styles.thick],
    color="purple",
    segment_options=[
        {"connector": "--"},  # horizontal segment: straight line
        {"connector": "--"},  # vertical segment: straight line
    ],
)


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=rectangle, fill=blue!15, draw=blue!70, minimum width=1.8cm, minimum height=0.8cm] (src) at ({0}, {0}) {source};
    \node[shape=rectangle, fill=orange!15, draw=orange!80, minimum width=1.8cm, minimum height=0.8cm] (dst) at ({5}, {3}) {dest};
    \coordinate (corner) at ({5}, {0});
    \draw[thick, ->, color=purple] (src.east) -- (corner) -- (dst.south);
\end{tikzpicture}

Coordinates from expressions (calc library)

Section titled “Coordinates from expressions (calc library)”

When you add \usetikzlibrary{calc} via document_setup, the at parameter of fig.coordinate() accepts full calc expressions. The $(A)!t!(B)$ syntax places a point a fraction t of the way from A to B.

fig = TikzFigure()
fig.usetikzlibrary("calc")


fig.node(
    (0, 0),
    label="A",
    shape="circle",
    fill="blue!20",
    draw="blue!70",
    minimum_size="1cm",
    content="$A$",
)
fig.node(
    (8, 0),
    label="B",
    shape="circle",
    fill="red!20",
    draw="red!70",
    minimum_size="1cm",
    content="$B$",
)
fig.node(
    (4, 5),
    label="C",
    shape="circle",
    fill="green!20",
    draw="green!70",
    minimum_size="1cm",
    content="$C$",
)


# Invisible midpoints of each edge using calc expressions
fig.coordinate("mAB", at="$(A)!0.5!(B)$")
fig.coordinate("mBC", at="$(B)!0.5!(C)$")
fig.coordinate("mCA", at="$(C)!0.5!(A)$")


# Outline triangle
fig.draw(
    ["A.center", "B.center", "C.center"],
    cycle=True,
    color="gray!50",
    line_width=1,
)


# Medial triangle connecting the three edge midpoints
fig.draw(
    ["mAB", "mBC", "mCA"],
    cycle=True,
    color="purple",
    line_width=2,
    fill="purple!10",
    fill_opacity=0.5,
)


fig.show()

Show Tikz code 
print(fig)
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.3.1     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=circle, fill=blue!20, draw=blue!70, minimum size=1cm] (A) at ({0}, {0}) {$A$};
    \node[shape=circle, fill=red!20, draw=red!70, minimum size=1cm] (B) at ({8}, {0}) {$B$};
    \node[shape=circle, fill=green!20, draw=green!70, minimum size=1cm] (C) at ({4}, {5}) {$C$};
    \coordinate (mAB) at ($(A)!0.5!(B)$);
    \coordinate (mBC) at ($(B)!0.5!(C)$);
    \coordinate (mCA) at ($(C)!0.5!(A)$);
    \draw[color=gray!50, line width=1] (A.center) to (B.center) to (C.center) -- cycle;
    \draw[color=purple, fill=purple!10, fill opacity=0.5, line width=2] (mAB) to (mBC) to (mCA) -- cycle;
\end{tikzpicture}