Custum build of stapix for tikz.pablopie.xyz
Rewrote all of the text alternatives and captions
Also renamed files to better convey their meaning
Also removed sphere-quotient.tex
9 files changed, 219 insertions, 162 deletions
| Status | File Name | N° Changes | Insertions | Deletions |
| Modified | examples/config.yml | 243 | 165 | 78 |
| Added | examples/images/geodesic-min.tex | 54 | 54 | 0 |
| Deleted | examples/images/geodesic.tex | 54 | 0 | 54 |
| Renamed | examples/images/j-function.jpg -> examples/images/j-function-color.jpg | 0 | 0 | 0 |
| Renamed | examples/images/j-function.svg -> examples/images/j-function-relief.svg | 0 | 0 | 0 |
| Renamed | examples/images/complex-lattice.tex -> examples/images/lattice.tex | 0 | 0 | 0 |
| Renamed | examples/images/smooth-manifold.tex -> examples/images/manifold-charts.tex | 0 | 0 | 0 |
| Renamed | examples/images/riemannian-metric.tex -> examples/images/sphere-metric-comparison.tex | 0 | 0 | 0 |
| Deleted | examples/images/sphere-quotient.tex | 30 | 0 | 30 |
diff --git a/examples/config.yml b/examples/config.yml @@ -1,94 +1,137 @@ -# TODO: Differenciate between alt texts and captions +# TODOO: Reorder the content to group images by theme +# TODOO: Revise all text alternatives and captions +# TODOO: Make text alternatives concise - path: ./images/26-nodes-diagram.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The 26-nodes diagram + alt: A circular, symmetric array of 26 points connected by lines + caption: "The 26-nodes diagram: a graph encoding certain relations of the + Monster simple group" - path: ./images/caleb-yau.png license: CC-BY-SA-2.5 author: Lunch source: https://commons.wikimedia.org/wiki/File:Calabi-Yau-alternate.png - alt: A visual representation of the Calebi-Yau manifold + alt: A convoluted self-intersecting surface in pastel shades of pink and blue + caption: A visual representation of the Calabi-Yau manifold -- path: ./images/complex-lattice.tex +- path: ./images/lattice.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: A complex lattice with two linearly independent periods + alt: Cyan lines highlight the contours of a lattice on the Cartesian plane. + Two blue vectors, each corresponding to one of the periods of the lattice, + highlight the bounds of its fundamental domain. + caption: A 2-dimensional lattice - path: ./images/complex-surreal-venn.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: This picture represents the relationship between the real, - complex and surreal numbers + alt: Two circles, the first representing the complex numbers and the second + representing the surreal numbers, intersect in the middle of picture. Their + intersection is labeled as the set of real numbers. + caption: A Venn diagram representation of the relationship between the real, + complex and surreal numbers (denoted by "No") - path: ./images/cube.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: A cube + alt: A 3-dimensional cube - path: ./images/diamond.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: A domond-like shape + alt: A diamond-like shape -- path: ./images/dihedral-representation-is-irreducible.tex +- path: ./images/dihedral-representation.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: An ilustration of the proof that the natural real representation - of the Dihidral group is irreducible + alt: Two axis labeled "x" and "y" span a plane with a triangle on its center. + A curve arrow labeled "sigma" represents the action of rotating the + triangle by 60°, while an horizontal two-headed arrow labeled "tau" + represents reflecting it through the "y" axis. + caption: The action of the Dihedral group in the Cartesian plane -- path: ./images/dihedral-representation.tex +- path: ./images/dihedral-representation-is-irreducible.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The action of the dihedral group in the real plain + alt: Two axis labeled "x" and "y" span the Cartesian plane. A curvy arrow + labeled "sigma" joins a point "v" and a point labeled "sigma times v". + caption: "An illustration of the proof that the natural representation of the + Dihidral group is irreducible: the rotational generator of the Dihidral + group rotates any vector v by 60° and hence cannot preserve a line + through the origin" - path: ./images/elliptic-curve-group-structure.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The group structure of the points of an elliptic curve + alt: Two axis span a plane containing a curve. Two points on the curve are + labeled "P" and "Q", and a violet line passing through them intersects the + curve in a third point. A violet vertical line passing through this third + point intersects the curve at a fourth point, labeled "P + Q". + caption: The geometric group law of an elliptic curve - path: ./images/euclidian-plane.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The Cartesian plane + alt: A tilted rectangle labeled "R²" + caption: The Cartesian plane - path: ./images/finite-topological-plot.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: A plot of the number of topological spaces of n points in - logarithmic scale + alt: A bar chart with thin blue bars marked by thick circles on their tops. + The x-axis is labeled "n" and ranges from 0 to 20. The y-axis is labeled + "log(# topological spaces of n points)" and ranges from 0 to a little over + 80. On the top of the figure a title reads "Finite Topological Spaces". + caption: Log of the number of distinct topologies (counting homeomorphic + topologies) one can endow a finite set - path: ./images/galois-lattice-antisomorphism.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The lattice anti-isomorphism between the lattice of the - subgroups of the Galois group of a Galois extension and the lattice of - intermediary subfields of such extension. + alt: The contours of two order-theoretic lattices lie side by side. The + lattices are organized in stages, marked by different labels. At each stage + the two lattices are connected by a thing dotted horizontal line. + caption: The lattice anti-isomorphism between the lattice of the subgroups of + the Galois group of an extension K/k and the lattice of intermediary + subfields of K -- path: ./images/geodesic.tex +- path: ./images/geodesic-min.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: This picture represents the fact that geodesics locally minimize - distances + alt: A 2-dimensional sphere is marked by a violet curve connecting the north + pole to a point close to the equator. The violet curve runs across a + meridian, passing through the south pole along the way. On the left, a + circle highlights a small region around a point on the violet curve. In the + circle we can see a violet straight line representing the correspoding arc + of the violet curve and a winding dotted path joining its endpoints. + caption: "This picture represents the fact that geodesics locally minimize + distances: eventhough the violet great circle does not globally minimize the + distance between the marked points in the sphere, at each point in the + violet curve we can find a small neightborhood such that the purple arc in + this neightborhood minimizes the distance between the correspoing endpoints" +# TODO: Track the source for this drawing? (i.e track the manuscript) - path: ./images/grothendieck-riemann-roch.tex license: PD author: Alexander Grothendieck author-url: https://grothendieckcircle.org/ - alt: The commutative diagram from the Grothendieck-Riemann-Roch - theorem, surrounded by fire and two devils carrying forks + alt: A hand-drawn commutative diagram surrounded by fire and devils carrying + forks + caption: The infamous commutative diagram from Gothendieck's 1971 manuscript + on the Grothendieck-Riemann-Roch theorem - path: ./images/groups-periodic-table.svg # TODO: Figure out the actual license @@ -103,26 +146,30 @@ license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The Poincaré disc model of the hyperbolic plane + alt: A circle with an arc highleghted on its interior + caption: The Poincaré disc model of the hyperbolic plane -- path: ./images/j-function.svg +- path: ./images/j-function-relief.svg license: proprietary author: Eugene Jahnke & Fritz Emde source: https://archive.org/details/tablesoffunction00jahn/mode/2up - alt: Relief representation of the j-invariant elliptic modular - function + alt: Relief representation of a function of two variables + caption: Relief representation of the j-invariant modular function from the + book “Tables of Functions with Formulae and Curves” -- path: ./images/j-function.jpg +- path: ./images/j-function-color.jpg license: PD author: Jan Homann source: https://commons.wikimedia.org/wiki/File:KleinInvariantJ.jpg - alt: The j-invariant Klein function in the complex plane + alt: Domain coloring representation of a complex function + caption: The j-invariant Klein function - path: ./images/k4.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The complete graph of four vertices + alt: A triangle with marked vertices and a marked point on its barycenter + caption: The complete graph of four vertices - path: ./images/mobius.tex license: CC-BY-4 @@ -134,8 +181,8 @@ license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The first columns of the chacter table of the monster simple - group in characteristic zero + alt: An increadibly big table of numbers + caption: The chacter table of the Monster simple group in characteristic zero - path: ./images/natural-number-line.tex license: CC-BY-4 @@ -143,77 +190,90 @@ author-url: https://pablopie.xyz alt: The natural number line -- path: ./images/ordinal-number-line.tex +- path: ./images/real-number-line.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The ordinal number line + alt: The real number line -- path: ./images/quaternion-rotation.tex +- path: ./images/ordinal-number-line.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: "This drawing represents the correspondence between conjugation - by pure unitary quaternions and rotations in the 3-dimensional Euclidean - space: the coordinates of a unitary quaternion p number with zero real - coefficient induce a line through the origin in the 3-dimensional Euclidean - space, and conjugation by cos t + p sin t acts as rotation by 2 t around - this axis." + alt: "The ordinal number line: the natural numbers accumulate around ω, + followed by ω-translates of the natural numbers and so on" + caption: The ordinal number line -- path: ./images/real-number-line.tex +- path: ./images/quaternion-rotation.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The real number line + alt: A sphere with a rotation axis marked as "p". A curly arrow donotes + rotation by 2θ. + caption: "This drawing represents the correspondence between conjugation by + pure unitary quaternions and rotations in the 3-space: the coordinates of a + unitary quaternion number p with zero real coefficient define a line + through the origin in 3-space, and conjugation by cos θ + p sin θ acts as + rotation by 2θ around this axis." - path: ./images/real-ordinal-surreal-venn.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: This picture represents the relationship between the real, - ordinal and surreal numbers + alt: Two circles, the first representing the real numbers and the second + representing the ordinal numbers, intersect in the middle of picture. Their + intersection is labeled as the set of natural numbers. A rectangle labeled + as the set of surreal numbers surrounds both circles. + caption: Venn diagram representation of the relationship between the real, + natural and surreal numbers (denoted by "No") -- path: ./images/riemannian-metric.tex +- path: ./images/sphere-metric-comparison.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: This picture is a comparison between the Euclidean distance and - the Riemannian distance in a 3-dimensional sphere + alt: "A sphere is marked by two points and two curves connecting them: a + great circle and a straigh line passing through the interior of the sphere" + caption: "This picture is a comparison between the Euclidean metric and the + Riemannian metric of the 2-sphere: in 3-space the shortest distance between + the north pole and the point close to the equator is realized by the + straight line connecting them, but in the 2-sphere their distance is + realized by a great circle instead" - path: ./images/rigid-motion-reflections.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: This picture represents the fact that reflections are rigid - motions + alt: Two squares with complex patterns in their interiors are placed side by + side, with a squily arrow pointing from the first square to the second + square. The pattern on the second square is a reflection of that on the + first square. + caption: Reflection on the y-axis - path: ./images/rigid-motion-rotation.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: This picture represents the fact that rotations are rigid - motions + alt: Two squares and a curvy arrow representing the action of rotating one + into the other + caption: Rotation by 45° on the Cartesian plane -- path: ./images/smooth-function.tex +- path: ./images/manifold-charts.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: This picture represents the definition of a smooth map between - manifolds + alt: Two small regions U and V in a surface M are highlighted, as well as + their intersection. On the bottom, a map labeled "φ_V ∘ φ_U⁻¹" indicates + the transition of charts. + caption: Transition of charts in a manifold M -- path: ./images/smooth-manifold.tex - license: CC-BY-4 - author: Pablo - author-url: https://pablopie.xyz - alt: This picture represents the definition of a smooth manifold - -- path: ./images/sphere-quotient.tex +# TODO: Not sure I'm happy with this caption +- path: ./images/smooth-function.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The isomorphism between the n-dimensional sphere and the - quotient of the (n + 1)-dimensional simple orthogonal group by the - n-dimensional simple orthogonal group + alt: A map f between two surfaces M and N with its representation in local + coordinates highlighted on the bottom of the figure + caption: A smooth function in local coordinates φ and ψ - path: ./images/sphere.tex license: CC-BY-4 @@ -225,63 +285,90 @@ license: CC-BY-SA-3 author: Drschawrz source: https://en.wikipedia.org/wiki/File:SporadicGroups.svg - alt: All the Sporadic groups in their subquotient relationship + alt: Graph representation of the subquotients of Sporadic groups + caption: "All the Sporadic groups and their subquotient relationships: an + edge from a group G on the top to a group H on the bottom means H is a + subquotient of G. Mathieu groups are collored red, Leech lattice groups are + colored green, other subquotients of the Monster are collored blue and the + rest of the groups are collored white." - path: ./images/square-to-circle-projection.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: "The projection from the square to the circle: we map a point in + alt: A circle and a square. A dotted ray connects the center of the square to + a point in the circle, passing through a point in the perimeter of the + square. + caption: "The projection from the square to the circle: we map a point in the square of length √2/2 onto the unit circle by normalizing it" - path: ./images/standard-sets-venn.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: This diagram represents the relationship between standard number sets + alt: Venn diagram representation of the containment relations between the + natural numbers, integers, rational number, real numbers and complex + numbers - path: ./images/stereographic-projection.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The stereographic projection + alt: A sphere sits on top of plane, with a line connecting the north pole to + the a point on the plane, passing thought another point in the sphere + caption: "The stereographic projection: for each point P in the sphere we + cast a ray from the north pole, identifying P with the point of + intersection of this ray and the plane just bellow the sphere" # TODO: Get the TikZ code for this somehow? - path: ./images/surreal-number-tree.svg license: CC-BY-SA-3 author: Lukáš Lánský source: https://en.wikipedia.org/wiki/File:Surreal_number_tree.svg - alt: Visualization of the surreal number tree + alt: "A complex tree with vertices organized by stages and labelled by + different real and natural numbers" + caption: Visualization of the surreal number tree - path: ./images/tangent-space.tex license: CC-BY-4 author: Gustavo Mezzovilla - alt: The tangent space of a smooth manifold at a point + alt: A surface with a highlighted point on its interior, together with the + plane tangent to the surface at that point + caption: The tangent space of a smooth manifold at a point - path: ./images/topology-mug-donut.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: A mug continuously morphing into a donut + caption: The homeomorphism between the surface of a mug and that of a donut - path: ./images/unit-circle-covering.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The universal covering of the unit circle + alt: A downwords spiral with a circle on its bottom and an arrow labelled "π" + pointing from the spiral to the circle + caption: "The universal covering of the circle: we can picture winding the + real line around the circle by identifying it with an infinite vertical + spiral whose “shadow” in the xy-plane is the circle" - path: ./images/unit-circle.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: The unit complex circle + alt: A circle with two highlighted points labelled "i" and "1" + caption: The unit complex circle - path: ./images/upper-central-projection.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz - alt: "A graphical depiction of the central projection between the + alt: The upper cap of a sphere sits just bellow a plane, with a line + connecting the center of the half-sphere to the a point on the plane, + passing thought another point in the sphere + caption: "A graphical depiction of the central projection between the upper semi-sphere and the Euclidean plane: we map each point in the upper half of the sphere to the projection of this point in the tangent plane at the north pole by drawing a line between this point and the center of the - sphere and then taking the intersection of this line with the plane." + sphere and then taking the intersection of such line with the plane."
diff --git a/examples/images/geodesic-min.tex b/examples/images/geodesic-min.tex @@ -0,0 +1,54 @@ +% This picture represents the fact that geodesics locally minimize distances +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=0.5] + % The cirference + \draw (0, 0) circle (3); + + % The equator + \begin{scope} + \clip (-3, 0) rectangle (3, -3); + \draw ellipse (3 and 1); + \end{scope} + + % Greenwhich + \begin{scope} + \clip (-3, -3) rectangle (0, 3); + \draw ellipse (1 and 3); + \end{scope} + + % The curve + \begin{scope} + \clip (-3, 0) rectangle (0, -3); + \draw[thick, color=violet] ellipse (1 and 3); + \end{scope} + \begin{scope} + \clip (3, -3) rectangle (0, 3); + \draw[thick, dotted, color=violet] ellipse (1 and 3); + \end{scope} + + % The ends + \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt); + + \draw (-0.87, -1.5) circle (0.3); + \draw (-1.17, -1.5) -- (-4, 1); + + % Zoom in ares + \begin{scope}[shift={(-6, 1)}] + \draw (0, 0) circle (2); + + % The geodesic + \draw[thick, color=violet] (0, -2) -- (0, 2); + \filldraw (0, -2) circle (2pt) (0, 2) circle (2pt); + + % Another curve + \draw[dotted] ( 0, 2) to[out=180, in=90] + (-0.6, 1.4) to[out=270, in=150] + ( 0.5, 0.7) to[out=-30, in=0] + ( 0.3, 0.1) to[out=180, in=180] + ( 0.5, 0.6) to[out=0, in=120] + ( 1.3, 0.7) to[out=-60, in=60] + ( 0.4, -0.5) to[out=240, in=90] + ( 0, -2); + \end{scope} +\end{tikzpicture} +
diff --git a/examples/images/geodesic.tex b/examples/images/geodesic.tex @@ -1,54 +0,0 @@ -% This picture represents the fact that geodesics locally minimize distances -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=0.5] - % The cirference - \draw (0, 0) circle (3); - - % The equator - \begin{scope} - \clip (-3, 0) rectangle (3, -3); - \draw ellipse (3 and 1); - \end{scope} - - % Greenwhich - \begin{scope} - \clip (-3, -3) rectangle (0, 3); - \draw ellipse (1 and 3); - \end{scope} - - % The curve - \begin{scope} - \clip (-3, 0) rectangle (0, -3); - \draw[very thick] ellipse (1 and 3); - \end{scope} - \begin{scope} - \clip (3, -3) rectangle (0, 3); - \draw[very thick, dotted] ellipse (1 and 3); - \end{scope} - - % The ends - \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt); - - \draw (-0.87, -1.5) circle (0.3); - \draw (-1.17, -1.5) -- (-4, 1); - - % Zoom in ares - \begin{scope}[shift={(-6, 1)}] - \draw (0, 0) circle (2); - - % The geodesic - \draw[very thick] (0, -2) -- (0, 2); - \filldraw (0, -2) circle (2pt) (0, 2) circle (2pt); - - % Another curve - \draw[dotted] ( 0, 2) to[out=180, in=90] - (-0.6, 1.4) to[out=270, in=150] - ( 0.5, 0.7) to[out=-30, in=0] - ( 0.3, 0.1) to[out=180, in=180] - ( 0.5, 0.6) to[out=0, in=120] - ( 1.3, 0.7) to[out=-60, in=60] - ( 0.4, -0.5) to[out=240, in=90] - ( 0, -2); - \end{scope} -\end{tikzpicture} -
diff --git a/examples/images/j-function.jpg b/examples/images/j-function-color.jpg Binary files differ.
diff --git a/examples/images/complex-lattice.tex b/examples/images/lattice.tex
diff --git a/examples/images/sphere-quotient.tex b/examples/images/sphere-quotient.tex @@ -1,30 +0,0 @@ -% This picture represents the isomorphism between the n-dimensional sphere and -% the quotient of the (n + 1)-dimensional simple orthogonal group by the -% n-dimensional simple orthogonal group -% Copyright Pablo (C) 2023 -\begin{tikzpicture}[scale=0.5] - % The sphere - \begin{scope} - \clip (-3, -3) rectangle (3, 2.625); - \draw (0, 0) circle (3); - \end{scope} - - % The equator - \begin{scope} - \clip (-3, 0) rectangle (3, -3); - \draw ellipse (3 and 1); - \end{scope} - - % Greenwhich - \begin{scope} - \clip (-3, -3) rectangle (0, 2.625); - \draw ellipse (1 and 3); - \end{scope} - - \draw (-3, 2.625) -- ( 1.5, 2.625) - -- ( 3, 3.375) node[right]{$T_p \mathbb{S}^n$} - -- (-1.5, 3.375) - -- cycle; - \filldraw[black] (0, 3) circle (2pt) node[right]{$p$}; - \draw (0, 3.375) node[above]{$\operatorname{SO}_n$}; -\end{tikzpicture}
