Xah Talk Show 2025-09-05 Ep697 Wolfram Language Coding Session, Write Custom Command Export 2D Graphics to SVG

video summary

• The video discusses the process of writing a custom Wolfram Language function to export 2D graphics to SVG format.
• The creator explains that the built-in export function in Wolfram Language produces inefficient SVG files, often generating large file sizes by representing simple shapes like circles using complex Bezier curves instead of direct SVG circle tags (0:50, 1:35, 1:50, 2:00).

• The goal is to create a more efficient export function.
• The creator outlines the challenges involved, such as handling coordinate transformations (scaling, translation, and y-axis flipping) from Wolfram Language's mathematical coordinate system to SVG's top-left origin system, and managing hierarchical and sequential styling directives in Wolfram Language graphics to apply them correctly in SVG (37:02, 48:37, 53:01).
• The video highlights the complexity of the task, estimating it would take significant time to implement robustly.

• Wolfram Language Tutorial
• Wolfram: Download Wolfram Engine
• Geometric Inversion
• Circle Inversion Gallery

geoInv = ((With[{x662 = #.#}, If[ x662 < 0.00000001, #, #/x662] ]) &);
cArray = CoordinateBoundsArray[{{-1, 1}, {-1, 1}}, Into[10] ];
hLines= (BlockMap[Line,#,2,1]&) /@ cArray;
vLines= (BlockMap[Line,#,2,1]&) /@ Transpose @ cArray;
gp1 = {hLines , vLines};
gp2 = gp1 /. Line[x_] :> Line[ geoInv /@ x ];

Graphics[gp1, Axes->True ]

Graphics[gp2, Axes->True ]

Export[
"xxy.svg",
Graphics[gp2, Axes->True ]
]

(*
write a command to export 2d graphics to svg.
we want to do this because the bultin Export function creates huge file size.
 *)

prim = Circle[{0,0}, 1]
Graphics[ prim, Axes -> True ]

Export["xxcircle.svg" , Graphics[ prim]]

(* HHHH------------------------------ *)

Clear[graphicsToString]

graphicsToString::usage = "
graphicsToString[g]
return a string, that is a svg format, representing Graphics object g.";

graphicsToString[ gra_Graphics ] := "
<?xml version=\"1.0\" encoding=\"UTF-8\"?>
<svg xmlns=\"http://www.w3.org/2000/svg\"
xmlns:xlink=\"http://www.w3.org/1999/xlink\"
width=\"1000\" height=\"1000\"

viewBox=\"0 0
1000 * x-scale + xtranvector,
1000 * y-scale + ytranvector \"
version=\"1.1\">
</svg>
"
Graphics[
{
Red,
Circle[{0,0}, 1],
Circle[{0,0}, 1],
Circle[{0,0}, 1], {
Red,
Circle[{0,0}, 1],
Circle[{0,0}, 1],
Circle[{0,0}, 1],
Blue, Thickness[],
Circle[{0,0}, 1],
Circle[{0,0}, 1],{
Red,
Circle[{0,0}, 1],
Circle[{0,0}, 1],
Circle[{0,0}, 1],
Blue, Thickness[],
Circle[{0,0}, 1],
Circle[{0,0}, 1],
Line[[{0,0}, {1,2}]],
Line[[{0,0}, {1,2}]],
Line[[{0,0}, {1,2}]]},
Line[[{0,0}, {1,2}]],
Line[[{0,0}, {1,2}]],
Line[[{0,0}, {1,2}]]},
Blue, Thickness[],
Circle[{0,0}, 1],
Circle[{0,0}, 1],
Line[[{0,0}, {1,2}]],
Line[[{0,0}, {1,2}]],
Line[[{0,0}, {1,2}]]}
]

<circle cx="0" cy="0" r="1"
 style="fill:yellow; stroke:blue; stroke-width:5" />

(* HHHH------------------------------ *)

exportGraphics::usage = "
exportGraphics[g, name]
export Graphics object g, to a file named name in current dir, in svg format.
g is a Graphics[] oject.
name is a string.";

exportGraphics[ gra_Graphics, filename_ ] := ""

(* HHHH------------------------------ *)

ExportString