How To Produce Ultra-Compact Vector Graphic Plots With Orthogonal Distance Fitting

2026-04-14 · Source: Towards Data Science · Field: Technology & Digital — Software Development & Engineering, Mathematics & Computational Sciences · Depth: Expert, long

Summary

A new algorithm, Algorithm F, and its Python implementation in the `bbai` package, efficiently generate minimal Bézier path representations for mathematical functions, suitable for vector graphics. Unlike traditional methods like Matplotlib which use many piecewise linear segments (e.g., 250 for `exp(−t)cos(−2πt)`), this approach approximates functions using significantly fewer cubic Bézier curves (e.g., 8 for the same function), resulting in smaller, visually indistinguishable vector graphics. The algorithm leverages Chebyshev series fitting for rapid convergence and a trust-region optimizer to fit Bézier curves, iteratively splitting the domain until a target orthogonal distance threshold (default 1.0 × 10^-2) is met. It also details how to convert the generated TikZ commands into SVG images using MetaPost, offering a practical workflow for producing high-quality, scalable vector plots.

Key takeaway

For AI Scientists or data visualization engineers creating scalable plots, adopting the `bbai` package for vector graphics generation can drastically reduce file sizes without compromising visual quality. You should consider integrating this Bézier path fitting approach, especially for analytic or highly differentiable functions, to produce more efficient and portable SVG outputs compared to traditional piecewise linear approximations. This method streamlines the creation of crisp, zoom-independent mathematical visualizations for web or print.

Key insights

Efficiently generate minimal Bézier path representations for functions using Chebyshev series and trust-region optimization.

Principles

• Vector graphics benefit from minimal Bézier curve representations.
• Chebyshev series fitting offers rapid geometric convergence.
• Trust-region optimizers avoid saddle points in curve fitting.

Method

Algorithm F fits a Chebyshev series to a function, then uses a trust-region optimizer to find an optimal cubic Bézier curve. If the orthogonal distance exceeds a threshold, the domain is split, and the process repeats.

In practice

• Use `bbai.graphics.BezierPath` to fit functions.
• Export TikZ output to SVG using MetaPost.
• Specify `dst_xmin`, `dst_xmax`, `dst_ymin`, `dst_ymax` for plot scaling.

Topics

• Orthogonal Distance Fitting
• Cubic Bézier Curves
• Chebyshev Series
• Vector Graphics
• SVG Generation

Code references

• rnburn/bbai

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Editorial summary, takeaway, and curation by AIssential. Original article published by Towards Data Science.