infinite_math_plot 0.1.0

A Flutter package that renders interactive mathematical graphs on a simulated infinite coordinate plane.

Changelog

All notable changes to this package will be documented here.

The format follows Keep a Changelog, and this project uses Semantic Versioning.

---

0.1.0 - 2026-05-12

First public release. This is the initial version of the package, so everything listed here is new.

Added

Core widget

• InfiniteMathPlot — a StatefulWidget that accepts an equation string and renders an interactive graph
• Single-equation mode via the equation parameter
• Multi-equation mode via the equations parameter (list of EquationConfig)
• Mutual exclusion assertion: providing both equation and equations, or neither, throws at construction time
• xMin, xMax, yMin, yMax parameters to set the initial viewport (default: -10 to 10 on both axes)
• showGrid, showAxes, enableZoom, enablePan boolean flags, all defaulting to true
• graphColor and strokeWidth for single-equation styling
• samplingPrecision to control sample density (default: 2.0 points per logical pixel)
• Adaptive layout via LayoutBuilder — fills available space and maintains math aspect ratio on resize

Equation parser

• Parses Cartesian (y = f(x)), implicit (F(x,y) = 0), parametric (x = f(t), y = g(t)), and polar (r = f(θ)) equations from plain strings
• Supported functions: sin, cos, tan, asin, acos, atan, sqrt, abs, exp, log, pow
• Supported constants: pi, π, e, theta, θ
• ParseException with a human-readable message and character position on invalid input
• Canonical serialization via serialize(Expression) — stable across round-trips

Sampling

• Cartesian sampling: iterates x over the viewport, evaluates y = f(x)
• Polar sampling: iterates θ from 0 to 2π, computes x = r·cos(θ), y = r·sin(θ)
• Parametric sampling: iterates t from 0 to 2π, evaluates x = f(t) and y = g(t) independently
• Implicit sampling: marching squares over a 50×50 grid, linear interpolation of zero-crossings
• Sample cache keyed on (equation, viewport, samplingPrecision, screenWidth) — no recomputation when nothing changes

Discontinuity detection

• isUndefined: classifies NaN, +Infinity, -Infinity as undefined — path is lifted at these points
• isAsymptote: detects true vertical asymptotes (values straddling the viewport from above and below) without breaking steep-but-continuous functions like y = x³

Rendering

• GraphPainter (CustomPainter) draws grid → axes → curves in that order
• Grid interval snaps to "nice" numbers (1, 2, 5, 10, 20, 50, …) based on the current viewport scale
• Axes drawn only when x=0 or y=0 is within the viewport
• Tick marks with numeric labels on both axes
• Curve paths use moveTo after null entries (discontinuities) and lineTo otherwise
• shouldRepaint returns false when nothing has changed — avoids unnecessary redraws

Gesture handling

• Pinch-to-zoom: applies incremental scale delta each frame (not cumulative), centered on the focal point
• Scroll-wheel zoom: scroll down = zoom out (×0.9), scroll up = zoom in (×1.1)
• Drag-to-pan: converts screen delta to math units via the coordinate transformer
• All gestures respect enableZoom and enablePan flags

Coordinate transformer

• toScreen(x, y) — linear mapping from math coordinates to screen pixels, Y-axis inverted
• toMath(screenOffset) — algebraic inverse of the forward transform
• Round-trip accuracy within floating-point tolerance (< 1e-10)

Data models

• Viewport — immutable value class with copyWith, structural equality, and hashCode
• ParsedEquation — holds the expression tree, equation type, and canonical serialized form
• ParseException — implements Exception with message and position
• EquationConfig — equation string + color + strokeWidth with structural equality
• SampleCacheKey — composite cache key with structural equality on all four fields
• GraphState — runtime state with copyWith
• EquationType enum — cartesian, implicit, parametric, polar

Example app

• Interactive demo in example/ with 8 presets, a custom equation input field, and toggles for all display and gesture options

Tests

• 241 tests covering all components
• Property-based round-trip tests for the equation parser and coordinate transformer
• Property-based classification test for the discontinuity detector
• Unit tests for all components
• Widget tests for InfiniteMathPlot

---

Upcoming

Things I'm planning for future releases:

• Configurable parametric t-range (currently fixed at 0 to 2π)
• Tap-to-inspect: show the y-value at a tapped x position
• Isolate-based sampling for very high precision or many simultaneous equations
• Animation support for time-varying equations
• Export to image

---