Scale and Ticks

Scale maps data domains to coordinate domains and handles tick generation and formatting (D3 mental model, design.md §7.3). It is the positioning foundation for M8 math constructs (axes/numberLine/functionGraph/riemann etc.). All Scales are pure TS and run headlessly.

Scale interface

interface Scale<TDomain = number, TRange = number> {
  (value: TDomain): TRange; // forward map (callable)
  invert(value: TRange): TDomain; // inverse map
  ticks(count?: number): TDomain[]; // ~count nice ticks
  tickFormat(count?: number, spec?: string): (v: TDomain) => string;
  readonly domain: readonly [TDomain, TDomain];
  readonly range: readonly [TRange, TRange];
}

Four scale types

Factory	Purpose
linearScale(domain, range)	Linear mapping
powScale(domain, range, exponent?)	Power mapping (0.5 = sqrt scale)
logScale(domain, range, base?)	Log mapping (domain must be strictly positive)
timeScale([Date, Date], range)	Time scale; ticks aligned to calendar (UTC)

import { linearScale, logScale, powScale, timeScale } from "@intermact/core";

const x = linearScale([0, 100], [0, 10]);
x(50); // 5
x.invert(5); // 50
x.ticks(5); // [0, 20, 40, 60, 80, 100]
x.tickFormat(5)(20); // "20"

const y = logScale([1, 1000], [0, 3]);
y.ticks(3); // [1, 10, 100, 1000]

Tick algorithm

ticks uses D3's "nice number" algorithm: step is always 1 / 2 / 5 × 10^k. Decimal places in tickFormat derive from tick step; spec supports a minimal subset: "%" (percent) and ".<n>f" (fixed decimal).

logScale ticks fall on integer powers of base; for small spans, 1–9 subdivisions under decimal; timeScale picks calendar intervals (second/minute/hour/day/week/month/year) closest to target density.

Related examples

• scale/scale-playground — linear/pow/log/time tick distribution + tickFormat
• scale/log-plot — 2^x as a straight line on log y-axis