logic gauge

src/logic/gauge.ts — Gauge conversion

Converts a player-entered track gauge into the scale constant Create uses for curves — a quadratic y = a·x² + b·x + c fitted exactly through three anchors (Cramer's rule). Pure functions, Node-testable.

Conversion basis: 1 block = 1 m = 1000 mm = 16 px, so px = mm × 16 / 1000 (1 px = 62.5 mm); 1 inch = 25.4 mm. The gauge is the center distance between the left and right rails.

Types & constants

GaugeAnchor

export interface GaugeAnchor {
	gaugeMM: number;   // gauge in mm
	scale: number;     // Create curve scale constant
}

GAUGE_ANCHORS

The three known anchor points (measured in-game):

export const GAUGE_ANCHORS: GaugeAnchor[] = [
	{ gaugeMM: 1435, scale: 0.755 },  // standard gauge
	{ gaugeMM: 1600, scale: 0.965 },  // Create default gauge
	{ gaugeMM: 1000, scale: 0.525 },  // meter gauge
];

QuadraticCoeffs

export interface QuadraticCoeffs {
	a: number;
	b: number;
	c: number;
}

DEFAULT_FIT

export const DEFAULT_FIT: QuadraticCoeffs = fitQuadratic(GAUGE_ANCHORS)!;

DEFAULT_GAUGE_MM / DEFAULT_GAUGE_PX

Create's default nominal gauge 1600 mm and its model px equivalent (1600 mm → 25.6 px).

export const DEFAULT_GAUGE_MM = 1600;
export const DEFAULT_GAUGE_PX = mmToPx(DEFAULT_GAUGE_MM); // 25.6

Fitting & scaling

fitQuadratic(points)

Fits the quadratic coefficients through three points via Cramer's rule. Returns null for invalid input (not exactly three points, or duplicate x values).

export function fitQuadratic(points: GaugeAnchor[]): QuadraticCoeffs | null;

gaugeMMToScale(gaugeMM, coeffs?)

Gauge (mm) → curve scale constant.

export function gaugeMMToScale(gaugeMM: number, coeffs: QuadraticCoeffs = DEFAULT_FIT): number;

scaleForPx(gaugePx, coeffs?)

Gauge entered directly in px → curve scale constant (converts to mm first, then fits).

export function scaleForPx(gaugePx: number, coeffs: QuadraticCoeffs = DEFAULT_FIT): number;

formatFit(coeffs?)

Formats the fit coefficients as a human-readable formula (negative coefficients shown as − rather than + -). Example: y = 1.24e-6·x² - 0.0025·x + 1.7756.

export function formatFit(coeffs: QuadraticCoeffs = DEFAULT_FIT): string;

Unit conversion

export function mmToPx(gaugeMM: number): number;     // mm → model gauge px (1/16 block)
export function pxToMM(gaugePx: number): number;     // model gauge px → mm
export function mmToInch(gaugeMM: number): number;   // mm → inch
export function inchToMM(gaugeInch: number): number; // inch → mm
export function inchToPx(gaugeInch: number): number; // inch → model gauge px
export function pxToInch(gaugePx: number): number;   // model gauge px → inch

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