Parameters and expressions

Parameters turn one design document into a family of evaluated variants. InvariantCAD stores formulas as immutable expression trees instead of executing arbitrary JavaScript during evaluation.

Supported dimensions

Dimension	Constructors	Base unit
Length	`mm`, `cm`, `meters`, `inch`	millimetre
Angle	`rad`, `deg`	radian
Scalar	`scalar`	unitless
Mass density	`kgPerCubicMillimeter`, `kgPerCubicMeter`, `gramsPerCubicCentimeter`	kg/mm³

const width = cad.parameter.length("width", mm(80), {
  min: mm(20),
  max: mm(200),
  label: "Width",
  description: "Overall body width",
});

const taper = cad.parameter.angle("taper", deg(3));
const scale = cad.parameter.scalar("scale", scalar(1));
const density = cad.parameter.massDensity(
  "density",
  kgPerCubicMeter(2700),
);

Defaults and bounds may themselves reference parameters that belong to the same design. Evaluation resolves the complete dependency graph and reports cycles, missing values, non-finite results, and bound violations as diagnostics.

Arithmetic

Every expression exposes immutable arithmetic methods:

const wall = cad.parameter.length("wall", mm(3));
const clearance = cad.parameter.length("clearance", mm(0.25));
const outside = cad.parameter.length("outside", mm(40));

const inside = outside.sub(wall.mul(2)).sub(clearance.mul(2));
const halfOutside = outside.div(2);
const positiveOffset = clearance.abs();

add and sub require the same dimension.
mul and div accept a scalar expression or finite number.
neg and abs preserve the dimension.
expr.min, expr.max, and trigonometric helpers construct additional serializable operations.

TypeScript prevents many dimension mistakes, while runtime validation protects documents received from untyped or hostile sources.

Vectors

Use vector helpers to preserve component dimensions:

const size = vec3(width, mm(30), wall);
const point = vec2(width.mul(0.25), mm(0));
const scale3d = scalarVec3(scale, scalar(1), scalar(1));
const rotation = angleVec3(deg(0), taper, deg(90));

vec2 and vec3 contain lengths. scalarVec3 is used for scale and directions; angleVec3 is used for Euler rotations.

Evaluation overrides

Override values by parameter ID:

const result = await evaluator.evaluate(document, {
  parameters: {
    width: 125,
    taper: Math.PI / 36,
    density: 2.7e-6,
  },
});

Override numbers use base units, not the constructor originally used by the author. width: 125 means 125 mm, even if the default was written as inch(4.5).

Do not pass deg(5) or mm(20) as evaluation override values. Overrides are plain finite numbers because evaluation options are data, while expression objects belong to authoring.

Configuration overrides

A named configuration can bind parameters inside the document:

const compact = cad.configuration("compact", (configuration) => {
  configuration.parameter(width, mm(60));
  configuration.parameter(wall, mm(2.5));
});

At evaluation, select it by reference during authoring or by stable ID after serialization. Explicit evaluation overrides apply within the selected configuration context. See configurations and BOMs.

Parameter ownership

Parameters are bound to the DesignBuilder that created them. Cross-design use throws immediately:

const first = design("first");
const foreignWidth = first.parameter.length("width", mm(10));

const second = design("second");
// second.box(...foreignWidth...) is rejected during authoring.

This restriction guarantees that every expression reference can be represented inside one closed document.

Getting started

Modeling

Evaluation

Analysis and interchange

Parameters and expressions

Supported dimensions

Arithmetic

Vectors

Evaluation overrides

Configuration overrides

Parameter ownership

​Supported dimensions

​Arithmetic

​Vectors

​Evaluation overrides

​Configuration overrides

​Parameter ownership

Supported dimensions

Arithmetic

Vectors

Evaluation overrides

Configuration overrides

Parameter ownership