Euclid library

The optional cel-euclid library provides concrete two-dimensional geometry types and operations. A host installs it once on a fresh OpLookup with cel_euclid::install. The core language does not install geometry implicitly. Install cel-std separately for scalar operations; either installation order preserves both libraries’ overloads.

Conventions

Every coordinate, extent, angle component, and matrix coefficient has type f64. The Rust types use Euclid’s unknown units; CEL does not expose generic unit parameters. Operand types must match the listed signatures exactly: write 1.0, 1f64, or 1 as f64 where an operation requires f64. There are no implicit numeric casts or return-type-only overloads.

Signatures use Rust-style parameter and return-type notation to describe CEL calls, not to declare functions. T denotes only the concrete alternatives listed with a signature; it is not CEL generic syntax.

Every named operation with a first argument also accepts receiver syntax: name(value, args...) and value.name(args...) are equivalent. A unary operation additionally accepts value.name. Only identity_transform() has no receiver. Operators use their ordinary CEL spelling.

Except for normalize, inverse, and outer_transformed_rect, operations preserve Euclid’s ordinary floating-point behavior. Overflow, division by zero, NaNs, and infinities do not by themselves produce evaluation errors. Record construction does not validate finiteness, order bounds, or require nonnegative sizes.

Types

Each record requires every listed field exactly once, in any order. Fields must have the indicated types. Missing, repeated, unknown, or incorrectly typed fields cause a parse error. Record construction takes constant time and space.

Point2D

A position with fields x: f64 and y: f64.

Point2D { x: 1.0, y: 2.0 }
// => Point2D { y: 2.0, x: 1.0 }

Adding a vector produces a point; subtracting two points produces a vector. Access coordinates with x and y.

Vector2D

A displacement with fields x: f64 and y: f64.

Vector2D { x: 3.0, y: 4.0 }
// => Vector2D { y: 4.0, x: 3.0 }

Vectors support arithmetic, dot, cross, length, and normalize.

Size2D

Two extents with fields width: f64 and height: f64. Construction permits zero and negative extents.

Size2D { width: 4.0, height: 6.0 }
// => Size2D { height: 6.0, width: 4.0 }

Access extents with width and height.

Rect

An axis-aligned rectangle with fields origin: Point2D and size: Size2D. Its maximum coordinates are the origin coordinates plus the extents. Construction does not reorder negative extents.

Rect {
    origin: Point2D { x: 1.0, y: 2.0 },
    size: Size2D { width: 4.0, height: 6.0 }
}
// => Rect { size: Size2D { width: 4.0, height: 6.0 }, origin: Point2D { x: 1.0, y: 2.0 } }

See origin, size, and contains.

Box2D

An axis-aligned box with fields min: Point2D and max: Point2D. Construction stores the supplied endpoints without sorting them.

Box2D {
    min: Point2D { x: 1.0, y: 2.0 },
    max: Point2D { x: 5.0, y: 8.0 }
}
// => Box2D { max: Point2D { x: 5.0, y: 8.0 }, min: Point2D { x: 1.0, y: 2.0 } }

See min and max, size, and contains.

Angle

An angle with one field, radians: f64. Construction does not wrap the value to a particular interval.

Angle { radians: 1.5 }
// => radians(1.5)

Use degrees or radians to construct an angle from a scalar or extract its magnitude.

Transform2D

An affine transform with six f64 fields: m11, m12, m21, m22, m31, and m32. It maps a point (x, y) to:

x' = m11 * x + m21 * y + m31
y' = m12 * x + m22 * y + m32

Transform2D {
    m11: 1.0, m12: 0.0,
    m21: 0.0, m22: 1.0,
    m31: 0.0, m32: 0.0
}
// => identity_transform()

Use then to compose transforms. Vectors use only the linear coefficients and ignore translation.

Operators

Equality: `==`, `!=`

a: T == b: T -> bool
a: T != b: T -> bool

T is any one of the seven geometry types. Compares corresponding stored components using f64 equality; it does not compare geometric equivalence.

Parameters

Parameter	Description
`a`, `b`	Geometry values of the same type.

Parameter	Description
`value`	A vector or size.
`factor`	The scalar multiplier or divisor.

Parameter	Description
`value`	The rectangle or box to expand.
`dx`, `dy`	Expansion on each horizontal and vertical side. Negative values shrink.

Parameter	Description
`outer`	The containing rectangle.
`inner`	The rectangle to test.

Parameter	Description
`outer`	The containing box.
`inner`	The box to test.

Keyboard shortcuts

The Common Expression Language