Math

Math

math/vector2.mojo, math/vector3.mojo, math/matrix4.mojo and math/projection.mojo. Ported from three.js with the same conventions.

three.js: Vector2, Vector3, Matrix4, Matrix4.makePerspective, makeOrthographic, lookAt.

Vector2 and Vector3

Vector2(x, y) and Vector3(x, y, z) hold Float32 components. Both are value types. Assignment copies.

Vector3 member	Meaning
dot(other) -> Float32	The dot product.
length() -> Float32	The Euclidean length.
add(other), sub(other)	Change self in place.
cross(other)	self = self × other.
normalize()	Scale to unit length. A zero vector stays zero.
a + b, a - b, a * f, -a	Return a new vector.

Matrix4

Column-major storage, as three.js and OpenGL. Element (row, col) is at col * 4 + row. The translation is at elements 12 to 14.

set takes its sixteen arguments in row-major order, so a matrix in source reads as it does on paper. That asymmetry is three.js's.

Member	Meaning
Matrix4()	The identity.
set(n11, n12, ..., n44)	Every element, row by row.
get(row, col), put(row, col, value)	One element.
multiply(other)	self = self * other. The right-hand matrix applies first.
premultiply(other)	self = other * self.
transpose(), invert(), determinant()	As named. A singular matrix inverts to zeros.
normal_matrix() -> Matrix4	The inverse transpose, for normals.
extract_rotation() -> Matrix4	The rotation with scale and translation removed.
transform_point(p) -> Vector3	Apply with w = 1 and divide by w.
transform_w(p) -> Float32	The w that transform_point divides by.
transform_direction(d) -> Vector3	Apply with w = 0.

Builders: translation(x, y, z), scaling(x, y, z), rotation_x(angle), rotation_y(angle), rotation_z(angle). A rotation takes an Angle, so rotation_z(90.0) does not compile.

var m = translation(10, 0, 0)
m.multiply(rotation_z(Angle(90.0, DEGREE)))
m.multiply(translation(-10, 0, 0))     # a rotation about (10, 0, 0)

Projection

Function	Meaning
perspective(left, right, top, bottom, near, far)	Camera space to normalized device space, with perspective.
orthographic(left, right, top, bottom, near, far)	The same without perspective. w stays one.
look_at(eye, target, up)	The view matrix of a camera at eye.
viewport(width, height)	Normalized device space to pixels. Rows count down.

Each raises for a degenerate volume, a camera at its own target, or an up vector along the view direction.

Normalized device space is unitless. World space is meters and screen space is pixels. The matrices meet in the middle.