Struct Motion 

pub struct Motion<T: Number = Scalar> { /* private fields */ }

An affine map as it moves geometry: a Pose’s rigid motion (see Pose::motion), a plain translation, a mirror in a plane, or a scaling (Motion::scaling, the one that is no isometry) — what a body is moved, patterned, mirrored or scaled by.

A point p goes to A p + position, with A the matrix whose columns are axes: a rotation’s, a mirror’s reflection or a scaling’s diagonal. Without axes A is the identity and nothing is multiplied: a translation moves every point by one addition per coordinate, as exactly as an interval addition can.

Implementations

impl<T: Number> Motion<T>

pub fn translation(offset: Vector3<T>) -> Self

Moving every point by offset.

pub fn mirror(point: &Vector3<T>, normal: &Vector3<T>) -> GeopResult<Self>

Mirroring in the plane through point with the normal normal, which need not be unit: with n the unit normal, p goes to p - 2 ((p - point) . n) n — A = I - 2 n nᵀ, and the position 2 (point . n) n.

pub fn mirrors(&self) -> bool

Whether it mirrors: turns a right-handed frame into a left-handed one, and with it the side of a surface its normal points to.

pub fn turns(&self) -> bool

Whether it turns or mirrors directions at all, rather than only moving points.

pub fn position(&self) -> Vector3<T>

Where it moves the origin to: what it adds to every point it has turned.

pub fn rotate(&self, d: &Vector3<T>) -> Vector3<T>

The direction d turned — or mirrored; a translation leaves it as it is.

pub fn apply(&self, p: &Vector3<T>) -> Vector3<T>

The point p moved.

impl Motion

pub fn affine(columns: [Vector3; 3], position: Vector3) -> GeopResult<Self>

The affine map p -> A p + position, A the matrix whose columns are columns: what a body is scaled by, or carried by past the end of a deformation’s zone (geop_core_geometry::deform). No isometry in general — lengths and angles change, directions it turns are no longer unit, and only a body’s geometry is moved by it, whose NURBS map exactly (an affine map of their homogeneous control points). It mirrors where the determinant of A is negative, and fails where the determinant could be zero, which would flatten everything.

pub fn scaling(center: &Vector3, factors: [Scalar; 3]) -> GeopResult<Self>

Scaling about center by factors along x, y and z: p goes to center + diag(factors) (p - center) (see Motion::affine). An odd number of negative factors mirrors. Fails for a factor that could be zero.

pub fn apply_frame( &self, frame: &CoordinateSystem, ) -> GeopResult<CoordinateSystem>

The frame frame moved. Fails for a mirror, which would leave it left-handed.

Trait Implementations

impl<T: Clone + Number> Clone for Motion<T>

fn clone(&self) -> Motion<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Copy + Number> Copy for Motion<T>

impl<T: Debug + Number> Debug for Motion<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: PartialEq + Number> PartialEq for Motion<T>

fn eq(&self, other: &Motion<T>) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl<T: PartialEq + Number> StructuralPartialEq for Motion<T>