Interface EuclideanSpace<V>

All Superinterfaces:

AffineSpace<V>

public interface EuclideanSpace<V>
extends AffineSpace<V>

Represents a Euclidean space.

A Euclidean space is an affine space equipped with a metric (distance function) and an inner product. This allows measurement of distances, angles, and norms.

Key properties: - All affine space operations - Distance measurement between points - Norm (length) of vectors - Inner product (dot product)

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Method Summary

Modifier and Type	Method	Description
default Real	angle(V u, V v)	Computes the angle between two vectors.
default boolean	areOrthogonal(V u, V v)	Checks if two vectors are orthogonal (perpendicular).
default Real	distance(V a, V b)	Computes the distance between two points.
Real	innerProduct(V u, V v)	Computes the inner product (dot product) of two vectors.
Metric<V>	metric()	Returns the metric for this Euclidean space.
Real	norm(V vector)	Computes the norm (length) of a vector.

Methods inherited from interface AffineSpace

barycenter, difference, interpolate, translate

Method Details

metric

Metric<V> metric()

Returns the metric for this Euclidean space.

The metric defines the distance function d(x,y).

Returns:

the metric

distance

default Real distance(V a,
 V b)

Computes the distance between two points.

This is a convenience method that delegates to the metric.

Parameters:

a - the first point

b - the second point

Returns:

the distance between a and b

norm

Real norm(V vector)

Computes the norm (length) of a vector.

For Euclidean spaces, this is the L2 norm: √(x₁² + x₂² + ... + xₙ²)

Parameters:

vector - the vector

Returns:

the norm of the vector

innerProduct

Real innerProduct(V u,
 V v)

Computes the inner product (dot product) of two vectors.

For Euclidean spaces: ⟨u,v⟩ = u₁v₁ + u₂v₂ + ... + uₙvₙ

Parameters:

u - the first vector

v - the second vector

Returns:

the inner product

angle

default Real angle(V u,
 V v)

Computes the angle between two vectors.

Returns the angle in radians, in the range [0, π]. Uses the formula: cos(θ) = ⟨u,v⟩ / (‖u‖ ‖v‖)

Parameters:

u - the first vector

v - the second vector

Returns:

the angle in radians

areOrthogonal

default boolean areOrthogonal(V u,
 V v)

Checks if two vectors are orthogonal (perpendicular).

Vectors are orthogonal if their inner product is zero.

Parameters:

u - the first vector

v - the second vector

Returns:

true if orthogonal