Vector-Library

Vector-Library consists of vector properties and common vector algebraic functions to perform various arithmetic operations on any dimensional vectors and scalars. This is a reusable library that any .NET 5.0 or above projects can utilize as an application dependency.

Vector-Master Demo

Try vector-master demo application built on top of this library at,
vector-master.azurewebsites.net.

Prerequisites

Currently, Vector-Library dependency is available for local installation only.
Vector-Library requires .NET 5.0 (v5.#.#) or .NET 6.0 (v6.#.#).

Get Started

Add VectorLibrary.dll to project dependencies.
Refer the content from the code by adding using VectorLibrary; at top-level statements or global usings.

Implementation Overview

VectorLibray is formed with following class-object structure.

ICommonVectorOperation interface

This provide common vector operations which are applied to both 3-dimensional and n-dimensional (higher than 3-dimensional) vectors.

I3DVectorOperations interface

This provides vector operations which only 3-dimensional vectors can perform.

IVector interface

This element reference the both 3-dimensional and n-dimensional vector types.

public interface IVector : ICommonVectorOperations

Vector class

This is an abstract element which provide common functionable operations to both 3-dimensional and n-dimensional vectors.

public abstract class Vector : IVector

Vector3D class

This is the main class which represents 3-dimensional vector in action.

public class Vector3D : Vector, I3DVectorOperations

VectorND class

This is the main class which represents n-dimensional ((higher than 3-dimensional)) vector in action.

public class VectorND : Vector

Following tables indicate the implementation structure of VectorLibray for both 3-dimensional Vector3D and n-dimensional VectorND vectors.

Properties

Name	Type	Availability	Description
I	decimal	Vector3D only	Get the i component of the vector
J	decimal	Vector3D only	Get the j component of the vector
K	decimal	Vector3D only	Get the k component of the vector

Constructors

For Vector3D

Name	Description
Vector3D(decimal i, decimal j, decimal k)	Initializes Vector3D instance

For VectorND

Name	Description
VectorND(params decimal[] vector)	Initializes VectorND instance

Enums

AngleUnit enumeration defines the unit of angle when calculating the angle between two vectors.

Option	Description
Degree	Unit of angle with Radians (θ°)
Radian	Unit of angle with Degrees (θ rad)

DivisionMode enumeration defines the ratio division method to follow when performing vector division.

Option	Description
Internal	Internal ratio division
External	External ratio division

Methods

Name	Return Type	Availability	Description
AddTo(IVector)	IVector	Vector3D and VectorND	Addition of this vector with provided IVector
AngleWith(IVector, [AngleUnit])	IVector	Vector3D and VectorND	Compute the angle between this vector and provided IVector
CrossProduct(IVector)	Vector3D	Vector3D only	Perform the vector product with this vector and provided IVector
DistanceWith(IVector)	IVector	Vector3D only	Calculate the Euclidean distance between this vector and provided vector
DivideInto(decimal, [DivisionMode])	IVector	Vector3D and VectorND	Divide this vector into the given ratio internally or externally
DotProduct(IVector)	decimal	Vector3D and VectorND	Perform the scalar product with this vector and provided IVector
GetDimension()	int	Vector3D and VectorND	Calculate the vector dimension
GetMagnitude()	decimal	Vector3D and VectorND	Calculate the magnitude of this vector
GetUnitVector()	IVector	Vector3D and VectorND	Calculate the unit vector along this vector
MultiplyByScalar(decimal)	IVector	Vector3D and VectorND	Perform scalar multiplication with this vector
Negate()	IVector	Vector3D and VectorND	Negate this vector
Print([int])	string	Vector3D and VectorND	Format this vector as row matrix notation
PrintF([int])	string	Vector3D only	Format this vector as cartesian positional vector notation with i, j, k unit vectors
ScalarProjectionOn(IVector)	decimal	Vector3D and VectorND	Scalar projection of this vector on to provided IVector
SubtractFrom(IVector)	IVector	Vector3D and VectorND	Subtraction of this vector from provided IVector
ToArray()	decimal[]	Vector3D and VectorND	Convert this vector to an array
ToVector3D()	Vector3D	VectorND only	Convert this vector to Vector3D
ToVectorND()	VectorND	Vector3D only	Convert this vector to VectorND
VectorProjectionOn(IVector)	IVector	Vector3D and VectorND	Vector projection of this vector on to provided IVector

Usage

Following section describe the general usage of VectorLibrary to perform vector operations.

Initialize New Vector

Define new 3-dimensional vector u = 2i + 3j - k

Vector3D u = new(2, 3, -1);

Initialize New n-dimensional Vector
Define new n-dimensional vector u = [1, 3, -5, 6, -2]

VectorND u = new(new decimal[] { 1, 3, -5, 6, -2 });

Or simply

VectorND u = new(1, 3, -5, 6, -2);

Read Vector

Any defined vector can be read in two ways as either a string formatted text or an array. If the vector is null, the function throws VectorNotInitializedException. Using Print function, a vector can be read as a string.

Console.WriteLine(u.Print());

Using PrintF function, a 3-dimensional vector can be read as a string.

Console.WriteLine(u.PrintF());

The Print and PrintF function takes optional parameter int precision to round-off decimal figures when reading. The default precision is 2 decimals.

Bothe of the vector types can be converted to decimal[] array using ToArray function.

decimal[] array = u.ToArray();

Vector Properties

Any vector has three main alias properties as Dimension, Magnitude and UnitVector. These properties can be calculate as follows.

int dimension = u.GetDimension();
decimal magnitude = u.GetMagntude();
IVector unitVector = u.GetUnitVector();

Vector Conversion

Convert a 3-dimensional vector u to an n-dimensional vector v.

VectorND v = u.ToVector3D();

Convert a 3-dimensional vector v to an n-dimensional vector u. However, the vector v's order must be 3 to perform this conversion, otherwise the function throws InvalidCastException.

Vector3D v = u.ToVectorND();

Negate Vector

Negating results the negative vector of current vector u and v as follows.

Vector3D u = new(1, -3, 2);
IVector negativeOfU = u.Negate();

VectorND v = new(-2, 1, 4, -3);
IVector negativeOfV = v.Negate();

Distance between Vectors

The Euclidean distance of two vectors u to v and u to w can be calculated as follows. The function throws VectorNotInitializedException if vector u, v or w is null and throws InvalidVectorOperationException when provided any non 3-dimensional vector.

Vector3D u = new(1, 5, 3);
IVector v = new Vector3D(2, -3, 4);
IVector w = new VectorND(4, 1, -7);

decimal distanceFromUtoV = u.DistanceWith(v);
decimal distanceFromUtoW = u.DistanceWith(w);

Vector Operations

IVector object can perform following operations.

Addition

Add two same-dimensional vectors u and v. The function throws VectorNotInitializedException if vector u or v is null and throws VectorSpaceNotMatchException if the dimension of both vectors do not match.

IVector result = u.AddTo(v);

Subtraction

Subtract two same-dimensional vectors u from v. The function throws VectorNotInitializedException if vector u or v is null and throws VectorSpaceNotMatchException if the dimension of both vectors do not match.

IVector result = u.SubtractFrom(v);

Scalar Multiplication

Multiply vector u by scalar value k. The function throws VectorNotInitializedException if vector u is null.

IVector result = u.MultiplyByScalar(k);

Ratio Division

A vector can be divided into a given ratio r internally or externally. Note that the ratio will be taken as r:1 while performing this action. The function throws VectorNotInitializedException if vector current is null, throws InvalidVectorOperationException if the ratio is negative and throws ZeroExternalDivisionException if attempt to perform 1:1 external division.

IVector u = new Vector3D(1, 5, -2);
// Divide u into 3:1 ratio internally
IVector result1 = u.DivideInto(3, DivisionMode.Internal);
// Divide u into 3:4 ratio externally
IVector result2 = u.DivideInto(0.75, DivisionMode.External);

IVector v = new VectorND(2, -3, -1, 5);
// Divide v into 1:1 ratio internally (exactly into two halves)
IVector result3 = v.DivideInto(1, DivisionMode.Internal);
// Divide v into 5:2 ratio externally
IVector result4 = v.DivideInto(2.5, DivisionMode.External);

Dot Product (Scalar Product)

Calculate dot product of two same-dimensional vectors u from v. The function throws VectorNotInitializedException if vector u or v is null and throws VectorSpaceNotMatchException if the dimension of both vectors do not match.

decimal result = u.DotProduct(v);

Cross Product (Vector Product)

Calculate cross product of two 3-dimensional vectors u from v. The function throws VectorNotInitializedException if vector u or v is null, throws VectorSpaceNotMatchException if the dimension of both vectors do not match and throws InvalidVectorOperationException when provided any non 3-dimensional vector. VectorSpaceNotMatchException if the dimension of both vectors do not match.

Vector3D result = u.CrossProduct(v);

Angle within Vectors

Calculate the angle between two same-dimensional vectors u from v. The function throws VectorNotInitializedException if vector u or v is null and throws VectorSpaceNotMatchException if the dimension of both vectors do not match. The unit of angle can be defined in the function argument AngleUnit enum. The default unit is radian.

decimal angleInDegree = u.AngleWith(v, AngleUnit.Degree);
decimal angleInRadian = u.AngleWith(v, AngleUnit.Radian);

Projection

Calculate the scalar projection of two same-dimensional vectors u on to v. The function throws VectorNotInitializedException if vector u or v is null and throws VectorSpaceNotMatchException if the dimension of both vectors do not match.

decimal projection = u.ScalarProjectionOn(v);

Calculate the vector projection of two same-dimensional vectors u on to v. The function throws VectorNotInitializedException if vector u or v is null and throws VectorSpaceNotMatchException if the dimension of both vectors do not match.

IVector projection = u.VectorProjectionOn(v);