V

Yet another, reinvented, multidimensional Vector library designed for work with changing dimensionality.

Requirements

• Microsoft .NET Standard 2.1
• Microsoft .NET 6.0

Projects

• V - Main functionality
• V.Samples - Usage samples
• V.UnitTests - Unit tests
• V.Benchmarks - Benchmarks

Setup

• Download repository
• Open V.sln in Visual Studio (i'm using 2019 Community)
• Build project V (check project properties for output path, most likely ./bin/Debug/)
• V.dll is now ready to be added as reference in your projects

Future / TODO

• Function RotateAroundAxis should work in all dimensions (currently only in 3)

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Samples

Here are some usage examples that might be helpful. Code used for samples and images is available in V.Samples project.

Vector arithmetic operators

Addition

Vector add1 = new Vector(1, 2) + new Vector(2, 1);
// add1 is now [3, 3]

Vector add2 = new Vector(1, 2) + 2;
// add2 is now [3, 4]

Vector add3 = 2 + new Vector(2, 1);
// add3 is now [4, 3]

Visualization of two 3 dimensional vectors (in green) resulting in third vector as a sum (in blue)

Subtraction

Vector sub1 = new Vector(1, 2) - new Vector(2, 1);
// sub1 is now [1, 1]

Vector sub2 = new Vector(1, 2) - 2;
// sub2 is now [-1, 0]

Vector sub3 = 2 - new Vector(2, 1);
// sub3 is now [0, 1]

Visualization of two 3 dimensional vectors (in green) resulting in third vector as a diffrence (in blue)

Multiplication

Vector mul1 = new Vector(1, 2) * new Vector(2, 1);
// mul1 is now [2, 2]

Vector mul2 = new Vector(1, 2) * 2;
// mul2 is now [2, 4]

Vector mul3 = 2 * new Vector(2, 1);
// mul3 is now [4, 2]

Division

Vector div1 = new Vector(1, 2) / new Vector(2, 1);
// div1 is now [0.5, 2]

Vector div2 = new Vector(1, 2) / 2;
// div2 is now [0.5, 1]

Vector div3 = 2 / new Vector(2, 1);
// div 3 is now [1, 2]

Inversion

Vector inv = -new Vector(1, -2, 3);
// inv is now [-1, 2, -3]

Functions

Min / Max

Produces vector with minimal/maximal values in every dimension.

Vector min1 = Vector.Min(new Vector(-1, 1, -1), new Vector(1, -1, 1));
// min1 is now [-1, -1, -1]

Vector min2 = Vector.Min(new Vector(1, 2, 3), new Vector(1, -1, 1), new Vector(5, 1, -1));
// min2 is now [1, -1, -1]

Vector max = Vector.Max(new Vector(-1, 1, -1), new Vector(1, -1, 1));
// max is now [1, 1, 1]

Normalize

Produces unit vector.

Vector nor = Vector.Normalize(new Vector(12, 0, 0));
// nor is now [1, 0, 0]

Dot

Produces dot product of two vectors.

double dot = Vector.Dot(new Vector(1, 0), new Vector(0.5, 0.5));
// dot is now 0.5

AngleDifference

Produces angle difference between two vectors (in radians).

double diff = Vector.AngleDifference(new Vector(0, 1), Vector.Create(2, 0), new Vector(1, 0));
// diff is now half PI

RotateAroundAxis

Rotates vector around specified axis by angle (in radians).

Vector raa = Vector.RotateAroundAxis(new Vector(1, 0, 0), new Vector(0, 1, 0), Math.PI / 2d);
// raa is now [0, 0, 1]

Visualization of 3 dimensional vector (in green) being rotated 180° around axis (in red) resulting in third vector (in blue)

CloseEnough

Checks proximity of two vectors with specified tolerance.

bool closeEnough = Vector.CloseEnough(new Vector(0, 1, -0.1), new Vector(0, 1, 0.1), 0.5);
// closeEnough is True

bool notCloseEnough = Vector.CloseEnough(new Vector(0, 1, -0.1), new Vector(0, 1, 0.1), 0.01);
// notCloseEnough is False

Lerp

Produces interpolation of two vectors.

Vector inter = Vector.Lerp(new Vector(-0.8, 0.3, -0.5), new Vector(0.4, 0.5, 0.3), 0.5);
// inter is now [-0.2, 0.4, -0.1]

Visualization of two 3 dimensional vectors (in green) resulting in third vector (in blue)

Lerp can also be used for extrapolation.

Vector extra = Vector.Lerp(new Vector(-0.8, 0.3, -0.5), new Vector(0.4, 0.5, 0.3), 1.2);
// extra is now [0.64, 0.54, 0.46]

Visualization of two 3 dimensional vectors (in green) resulting in third vector (in blue)

Cross

Produces vector that is perpendicular to all provided vectors.

There is specific amount of vectors that is required for this function to work.

Vector cross2d = Vector.Cross(new Vector(1, 0));
// cross2d is now [0, -1]

Vector cross3d = Vector.Cross(new Vector(1, 0, 0), new Vector(0, 1, 0));
// cross3d is now [0, 0, 1]

Vector cross4d = Vector.Cross(new Vector(1, 0, 0, 0), new Vector(0, 1, 0, 0), new Vector(0, 0, 1, 0));
// cross4d is now [0, 0, 0, -1]

Visualization of two 3 dimensional vectors (in green) resulting in third vector as a cross product (in blue)