dvec 0.0.7

dvec - Easy linear algebra for D

dvec is a library that offers vector and matrix data structures and functions in a way that's intuitive, easy to use, tested, and well-documented. It takes advantage of the D language's advanced templating system and compile-time code-generation to help optimize performance and type safety.

dvec offers the basic linear algebra primitives:

• Vectors
• Matrices

Each of these can be of any desired integer size (within the limits of your system). For example, Vec!(float, 5) v; defines a 5-dimensional floating-point vector, and Mat!(int, 2, 3) m; defines a 2x3 (2 rows by 3 columns) integer matrix. However, this can get to be a bit tedious, so we've included the most common vectors and matrices as aliases for you:

• 2, 3, and 4-dimensional vectors of float, double, and int types: Vec3d, Vec2i, and Vec4f, for example.
• 2, 3, and 4-dimensional square matrices of float, double, and int types: Mat2f, Mat3i, and Mat4d, for example.

Each primitive is a simple struct with a fully transparent internal structure, and implements all the basic arithmetic operators, so you can do things like this easily:

Vec3f v = Vec3f(1f, 2f, 3f) * 5 - Vec3f(0.5f);
// v.data == [4.5f, 9.5f, 14.5f]

Besides the `toString()` methods, no parts of this library make use of the GC, and are thus @nogc compatible.

Vectors

Vectors are simply a fixed-size list of numerical elements, which implement a lot of mathematical operations that are useful in linear algebra.

The values of a vector can be accessed in the following ways:

• By index: v[1] gets the second element in vector v.
• By name: v.x, v.y, v.z, v.w gets the first, second, third, or fourth element of a vector, respectively.
• By the internal data: v.data gets the internal array.

Casting

You can cast vectors of different types and sizes using D's standard cast(type) syntax. Note that the individual elements are casted using cast as well, and that may result in data loss if you, for example, cast from a floating-point to integer vector. If you cast to a vector with a different size, the following rules apply:

• If the new vector type is smaller, extra elements are truncated.
• If the new vector type is larger, any missing elements are initialized to zero.

Specialization

Certain vector types get access to extra special functions:

• Any floating-point (float, double) vector supports the norm() method, to normalize the vector to a unit vector of length 1.
• Any floating-point (float, double) 2-dimensional vector supports the toPolar() and toCartesian() methods, so that the vector can be treated as polar or cartesian coordinates and converted between the two.
• Any floating-point (float, double) 3-dimensional vector supports the cross() method for computing the cross product with another 3-dimensional vector.

Matrices

Certain matrix types get access to extra special functions:

• Square matrices (NxM matrices where N = M) support a variety of additional methods that are useful for linear algebra, like det() (determinant), inv() (inverse), and so on.
• 3x3 matrices support linear transformation methods in 2 dimensions, like translation, rotation, skew, and scaling.
• 4x4 matrices support linear transformation methods in 3 dimensions.

For more information, please see dub project page and its associated documentation.

A lot of effort has gone into making sure everything in this library is well-documented and explained well. If you find that documentation is missing or insufficient for a certain part, please make an issue on GitHub!