JSMatrix

We will be dealing with lots of vectors and matrices. This course uses the JSMatrix library for all vector and matrix operations.

While probably not the fastest library, it should be decently feature complete, with some advanced features like matrix decompositions. Additionally it is designed to provide lots of ways to access and work with elements of matrices and vectors, such as non-copy transpose, block-views, reductions and more. I am also the author, so sorry about the blatant self promotion!

Documentation can be found at the linked repository.

All functions are accessible under the variable jsm.

Since JavaScript sadly does not have operator overloading, math operations such as $+$ have to be computed using functions, in this case jsm.add.

To make things slightly easier, a number of common functions are already provided at the scope of your scripts.

For any of these functions that take an out parameter, you can omit it, in which case a new matrix is created. This is mainly for optimization.

Here is a list of those:

• add(a, b, out): Add two matrices/vectors
• sub(a, b, out) : Subtract a matrix/vector from another one
• mult(a, b, out): Multiply two matrices
• scale(a, v, out): Scale a matrix/vector a by a scalar v
• dot(a, b: The dot product between two vectors
• cross(a, b, out): The cross product between two 3D vectors
• abs(a, out): Computes the element-wise absolute value of a matrix/vector
• normalize(a, out): Divides a vector by it's length
• cwiseMin(a, b, out): Compute the element-wise minimum of two matrices/vectors
• cwiseMax(a, b, out): Compute the element-wise maximum of two matrices/vectors
• cwiseMult(a, b, out): Compute the element-wise multiplication of two matrices/vectors
• subvec(v, start, rows): Get a view of a part of a vector, so it can match dimensions with other operations. Start indicates the index of the initial coordinate and rows the number of rows. Rows is optional and defaults to all remaining rows after start.
• diag(m): Get a view of the diagonal of a matrix. Behaves just like a vector
• block(m, i, j, rows = m.rows() - i, cols = m.cols() - j): Get a view of a part of a matrix, so it can match dimensions with other operations, such as multiplication or filling. rows and cols are optional and default to the remaining values from the starting point.
• transpose(m): Get a view of the transpose of a matrix
• insert(a, b): Fills a matrix/vectpr a with the values of another one b. The dimensions must match. Can be combined with views
• fill(a, v): Sets each element of a matrix/vector a to a scalar value v. Can be combined with views
• copy(m): Copy the given matrix/vector
• hvec(v, hcoord = 1): Creates a new vector from the given vector v with an additional constant coordinate (default = 1) equal to hcoord
• v32: Factory functions for float vectors. Equal to jsm.VecF32
• m32: Factory functions for float matrices. Equal to jsm.MatF32

Additionally, as it is commonly used, we defined some helper functions for the common 2D, 3D and 4D vectors:

• vec2(x = 0, y = 0): This is just a shorthand for v32.from([x,y])
• vec3(x = 0, y = 0, z = 0): This is just a shorthand for v32.from([x,y,z])
• vec4(x = 0, y = 0, z = 0, w = 0): This is just a shorthand for v32.from([x,y,z,w])
• mix(a, b, t): Computes a linear interpolation with the parameter t for the vectors/matrices a and b
• ceil(a, out): Computes the per component ceil function
• floor(a, out): Computes the per component floor function
• isAny(a, b, cmp): Does a element-wise comparison of a and b. Returns true, if any of those comparisons where true, falseotherwise. cmp is any function cmp(elem_a, elem_b) => {true|false}

You can try out these functions or any others below to get a feeling. The code section contains example code, but you can change it as you like.