The libgfx matrix math package is the companion to the vector package and are intended to provide a convenient way of writing vector/matrix equations. Currently, only square matrices of dimension 2x2 [Mat2], 3x3 [Mat3], and 4x4 [Mat4].
A matrix consists of n*n double precision floating point values. Unlike the vector package, the matrix package is not yet template-based. Matrix elements are accessed using 0-indexed (row, column) pairs. Thus, a 2x2 identity matrix can be constructed as follows:
Mat2 A;
A(0, 0) = 1.0;
A(0, 1) = 0.0;
A(1, 0) = 0.0;
A(1, 1) = 1.0;
The default constructors (as used above) initialize all elements to 0. All
matrix classes also provide constructors which accept a list of row vectors to
initialize their elements. Thus, the following example is equivalent to the
code above:
Mat2 A(Vec2(1.0, 0.0), Vec2(1.0, 0.0));
Matrices can also be automatically case to double pointers. Since
matrices are stored in row-major order, the follow code would change element
(0, 1) of the matrix above:
double *B = A;
B[1] = -1.0;
Warning: For efficiency reasons, accessors are not range checked. Thus you can legally write
Mat2 v;
v(-10, 37) = 1.0;
and generate an invalid memory access.
Like the vector package, one of the primary goals of the matrix package is to simplify the writing of vector/matrix equations. To accomplish this, it makes use of C++ operator overloading.
Assignment Matrices can be assigned the values of other matrices or scalars. A matrix assignment A = B copies the elements of B into the corresponding elements of A. A scalar assignment A = 1.0 copies the given scalar, in this case 1.0, into each of the elements of A.
Addition/Subtraction Matrices can be added together either with the binary addition operator (C = A + B) or the additive assignment operator (A += B). Subtraction operates similarly, using subtraction rather than addition operators.
Scalar Multiplication/Division Matrices can be multiplied by scalar values using either the binary operator (A * 2.0) or the accumulation operator (A *= 2.0). Scalar division operates similarly.
Matrix/Vector Multiplication Matrices can be multiplied together with a binary operator (A * B). Matrices can also multiply vectors (A * v) which returns a new vector.
All matrix classes support a standard set of functions for performing common operations on matrices. The functions are:
// Constructs the outer product of the two vectors Mat_ outer_product(const Vec_ &u, const Vec_ &v); // Returns the determinant of the matrix double det(const Mat_ &A); // Returns the trace of the matrix (the sum of the diagonals) double trace(const Mat_ &A); // Returns the transpose of A Mat_ transpose(const Mat_ &A); // Returns the adjoint of A Mat_ adjoint(const Mat_ &A); // Places the inverse of A in A_inv and returns det(A) // The contents of A_inv are undefined if the inverse doesn't exist. double invert(Mat_ &A_inv, const Mat_ &A);
Matrices can also be read from and written to C++ iostreams using the standard << and >> operators.