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vector2

Useful class when dealing in two dimensional space (R2). Completely inline for better performance.

• vector2.hpp

vector3

This class provides a big set of features needed when calculating with vectors in third space, in R3. This class is implemented completely inline for better performance.

• vector3.hpp

The methods should be self explained. Example:

vector3 a(...), b(...), c(...);      // corners

double area = (b-a).dot(c-a) * 0.5;  // solution 1
double area = (b-a) * (c-a) * 0.5;   // solution 2
vector3 n = (b-a).cross(c-a);        // normal vector on surface

vector4

Similar to the vector2 and vector3 classes but have four components. It is implemented completely inline as well.

• vector4.hpp

vectorn

This is a template, you may choose the size of the vector when using it.

• vectorn.hpp

Example:

vectorn<3> a;  a[0]=1.0; a[1]=2.0; a[2]=3.0;
a *= 0.5;

matrix2

Provides a class with many method for 2x2 matrices. It works together with the vector2 for some functions.

• matrix2.hpp

Example: Equation-System: A is a matrix with coeffitients, y is the known solution vector. x is the vector we’re looking for.

$A * \underline{x} = \underline{y} ~~~ \Rightarrow ~~~ A^{-1} * A * \underline{x} = A^{-1} * \underline{y} ~~~ \Rightarrow ~~~ \underline{x} = A^{-1} * \underline{y}$

All we need is the inverse matrix A-1 to get the solution.

vector2 y(...);
matrix2 A(...);

vector2 x = A.inv() * y;

matrix3

Similar to matrix2 but for 3x3 matrices. Works together with vector3, of course.

• matrix3.hpp

matrix4

Similar to matrix2 but for 4x4 matrices. Works together with vector4.

• matrix4.hpp

matrixn

Similar to matrix2 but for NxN matrices. Works together with vectorn. This class is also a template to let you choose the size. You can define N, the size of the matrix will be NxN.

• matrixn.hpp

quaternion

This is an implementation of a quaternion $(w,x,y,z)$. It is working tight with the class vector3. The implementation itself is as much inline as possible to get a good performance.

• quaternion.hpp

Example (rotation of a vector arround an arbitrary axis):

vector3 p(...);        // the vector
vector3 u(...);        // the rotation axis
double angle = 30.0;   // the rotation angle in degrees

quaternion q(angle, u);
q.rot(p);   // rotate vector p

The short form of this example would be:

vector3 p(...);

quaternion(30.0, vector3(...)).rot(p);    // temporary objects!

This quaternion class can do much more, of course (have a look at the header file)!