3.1 The Geometry Library

The geometry module is a collection of generic geometric objects. Also, classes that are required by more than one other module. This is done to avoid dependency problems.

3.2 Three_Vector

A Three_Vector represents a vector in three-dimensions. Some supported operations are

• subscripting using []
• vector addition and subtraction using + and -
• multiplication and division by a scalar using * and /
• left and right matrix multiplication using *
• dot and cross products using the dot() and cross()methods
• projection onto another vector using the project() method
• magnitude using the abs() method

Matrix multiplication is done with a Three_Matrix.

3.3 Three_Matrix

A Three_Matrix represents 3x3 matrix. It's suitable for representing a three-dimensional rotation matrix or inertia tensor. Some suported operations are

• subscripting using []
• matrix addition and subtraction using + and -
• multiplication and division by a scalar using * and /
• left and right vector multiplication using *
• matrix multiplication using *
• eigenvalue and eigenvector determination
• inversion

3.4 Inertia_Tensor

An inertia tensor is a matrix that describes a rigid body's responce to torques. The Inertia_Tensor generates the tensor from the locations of masses on a body. The masses and positions are specified using the add() method. The inertia() method returns the moment of inertia for a force applied at a particular point on the body.

3.5 Two_Point

A Two_Point describes a point in a plane. It is a struct with two data members, x and y. A constructor is provided for initializing the members. No vector operations are supported, and some of the supported operations are undefined for vectors. That's why this class is called Two_Point and not Two_Vector. The supported operations are scalar and member-wise addition, subtraction, multiplication, and division. For the scalar versions, the operation is performed on each member.

Spline is the only user of Two_Point. Perhaps it should be defined in Spline's header so that there's less temptation to use Two_Point inappropriately.

3.6 Spline

Spline is a class for a parametric cubic spline interpolation between points. A vector of Two_Points through which the curve passes and angle of the curve at the first and last points are passed to the constructor.

Splines are used to make smooth road elevation changes and banking transitions.

3.7 Surface

A Surface describes the friction, rolling resistance, restitution and texture image of a surface such as pavement, grass or gravel.

3.8 Texture_Image

The Texture Image class provides a convenient way of reading a *.ppm image file from the disk and for getting information about the image.

3.9 Conversions

The header file Conversions.h contains a few functions for performing frequently-used unit conversions. Currently, there are conversions for radians and degress, radians per second and revolutions per minute, and meters per second and kilometers per hour.