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### 4.5.1 Geometry Library (`csGeom`)

This library is used to perform any calculations dealing with 2D or 3D geometry. It contains several more or less independent classes. The most important classes are:

- Geometric Functionality

  These are functions that do not fit in one of the following classes, for example to calculate intersections. They are grouped as static member functions of one class. (It does not make sense to create objects of this class, as it only contains these static member functions).

- Vectors

  These classes represent 2D and 3D vectors. There is also a variant of the 3D vector class which uses double precision numbers to represent its elements, rather than the single precision numbers used by the standard 3D vector class. These classes supply specially overloaded operators so you can use them in calculations as you can use integer or float values. The possible operators are:

  - Add two vectors
  - Subtract two vectors
  - Multiply a vector and a scalar
  - Divide a vector by a scalar
  - Dot product (uses ``*'` operator)
  - Cross product (uses ``%'` operator)
  - Comparison of two vectors (``=='` and ``!='`)
  - Projecting one vector on another (``<<'` and ``>>'`)
  - Inverting a vector (``-'` operator)
  - Comparing all components with a small epsilon value (``<'` and ``>'`)

  They also contain some functions to normalize the vector or return its length. Single and double precision vectors can be mixed in calculations.

- Matrices

  These are 2D and 3D matrices. They are used to transform (rotate, scale etc.) vectors. They also use their own operators for easier usage (for example to multiply a matrix and a vector).

- Transforms

  A transformation consists of a matrix and a vector. In contrast to just a matrix you can also include movement in a transform. It also uses its own operators.

- Quaternions

  Encapsulation of quaternion functionality.

- Planes

  These classes represent 2D and 3D planes. They can, for example, be used to split polygons or to calculate the distance of a point from a polygon (or line segments instead of polygons for 2D planes).

- Line Segments

  A line segment is a straight line between two points, which ends at these points. It could for example be used to define start and finish point of straight movement. There are 2D and 3D segments.

- Polygons

  Polygons are an important class used heavily in the 3D engine. A polygon is built from at least three points, called vertices. All vertices must be on the same plane in space. The polygons outline consists of all line segments from one vertex to the next one, including the segment from the last vertex to the first one. These segments may not cross. Also, the polygon must be convex, which means that if you take two arbitrary points inside the polygon and draw a straight line between them, it may not cross any of the polygon's edges. A polygon has two faces, defined by the order of the vertices: If you count through all vertices, and from your position they appear in clockwise order, then you are viewing the front face, otherwise you are viewing the back face. The normal vector of the polygon always points out perpendicular from the front face.

  There are different types of polygons concerning management of the vertices and how they can be used. First, there are the basic 2D and 3D polygons that store their vertices as 3D vectors. The clippers are similar to this but they are specialized on clipping other polygons (you lay the clipper somewhere on a polygon and cut everything away of the polygon that is outside the clipper, resulting in a new, smaller polygon). Then there is a 2D polygon that stores its sides as line segments, not its vertices as vectors. The most important type for the engine is the indexed polygon, which does not store its vertices as 3D vectors but only as indices in a table.

There are also other classes that are mostly used inside the engine, such as bounding boxes, frustums, polygon pools, etc.

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