Now we have a coordinate system that describes every point on Earth in three-dimensional Cartesian coordinates. In this coordinate system, we are now modeling the principles of our world, mountains, valleys and oceans. Note: Aside from computer geometry, geographic coordinates are used for the earth, ie, latitude and longitude, as well as altitudes above sea level. The approximate conversion - if one does not consider the fact that the earth is not an exact sphere - is simple: with R = Radius of the earth [6.378.137m], lat = Latitude, long = Longitude, hasl = height above sea level. All of the following examples apply in a right-handed system. For a left-handed system the signs may need to be interchanged. The objects contained within the scene (houses, trees, cars) are often designed in their own object coordinate system (also called model coordinate system or local coordinate system) for reasons of simpler modeling. To assign these objects to coordinates in the world coordinate system or global coordinate system of the entire scene, the object coordinates are transformed by means of translation, rotation or scaling. This is done by multiplying the corresponding transformation matrices. In addition, several differently transformed copies can be formed from one object, for example a forest from a tree; This technique is called instancing. In order to place a model of an aircraft in the world, we first determine four matrices. Since we work in three-dimensional space, we need four-dimensional homogeneous matrices for our calculations. First, we need three rotation matrices, namely one for each of the three aircraft axes (vertical axis, transverse axis, longitudinal axis). Around the X axis (usually defined as a longitudinal axis in the object coordinate system) Around the Y axis (usually defined as the transverse axis in the object coordinate system) Around the Z axis (usually defined as vertical axis in the object coordinate system) We also use a translation matrix that moves the aircraft to the desired point in our world: . Remark: The above matrices are transposed with respect to the ones in the article rotation matrix. See further down for an explanation why. Now we could calculate the position of the vertices of the aircraft in world coordinates by multiplying each point successively with these four matrices. Since the multiplication of a matrix with a vector is quite expensive (time-consuming), one usually takes another path and first multiplies the four matrices