The most popular three-dimensional coordinate system is Cartesian coordinate system. It consists of a fixed point (point of origin) and three straight lines (coordinate axes) intersecting in this point: they belong to different planes and are pair-wise orthogonal* (the angle between each pair is 90 degrees) . Each coordinate axis is given a direction in which its values grow and a scale. One coordinate axis (X-axis) is called abscissa axis, the second (Y-axis) is called ordinate axis and the third (Z-axis) is called applicate axis. A point in Cartesian coordinate system is specified by 3 coordinates (x; y; z). *Sometimes it is more convenient to use a system with an angle between the coordinate axes different from 90 degrees (such systems are called non-orthogonal).	Cartesian coordinate system
In Cartesian system functions may be given as dependence z = f(x; y), x = f(y; z) or y = f(x; z). For example, the hyperbolic paraboloid is given as z = (x2 - y2)/20. The Z-values of this function in node points are presented in the table (built manually or using a software product): y x -10 -8 -6 -4 -2 0 2 4 6 8 10   -10 0 1,8 3,2 4,2 4,8 5 4,8 4,2 3,2 1,8 0   -8 -1,8 0 1,4 2,4 3 3,2 3 2,4 1,4 0 -1,8   -6 -3,2 -1,4 0 1 1,6 1,8 1,6 1 0 -1,4 -3,2   -4 -4,2 -2,4 -1 0 0,6 0,8 0,6 0 -1 -2,4 -4,2   -2 -4,8 -3 -1,6 -0,6 0 0,2 0 -0,6 -1,6 -3 -4,8   0 -5 -3,2 -1,8 -0,8 -0,2 0 -0,2 -0,8 -1,8 -3,2 -5   2 -4,8 -3 -1,6 -0,6 0 0,2 0 -0,6 -1,6 -3 -4,8   4 -4,2 -2,4 -1 0 0,6 0,8 0,6 0 -1 -2,4 -4,2   6 -3,2 -1,4 0 1 1,6 1,8 1,6 1 0 -1,4 -3,2   8 -1,8 0 1,4 2,4 3 3,2 3 2,4 1,4 0 -1,8   10 0 1,8 3,2 4,2 4,8 5 4,8 4,2 3,2 1,8 0   This points are drawn on the graph and linked with lines (each point is linked with points to the North, to the West, to the East and to the South of it in the table. For example, the point with Z = -3,2 is linked with points -3; -5; -1,8 and -3).	Hyperbolic paraboloid
The dependence may be given in an implicit way as F(x; y; z) = 0 (when it is hard or impossible to express one coordinate through other). For example, the sphere with the center at point (0; 0; 0) is given as x2 + y2 + z2 = R2, where R is the radius of the sphere.
Other frequently used three-dimensional coordinate systems are spherical and cylindrical systems. They are curvilinear coordinate systems.
A point in spherical coordinate system is given by the end of the vector drawn from the point of origin and is specified by 3 coordinates: R - the length of the vector (the radius of the imaginary sphere), l - the latitude of the point and p - the longitude of the point. The latitude is the angle between the vector and the terrestrial axis (Z-axis in our case). The longitude is the angle between the projection of the vector on the equatorial plane (xOy plane) and the plane of the zero meridian (xOz plane).	Spherical coordinate system
In spherical system functions are usually given as dependence R = f(p; l). For example, the sphere with radius = 8 is given simply as R = 8 (parameter p changes from 0 to 360 degrees, parameter l - from 0 to 180 degrees).	Sphere
A point in cylindrical coordinate system is given by the end of the vector drawn from the point of origin and is specified by 3 coordinates: R - the length of the vector (the radius of the imaginary cylinder), z - the distance between the point and the equatorial plane (xOy plane in our case) and p - the longitude of the point. The longitude is the angle between the projection of the vector on the equatorial plane (xOy plane) and the plane of the zero meridian (xOz plane).	Cylindrical coordinate system
In cylindrical system functions are usually given as dependence R = f(p; z). For example, the cylinder with radius = 6 is given simply as R = 6 (parameter p changes from 0 to 360 degrees, parameter z - from -10 to 10).	Cylinder
The cone is given as R = z.	Cone
You can build any three-dimensional functions given in Cartesian, spherical and cylindrical coordinate systems using Tavrida Scientific Calculator (all above sample graphs are build with our program). You can build any number of functions on one graph, rotate graphs and explore the intersections of functions. You simply create the three-dimensional graph, add functions (for example, z = (x^2-y^2)/20 and R = 2 (in cylindrical system - cylinder with radius = 2 with the X-axis as the terrestrial axis)) and get the result (see sample graph to the right). Click here to download Tavrida Calculator.	Sample graph