of symmetry about a point, such as volume integrals inside a sphere, the potential energy field surrounding a concentrated mass or charge, or global weather simulation in a planet's atmosphere. A sphere that has the Cartesian equation has the simple equation in spherical coordinates. Two important partial differential equations that arise in many physical problems, Laplace's equation and the Helmholtz equation, allow a separation of variables in spherical coordinates. The angular portions of the solutions to such equations take the form of spherical harmonics. Another application is ergonomic design, where is the arm length of a stationary person and the angles describe the direction of the arm as it reaches out. Three dimensional modeling of loudspeaker output patterns can be used to predict their performance. A number of polar plots are required, taken at a wide selection of frequencies, as the pattern changes greatly with frequency. Polar plots help to show that many loudspeakers tend toward omnidirectionality at lower frequencies. The spherical coordinate system is also commonly used in 3D game development to rotate the camera around the player's position In geography To a first approximation, the geographic coordinate system uses elevation angle (latitude) in degrees north of the equator plane, in the range , instead of inclination. Latitude is either geocentric latitude, measured at the Earth's center and designated variously by or geodetic latitude, measured by the observer's local vertical, and commonly designated . The polar angle, which is 90° minus the latitude and ranges from 0 to 180°, is called colatitude in geography. The azimuth angle (longitude), commonly denoted by , is measured in degrees east or west from some conventional reference meridian (most commonly the IERS Reference Meridian), so its domain is . For positions on the Earth or other solid celestial body, the reference plane is usually taken to be the plane perpendicular to the axis of rotation. Instead of the radial distance, geographers commonly use altitude above or below some reference surface (vertical datum), which may be the mean sea level. The radial distance can be computed from the altitude by adding the radius of Earth, which is approximately . However, modern geographical coordinate systems are quite complex, and the positions implied by these simple formulae may be wrong by several kilometers. The precise standard meanings of latitude, longitude and altitude are currently defined by the World Geodetic System (WGS), and take into account the