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By employing fundamental methods from the theory of curves and surfaces, the concepts of different types of latitude and longitude (reduced latitude and longitude, geometric latitude and longitude, and geodetic latitude and longitude) at an arbitrary point on a triaxial ellipsoidal surface are proposed. Theoretical relationship models are established between Cartesian coordinates (spatial rectangular coordinates) and geodetic coordinates (geodetic latitude, longitude, and height), as well as between Cartesian coordinates and geometric coordinates (geometric latitude, longitude, and height), for any point in space both inside and outside the ellipsoid. Based on the theoretical relationships among the different latitude and longitude types, approximate geodetic coordinates of the study point are derived. Using these approximations as initial values, a novel method for the inverse transformation of coordinates is presented via Newton's iterative approach. Extensive numerical calculations demonstrate that, for any arbitrary point in space, the proposed method accomplishes the transformation from Cartesian to geodetic coordinates nearly instantaneously; even for points near the Earth's surface, only three iterations are required to achieve convergence.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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