Concise proof of Tienstra's formula

The resection problem consists in finding the location of an observer by measuring the angles subtended by lines of sight from this observer to three known stations. Many researchers and practitioners recognize that Tienstra’s formula provides the most compact and elegant solution to this problem. U...

Descripción completa

Detalles Bibliográficos
Autores: Porta, Josep M., Thomas, Federico
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2009
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/30496
Acceso en línea:http://hdl.handle.net/10261/30496
Access Level:acceso abierto
Palabra clave:Tienstra's formula
Triangulation
Resection
Global localization
Barycentric coordinates
Robotics
Robots
Descripción
Sumario:The resection problem consists in finding the location of an observer by measuring the angles subtended by lines of sight from this observer to three known stations. Many researchers and practitioners recognize that Tienstra’s formula provides the most compact and elegant solution to this problem. Unfortunately, all available proofs for this remarkable formula are intricate. This paper shows how, by using barycentric coordinates for the observer in terms of the locations of the stations, a neat and short proof is straightforwardly derived.