Positioning by Intersection Methods

  • Joseph L. Awange
  • Béla Paláncz


The similarity between resection methods presented in the previous chapter and intersection methods discussed herein is their application of angular observations. The distinction between the two however, is that for resection, the unknown station is occupied while for intersection, the unknown station is observed. Resection uses measuring devices (e.g., theodolite, total station, camera etc.) which occupy the unknown station. Angular (direction) observations are then measured to three or more known stations as we saw in the preceding chapter. Intersection approach on the contrary measures angular (direction) observations to the unknown station; with the measuring device occupying each of the three or more known stations. It has the advantage of being able to position an unknown station which can not be physically occupied. Such cases are encountered for instance during engineering constructions or cadastral surveying. During civil engineering construction for example, it may occur that a station can not be occupied because of swampiness or risk of sinking ground. In such a case, intersection approach can be used. The method is also widely applicable in photogrammetry. In aero-triangulation process, simultaneous resection and intersection are carried out where common rays from two or more overlapping photographs intersect at a common ground point (see e.g., Fig. 15.1).


  1. 20.
    Awange JL (2003) Buchberger algorithm applied to planar lateration and intersection problems. Surv Rev 37:319–329CrossRefGoogle Scholar
  2. 33.
    Awange JL, Grafarend EW (2005) From space angles to point position using sylvester resultant. Allgemeine Vermessungs-Nachrichten 112:265–269Google Scholar
  3. 36.
    Awange JL, Grafarend EW, Fukuda Y (2003) Closed form solution of the triple three-dimensional intersection problem. Zeitschrift für Geodaesie, Geoinfornation und Landmanagement 128:395–402Google Scholar
  4. 37.
    Awange JL, Fukuda Y, Takemoto S, Grafarend EW (2003) Resultants approach to the triple three-dimensional intersection problem. J Geodetic Soc Jpn 49:243–256Google Scholar
  5. 43.
    Awange JL, Grafarend EW, Fukuda Y (2004) A combinatorial scatter approach to the overdetermined three-dimensional intersection problem. Bollettino di Geodesia e Scienze Affini 63:235–248Google Scholar
  6. 49.
    Baarda W (1967) A generalization of the concept strength of the figure. Publications on geodesy, new series, vol 2, no 4. Netherlands Geodetic Commission, DelftGoogle Scholar
  7. 53.
    Baarda W (1973) S-transformation and criterion matrices. Netherlands geodetic commission. Publications on geodesy, new series vol 5, no 1. Rijkscommissie voor Geodesie, DelftGoogle Scholar
  8. 204.
    Grafarend EW (1989) Photogrammetrische Positionierung. Festschrift für Prof. Dr.-Ing. Dr. h.c Friedrich Ackermann zum 60. Geburtstag, Institut für Photogrammetrie, Univerität Stuttgart, Heft 14, pp 44–55, StuttgartGoogle Scholar
  9. 205.
    Grafarend EW (1990) Dreidimensionaler Vorwaertschnitt. Zeitschrift für Vermessungswesen 115:414–419Google Scholar
  10. 215.
    Grafarend EW, Mader A (1993) Robot vision based on an exact solution of the threedimensional resection-intersection. In: Linkwitz K, Eisele V, Moenicke H-J (eds) Applications of geodesy to engineering. Symposium No. 108. Spinger, Berlin/Heidelberg/Newyork/London/Paris/Tokyo/ HongKong/Barcelona/BudapestGoogle Scholar
  11. 224.
    Grafarend EW, Shan J (1997) Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates. J Geod 71:217–231CrossRefGoogle Scholar
  12. 225.
    Grafarend EW, Shan J (1997) Closed form solution of the twin P4P or the combined three dimensional resection-intersection problem in terms of Möbius barycentric coordinates. J Geod 71:232–239CrossRefGoogle Scholar
  13. 251.
    Hanusch T (2010) Texture mapping and true orthophoto generation of 3D objects. Ph.D. at Technical University of DresdenGoogle Scholar
  14. 296.
    Kahmen H, Faig W (1988) Surveying. Walter de Gruyter, BerlinCrossRefGoogle Scholar
  15. 370.
    Mikhail EM, Bethel JS, McGlone CJ (2001) Introduction to modern photogrammetry. Wiley, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Joseph L. Awange
    • 1
  • Béla Paláncz
    • 2
  1. 1.Curtin UniversityPerthAustralia
  2. 2.Budapest University of Technology and EconomicsBudapestHungary

Personalised recommendations