TECHNICAL PAPERS
Feb 1, 1998
Proof of Tienstra's Formula for an External Observation Point
Authors: W. C. Hu and J. S. Kuang, Member, ASCEAuthor Affiliations
Publication: Journal of Surveying Engineering
Volume 124, Issue 1
Abstract
As a continuation of the writers' previous work on establishment of Tienstra's formula via finite-element ideas for an internal observation point, the formula is proven for the case where the observation point lies outside the control triangle. Because of the loss of “rotational symmetry” in the present case, this proof differs from the previous one as more formulas have to be derived, and “reflection symmetry” of the new configuration becomes an important aid throughout the derivation. Furthermore, the lengthy computer algebra needed to complete the previous proof has a much simpler counterpart here, requiring only one line of computer simplification.
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References
1.
Allan, A., Hollwey, J., and Maynes, J. (1968). Practical field surveying and computations. Elsevier Science Publication Co., Inc., New York, N.Y.
2.
Bannister, A., and Baker, R. (1989). Solving problems in surveying. Longman's, London.
3.
Bannister, A., and Raymond, S. (1992). Surveying, 6th Ed., Longman's, London.
4.
Hu, W. C., and Kuang, J. S.(1997). “Proof of Tienstra's formula by finite-element method.”J. of Surv. Engrg., ASCE, 123(1), 1–10.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 124 • Issue 1 • February 1998
Pages: 49 - 55
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Feb 1, 1998
Published in print: Feb 1998
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Authors
Affiliations
W. C. Hu
Demonstrator, Dept. of Civ. and Struct. Engrg., Hong Kong Univ. of Sci. and Technol., Clear Water Bay, Kowloon, Hong Kong.
J. S. Kuang, Member, ASCE
Assoc. Prof., Dept. of Civ. and Struct. Engrg., Hong Kong Univ. of Sci. and Technol., Clear Water Bay, Kowloon, Hong Kong.
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.