Smooth Boundary Approximation for Directly Computing Irregular Area
Publication: Journal of Surveying Engineering
Volume 119, Issue 3
Abstract
Existing surveying methods of computing the area of an irregular region approximate the boundary between offsets by linear or nonlinear polynomials. Most of these methods have the advantage of providing a formula for computing the area directly. However, the approximating boundary is discontinuous at the polynomial connections, which are often sharp. A recent method, based on a cubic spline, employs a smooth boundary but requires solving a system of linear equations and integration. In this paper, a method that combines the advantages (and avoids the reservations) of existing methods is presented. The method provides a formula for directly computing the area based on a smooth approximation of the boundary. The method is based on the cubic Hermite (CH) function and is applicable to any number of unequal intervals. The proposed method is applied to two examples and the results show that it is generally better than the trapezoidal and Simpson‐type formulas.
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References
1.
Ahmed, F. A. (1983). “Area computation using salient boundary points.” J. Surv. Engrg., ASCE, 109(1), 54–63.
2.
Anderson, J. M., Mikhail, E. M., and Woolnough, D. E. (1985). Introduction to surveying. McGraw‐Hill Ryerson, New York, N.Y.
3.
Burden, R. L., Faires, J. D., and Reynolds, A. C. (1978). Numerical analysis. Prindle, Weber & Schmidt, Boston, Mass.
4.
Chambers, D. W. (1989). “Estimating pit excavation volume using unequal intervals.” J. Surv. Engrg., ASCE, 115(4), 390–401.
5.
Chen, C., and Lin, H. (1991). “Using the cubic spline rule for computing the area enclosed by an irregular boundary.” Surv. and Land Information Systems, 51(2), 113–118.
6.
Easa, S. M. (1988). “Area of irregular region with unequal intervals.” J. Surv. Engrg., ASCE, 114(2), 50–58.
7.
Easa, S. M. (1989). Discussion of “Irregular boundary area computation by Simpson's 3/8 Rule,” by I. M. El‐hassan. J. Surv. Engrg., ASCE, 113(3), 355–356.
8.
Easa, S. M. (1991). Discussion of “Using the cubic spline rule for computing the area enclosed by an irregular boundary,” by C. Chen and H. Lin. Surv. and Land Information Systems, 51(4), 281–282.
9.
El‐Hassan, I. M. (1987). “Irregular boundary area computation by Simpson's 3/8 rule.” J. Surv. Engrg., ASCE, 113(3), 127–132.
10.
Gerald, C. F., and Wheatley, P. O. (1985). Applied numerical analysis. Addison‐Wesley, Reading, Mass.
11.
Moffit, F. H., and Bouchard, H. (1987). Surveying. Harper and Row, New York, N.Y.
12.
Rice, J. (1983). Numerical methods, software, and analysis. McGraw‐Hill, New York, N.Y.
13.
Schmidt, M. D., and Wong, K. W. (1985). Fundamentals of surveying. Prindle, Weber, and Schmidt, Boston, Mass.
14.
Wolf, P. R., and Brinker, R. C. (1989). Elementary surveying. Harper and Row, New York, N.Y.
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Copyright © 1993 American Society of Civil Engineers.
History
Received: Jul 23, 1992
Published online: Aug 1, 1993
Published in print: Aug 1993
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