Division 2.7.28 Tracing of contours
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A very time-efficient algorithm that eliminates the need to calculate a complete grid array of index values at the expense of a little more computational complexity is to trace the path of the contour, point by point. This option requires two basic steps to be performed and repeated (see Figure 2.7.u):
Figure 2.7.u
Concept of tracing algorithm
Step 1 is to find a first point P1 on the contour. This is done by calculating the noise index levels L in equidistant steps along a ‘search ray’ that is expected to cross the required contour of level LC . When the contour is crossed, the difference δ = LC – L changes sign. If this happens, the step-width along the ray is halved and the search direction is reversed. This is done until δ is smaller than a pre-defined accuracy threshold.
Step 2, which is repeated until the contour is sufficiently well defined, is to find the next point on the contour LC — which is at a specified straight line distance r from the current point. During consecutive angular steps, index levels and differences δ are calculated at the ends of vectors describing an arc with radius r. By similarly halving and reversing the increments, this time in the directions of the vector, the next contour point is determined within a predefined accuracy.
Figure 2.7.v
Geometric parameters defining conditions for the tracing algorithm
Some constraints shall be imposed to guarantee that the contour is estimated with a sufficient degree of accuracy (see Figure 2.7.v):
- (1)
The length of the chord Δc (the distance between two contour points) shall be within an interval [Δcmin , Δcmax ], e.g. [10 m, 200 m].
- (2)
The length ratio between two adjacent chords of lengths Δcn and Δcn+1 shall be limited, e.g. 0,5 < Δcn /Δcn + 1 < 2.
- (3)
With respect to a good fit of the chord length to the contour curvature the following condition shall be fulfilled:
Φn · max(Δcn – 1 , Δcn ) ≤ ε(ε≈ 15 m)
where Φn is the difference in the chord headings.
Experience with this algorithm has shown that, on an average, between 2 and 3 index values have to be calculated to determine a contour point with an accuracy of better than 0,01 dB.
Especially when large contours have to be calculated this algorithm speeds up computation time dramatically. However it should be noted that its implementation requires experience, especially when a contour breaks down into separate islands.