Patent GB-1249485-A (GB)
Title: Sequential production of contour lines from randomly scattered function values
Inventor: SATTLEGGER JOHANN WOLFGANG
IPC: G06K15/22
Filed: 1968-11-08
Abstract: 1,249,485. Contour line plotting. TEXAS INSTRUMENTS Inc. 8 Nov., 1968 [13 Dec., 1967], No. 52977/68. Heading G4A. A contour map of subsurface formations is produced from seismic data using a data processing machine and a graphic plotting device, the processing machine being arranged to store a number of data points, to detect a reference data point having a desired functional value, to fit a function through the values of data points within a first predetermined domain around the reference point, to determine a second data point on the above derived function which has the required functional value and which lies on the boundary of a smaller second predetermined domain around the reference data point, and to cause the plotting device to plot the portion of a contour line which extends from the reference data point to the second data point. The operation proceeds by treating the second data point determined above as if it were the reference point and repeating the operations given above. Reference point determination.-The processor searches through the stored data points until one is found having a functional value within #H of the required function value h. The system then determines a second data point using the stored point as a reference point as is described in more detail below. If the centre point of the line joining these two points is less than a predetermined distance, say d/4, from the point M which is the centre of a circle radius d/2 which passes through the reference point then the reference point is used as the initial point of a contour which is then computed. Contour line plotting.-Fig. 2 shows a portion A-B-C of a contour line which has already been plotted, the next point Q along the contour being determined as follows. The parameter d determines the maximum length of the contour line segments and may be varied, for instance, in the case of a large number of closely packed data points, d is made smaller to permit a more accurate determination of the contours. Utilizing the parameter d point M is established and a first domain 30 constructed. Parameter a must be of sufficient magnitude so that the domain 30 encompasses at least a predetermined number, preferably four, of data points. A second domain 32 is also constructed which limits, in accordance with the angle between the new, CQ, and old, BC, contour segments, the length of the new segment. From the co-ordinates of B and C the co-ordinates of M are computed and all the data points lying within domain 30 are looked up. Each of these points is then weighted with each weight w having a value dependent on the distance of the point from M to the power n (where n is at least two). A linear function is then fitted through the weighted data points using the method of least squares and the coefficients of the fitted function are determined. The function equation is then solved for points, P and Q, on the boundary of the domain 32 which have the required functional value h. Ideally P would coincide with C but due to unavoidable errors some small deviation (as shown) generally results. It is assumed that the point furthest from point C is the desired solution and point Q is therefore chosen if:- otherwise P is chosen. The plotter is then instructed to plot segment CQ, and the process is then repeated treating Q in the same manner as C above. The domain 32 is shown as a circle but it may equally well be some other geometric figure, e.g., an ellipse. The use of an ellipse with its major axis parallel to segment BC sharply reduces the length of the new segment CQ as the angle between it and segment BC increases thereby providing a more accurate determination of the position of highly curved contours. Bound evaluation.-During plotting the contour lines must be prevented from straying outside the inherent bounds of the function. Each newly determined point to be plotted is tested, e.g., in the case of a square boundary by comparing its co-ordinates to the maximum co-ordinates allowed and in the case of a circular boundary by determining its distance from the centre of the circle, and if the boundary has been violated the point along the new segment at which the segment -and boundary intersect is taken as the end of the segment. The tests to be performed for a polygonal boundary are also described. In this case lines from the newly determined point to all the data points lying within a circle radius a about that point are constructed and if any of the angles between adjacent ones of these lines exceeds 180 degrees the newly determined point is rejected. Again a point along the newly calculated segment is chosen such that the condition above is not violated. Contour termination.-Each time a new segment is computed a test is made to determine whether the start point of the contour lies within a circle radius a centred on the last found point. If the start point is found to lie within such a circle the contour is deemed to be finished and the contour line is closed. Following termination a test is made to determine whether any further points having a functional value h exist. If so a new branch of the contour is started, if not the value of h is incremented and the process repeated. Further details.-The specification states that an analogue system utilizing variable threshold devices may be used. The specification also states that the data points, in the case of a digital system, may be read from a magnetic tape into a drum store for use by the system. The system may utilize a computer, appropriately programmed, and a graphic plotter or a graphic plotter having suitable special purpose circuitry built in.