Basics of MATLAB and Beyond

x 294x1 ...y 294x1 ...z 294x1 ...Grand total is 1111 elements>> plot3(x,y,z,’.’)>> axis tightHere we have 294 measurements of x (latitude), y (longitude), and z(height above sea level, which is negative). They represent measurementsof a mountain under the sea. 17 The data are stored as column vectorsof x, y, and z values. Suppose we want to plot a surface and a contourmap representing this seamount data. If you try to type surf(x,y,z)or contour(x,y,z) with this data, you will not get any meaningful plot.Two ways of generating the desired plots are as follows:1. Interpolate the data over a rectangular grid.2. Use triangular gridding instead of rectangular gridding.Let us look at each of these.36.1 Interpolation over a Rectangular GridWe continue the example above and define vectors of uniformly spacedpoints between the minimum and maximum values of x and y:xiv = linspace(min(x),max(x),50);yiv = linspace(min(y),max(y),50);Each of these vectors has 50 elements. We now use the griddata interpolationfunction to do two things: (1) create matrices of the x and ygrids that correspond to a rectangular grid over the vectors xiv and yiv,and (2) interpolate the data over this new rectangular grid. In the callto griddata that follows, we need to transpose the vector yiv becausegriddata expects it to be a column vector in this case:>> [xi,yi,zi] = griddata(x,y,z,xiv,yiv’);>> whosName Size Bytes Classcaption 1x229 458 char array17 The reference can be found by typing the caption variable:>> captioncaption=Parker, R. L., Shure, L. & Hildebrand, J., "The application of inversetheory to seamount magnetism", Reviews of Geophysics vol 25, pp 17-40,1987. x is latitude (degrees), y is longitude (degrees), z is negativedepth (meters).c○ 2000 by CRC Press LLC