Matlab使用哪种算法生成等高线?换句话说,它如何将网格上的等值数据转换为一组线条?
我想要的是:
- 获取位于等高线上点的局部标准?
- 捕获所有等高线的全局过程?
我不需要关于底层代码的详细说明,但了解一般原理对我解释输出结果会有帮助。我在研究中使用contour
(及其衍生品),希望了解此步骤引入的数值误差。
这看起来是一个非常简单的问题,但我在Matlab的文档中找不到任何解释,在SO或其他地方也没有找到任何信息。如果最终证明很容易找到,请原谅我的无知。
来自MATLAB®-图形-R2012a,从第5-73页到第5-76页:
The Contouring Algorithm
The
contourc
function calculates the contour matrix for the other contour functions. It is a low-level function that is not called from the command line. The contouring algorithm first determines which contour levels to draw. If you specified the input vectorv
, the elements ofv
are the contour level values, andlength(v)
determines the number of contour levels generated. If you do not specifyv
, the algorithm chooses no more than 20 contour levels that are divisible by 2 or 5.The height matrix
Z
has associatedX
andY
matrices that locate each value inZ
at the intersection of a row and a column, or these matrices are inferred when they are unspecified. The row and column widths can vary, but typically they are constant (i.e.,Z
is a regular grid). Before callingcontourc
to interpolate contours,contourf
pads the height matrix with an extra row or column on each edge. It assigns z-values to the added grid cells that are well below the minimum value of the matrix. The padded values enable contours to close at the matrix boundary so that they can be filled with color. Whencontourc
creates the contour matrix, it replaces the x,y coordinates containing the low z-values with NaNs to prevent contour lines that pass along matrix edges from being displayed. This is why contour matrices returned bycontourf
sometimes contain NaN values. Set the current level,c
, equal to the lowest contour level to be plotted within the range[min(Z) max(Z)]
. The contouring algorithm checks each edge of every square in the grid to see ifc
is between the two z values for the edge points. If so, a contour at that level crosses the edge, and a linear interpolation is performed:t=(c-Z0)/(Z1-Z0)
Z0
is the z value at one edge point, andZ1
is the z value at the other edge point.Start indexing a new contour line (
i=1
) for level c by interpolating x and y:cx(i) = X0+t*(X1-X0) cy(i) = Y0+t*(Y1-Y0)
Walk around the edges of the square just entered; the contour exits at the next edge with z values that bracket
c
. Incrementi
, computet
for the edge, and then computecx(i)
andcy(i)
, as above. Mark the square as having been visited. Keep checking the edges of each square entered to determine the exit edge until the line(cx,cy
) closes on its initial point or exits the grid. If the square being entered is already marked, the contour line closes there. Copycx
,cy
,c
, andi
to the contour line data structure (the matrix returned by contouring functions, described shortly).Reinitialize
cx
,cy
, andi
. Move to an unmarked square and test its edges for intersections; when you find one at levelc
, repeat the preceding operations. Any number of contour lines can exist for a given level. Clear all the markers, increment the contour level, and repeat untilc
exceedsmax(Z)
. Extra logic is needed for squares where a contour passes through all four edges (saddle points) to determine which pairs of edges to connect.contour
,contour3
, andcontourf
return a two-row matrix that specifies all the contour lines:
C = [ value1 xdata(1) xdata(2)... numv ydata(1) ydata(2)...]
The first row of the column that begins each definition of a contour line contains the contour value, as specified by
v
and used byclabel
. Beneath that value is the number of (x,y) vertices in the contour line. Remaining columns contain the data for the (x,y) pairs. For example, the contour matrix calculated byC = contour(peaks(3))
is as follows.The circled values begin each definition of a contour line.
contourc
是contour
、contour3
和contourf
使用的底层函数。这是一个内置函数,因此它是编译代码,用户无法看到。在较新版本的MATLAB中,内联文档中并没有对算法进行真正的讨论。旧版本的MATLAB可能会有更多的内联细节。 - sco1