contour

contour — level curves on a 3D surface

Calling sequence

contour(x,y,z,nz,[theta,alpha,leg,flag,ebox,zlev])  
contour(x,y,z,nz,<opt_args>)

Parameters

x,y : two real row vectors of size n1 and n2.

z : real matrix of size (n1,n2), the values of the function.

nz

: the level values or the number of levels.

-

If nz is an integer, its value gives the number of level curves equally spaced from zmin to zmax as follows:



 z= zmin + (1:nz)*(zmax-zmin)/(nz+1)

Note that the zmin and zmax levels are not drawn (generically they are reduced to points) but they can be added with



 [im,jm] = find(z == zmin);     // or zmax 
 plot2d(x(im)',y(jm)',-9,"000")

- If nz is a vector, nz(i) gives the value of the ith level curve. Note that it can be useful in order to see zmin and zmax level curves to add an epsilon tolerance: nz=[ zmin+%eps,..,zmax-%eps].

<opt_args> : a sequence of statements key1=value1, key2=value2, ... where keys may be theta,alpha,leg,flag, ebox,zlev (see below). In this case, the order has no special meaning.

theta, alpha : real values giving in degree the spherical coordinates of the observation point.

leg : string defining the captions for each axis with @ as a field separator, for example "X@Y@Z".

flag

: a real vector of size three flag=[mode,type,box].

mode

: string (treatment of hidden parts).

`mode>0`	the hidden parts of the surface are removed and the surface is painted with color `mode`.
`mode=0`	the hidden parts of the surface are drawn.
`mode<0`	only the shadow of the surface is painted with color or pattern id `-mode`. Use `xset()` to see the meaning of the ids.

type

: an integer (scaling).

`type=0`	the plot is made using the current 3D scaling (set by a previous call to `param3d`, `plot3d`, `contour` or `plot3d1`).
`type=1`	rescales automatically 3d boxes with extreme aspect ratios, the boundaries are specified by the value of the optional argument `ebox`.
`type=2`	rescales automatically 3d boxes with extreme aspect ratios, the boundaries are computed using the given data.
`type=3`	3d isometric with box bounds given by optional `ebox`, similarily to `type=1`
`type=4`	3d isometric bounds derived from the data, to similarily`type=2`
`type=5`	3d expanded isometric bounds with box bounds given by optional `ebox`, similarily to `type=1`
`type=6`	3d expanded isometric bounds derived from the data, similarily to `type=2`

box

: an integer (frame around the plot).

`box=0`	nothing is drawn around the plot.
`box=1`	unimplemented (like box=0).
`box=2`	only the axes behind the surface are drawn.
`box=3`	a box surrounding the surface is drawn and captions are added.
`box=4`	a box surrounding the surface is drawn, captions and axes are added.

ebox : used when type in flag is 1. It specifies the boundaries of the plot as the vector [xmin,xmax,ymin,ymax,zmin,zmax].

zlev : real number.

Description

contour draws level curves of a surface z=f(x,y). The level curves are drawn on a 3D surface. The optional arguments are the same as for the function plot3d (except zlev) and their meanings are the same. They control the drawing of level curves on a 3D plot. Only flag(1)=mode has a special meaning.

`mode=0`	: the level curves are drawn on the surface defined by (x,y,z).
`mode=1`	: the level curves are drawn on a 3D plot and on the plan defined by the equation z=zlev.
`mode=2`	: the level curves are drawn on a 2D plot.

You can change the format of the floating point number printed on the levels by using xset("fpf",string) where string gives the format in C format syntax (for example string="%.3f"). Use string="" to switch back to default format and Use string=" " to suppress printing.

Usually we use contour2d to draw levels curves on a 2D plot.

Enter the command contour() to see a demo.

Examples



t=%pi*[-10:10]/10;
deff("[z]=surf(x,y)","z=sin(x)*cos(y)"); z=feval(t,t,surf);
rect=[-%pi,%pi,-%pi,%pi,-1,1];
contour(t,t,z,10,35,45," ",[0,1,0],rect)
// changing the format of the printing of the levels
xset("fpf","%.2f")
xbasc()
contour(t,t,z,10,flag=[0,1,0],ebox=rect)

Author

J.Ph.C.