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 or a Scilab function which defines the surface z=f(x,y) .
• 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 representation mode.
    • 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.
  • 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=linspace(-%pi,%pi,30);
function z=my_surface(x,y),z=x*sin(x)^2*cos(y),endfunction

contour(t,t,my_surface,10)
// changing the format of the printing of the levels
xset("fpf","%.1f")
xbasc()
contour(t,t,my_surface,10)
// 3D
xbasc()
z=feval(t,t,my_surface);
plot3d(t,t,z);contour(t,t,z+0.2*abs(z),20,flag=[0 2 4]);
//

 
  

See Also

contour2d ,   plot3d ,  

Author

J.Ph.C.