plot3d - 3D plot of a surface

Calling Sequence

plot3d(x,y,z,[theta,alpha,leg,flag,ebox])

plot3d(x,y,z,<opt_args>)

plot3d(xf,yf,zf,[theta,alpha,leg,flag,ebox])

plot3d(xf,yf,zf,<opt_args>)

plot3d(xf,yf,list(zf,colors),[theta,alpha,leg,flag,ebox])

plot3d(xf,yf,list(zf,colors),<opt_args>)

Parameters

• x,y : row vectors of sizes n1 and n2 (x-axis and y-axis coordinates). These coordinates must be monotone.
• z : matrix of size (n1,n2). z(i,j) is the value of the surface at the point (x(i),y(j)).
• xf,yf,zf : matrices of size (nf,n). They define the facets used to draw the surface. There are n facets. Each facet i is defined by a polygon with nf points. The x-axis, y-axis and z-axis coordinates of the points of the ith facet are given respectively by xf(:,i), yf(:,i) and zf(:,i).
• colors : a vector of size n giving the color of each facets or a matrix of size (nf,n) giving color near each facet boundary (facet color is interpolated )
• <opt_args> : This represents a sequence of statements key1=value1, key2=value2,... where key1, key2,... can be one of the following: theta, alpha ,leg,flag,ebox (see definition below)
• 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 backward facing facets are 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 similarilytype=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].

Description

plot3d(x,y,z,[theta,alpha,leg,flag,ebox]) draws the parametric surface z=f(x,y).

plot3d(xf,yf,zf,[theta,alpha,leg ,flag,ebox]) draws a surface defined by a set of facets. You can draw multiple plots by replacing xf, yf and zf by multiple matrices assembled by rows as [xf1 xf2 ...], [yf1 yf2 ...] and [zf1 zf2 ...].

You can give a specific color for each facet by using list(zf,colors) instead of zf, where colors is a vector of size n. If colors(i) is positive it gives the color of facet i and the boundary of the facet is drawn with current line style and color. If colors(i) is negative, color id -colors(i) is used and the boundary of the facet is not drawn. Use xset() to see the ids of the colors.

It is also possible to get interpolated color for facets. For that the color argument must be a matrix of size nfxn giving the color near each boundary of each facets. In this case positive values for colors mean that the boundary are not drawn.

The optional arguments theta,alpha,leg ,flag,ebox, can be passed by a sequence of statements key1=value1, key2=value2, ... In this case, the order has no special meaning.

You can use the function genfac3d to compute four sided facets from the surface z=f(x,y). eval3dp can also be used.

Enter the command plot3d() to see a demo.

Examples

// simple plot using z=f(x,y)
t=[0:0.3:2*%pi]'; z=sin(t)*cos(t');
plot3d(t,t,z)
// same plot using facets computed by genfac3d
[xx,yy,zz]=genfac3d(t,t,z);
xbasc()
plot3d(xx,yy,zz)
// multiple plots
xbasc()
plot3d([xx xx],[yy yy],[zz 4+zz])
// multiple plots using colors
xbasc()
plot3d([xx xx],[yy yy],list([zz zz+4],[4*ones(1,400) 5*ones(1,400)]))
// simple plot with viewpoint and captions
xbasc()
plot3d(1:10,1:20,10*rand(10,20),35,45,"X@Y@Z",[2,2,3])
// plot of a sphere using facets computed by eval3dp
deff("[x,y,z]=sph(alp,tet)",["x=r*cos(alp).*cos(tet)+orig(1)*ones(tet)";..
  "y=r*cos(alp).*sin(tet)+orig(2)*ones(tet)";..
  "z=r*sin(alp)+orig(3)*ones(tet)"]);
r=1; orig=[0 0 0];
[xx,yy,zz]=eval3dp(sph,linspace(-%pi/2,%pi/2,40),linspace(0,%pi*2,20));
xbasc();plot3d(xx,yy,zz)

xbasc();xset('colormap',hotcolormap(128));
r=0.3;orig=[1.5 0 0];
[xx1,yy1,zz1]=eval3dp(sph,linspace(-%pi/2,%pi/2,40),linspace(0,%pi*2,20));
cc=(xx+zz+2)*32;cc1=(xx1-orig(1)+zz1/r+2)*32;   
xbasc();plot3d1([xx xx1],[yy yy1],list([zz,zz1],[cc cc1]),70,80)

xbasc();plot3d1([xx xx1],[yy yy1],list([zz,zz1],[cc cc1]),theta=70,alpha=80,flag=[5,6,3])
 

See Also

eval3dp  genfac3d  geom3d  param3d  plot3d1  xset  

Author

J.Ph.C.