h37r.html

Function: crop - restrict a plot to a box

Calling sequence:

crop(P,[a..b,c..d],x);
crop(P,[a..b,c..d,e..f],x);

Parameters:

P - a two- or three-dimensional plot structure

a, b, c, d, e, f - real constants (possibly infinite)

x - (optional) anything

Description:

This procedure takes a plot and removes all parts of it that lie outside a given rectangular box:

and (in three dimensions)

Visually the effect is similar to using the view option. However, when the view option is used the rest of the plot is still present, only the rendering system is instructed not to show it. This can cause problems when the plot is combined with other plots using display .

The Maple Advisor Database patch displayarraypatch uses crop automatically to handle arrays of plots where some plots include the view option.

If the optional third argument x is present, invisible (zero-length) curves are added at corners of the box so that the complete box is shown, even if a smaller box would suffice to show the visible objects.

The crop procedure works with all plot elements: points, curves, polygons, surfaces (GRID, MESH and ISOSURFACE structures) and text, produced by any of the plotting commands.

Text is removed if the associated point is outside the box. No attempt is made to check what part of the actual text fits inside the box (that could vary, as plots can be resized).

Curves or polygons are truncated correctly at the edges of the box. In the case of three-dimensional GRID, MESH or ISOSURFACE structures, however, crop acts by making vertices outside the box undefined. This removes all surface elements that have one or more vertices outside the box. Thus the edge of the remaining surface may be rather ragged, and may not extend all the way to the sides of the box.

This procedure is part of the Maple Advisor Database.

Examples:

Two plots, and their combination using display .

> A:= plot(x,x=0..1,colour=red):
B:= plot(1-x,x=0..1,colour=blue):
plots[display]([A,B],scaling=constrained);

The view option works on each individually, but not with the combination: it uses the largest rectangle containing both of the view rectangles, which in this case contains more of the red line than we ask for.

> Av:= plot(x,x=0..1,colour=red,view=[0..0.5,0..0.5]):
Bv:=plot(1-x,x=0..1,colour=blue,view=[0.2..0.8,0.2..0.8]):
plots[display]([Av,Bv],scaling=constrained);

Combining plots together with the use of crop .

> Ac:= crop(A,[0..0.5,0..0.5]):
Bc:= crop(B,[0.2 .. 0.8, 0.2 .. 0.8]):
plots[display]([Ac,Bc],scaling=constrained);

An example with a line segment, points, text and a polygon.

> P:= plots[display]({plot([[0,0],[10,10]],colour=red),
plots[pointplot]({seq([i,i+1],i=0..10)},colour=black,symbol=box), plots[polygonplot]([seq([i,(i-5)^2/2],i=0..10)],colour=cyan),
plots[textplot]({seq([i,i-1,convert(i,string)],i=0..10)},colour=blue)}): P;

> crop(P,[1 .. 5,3 .. 5]);

Using the optional third argument to ensure the whole box is in the plot:

> crop(P,[1..5,3..5],true);

A three-dimensional example:

> Q:= plots[display]({
plots[spacecurve]([[0,0,-3],[0,0,3]],colour=green),
plots[tubeplot]([2*cos(t),2*sin(t),0],t=0..2*Pi,radius=1),
plots[pointplot3d]([seq([2*cos(j*Pi/5),2*sin(j*Pi/5),2],j=0..9)],symbol=box,symbolsize=15,colour=blue),
plots[textplot3d]({seq([2*cos(j*Pi/5),2*sin(j*Pi/5),3,convert([65+j],bytes)],j=0..9)},colour=red)
},scaling=constrained): Q; crop(Q,[0..3,-3..3,0..infinity]);

Ragged edges caused by removing surface elements.

> crop(Q,[-1.5..3,-3..3,-1..1]);

Maple Advisor Database R. Israel, 2000