MATH 261, Spring 2001 Due Date: Name(s):
Project 13.5b: 3-D Graphics, Lines and Planes
Objective
The objective of this project is to introduce some basic 3-dimensional graphics commands and to illustrate
them in the context of lines and planes.
Narrative
If you have not already done so, read Section 13.5 in the text.
In this project we introduce the commands implicitplot3d and setoptions3d in Maple's plots package.
The command implicitplot3d allows us to plot the graph of a surface defined implicitly by an equation
in x, y, and z, over specified ranges of x, y, and z. The command setoptions3d allows us to set certain
options to 3-dimensional plotting commands so that we do not have to repeatedly type them.
While certain options will be specified in the projects in this course, it may be necessary to modify some
options because of differences in hardware and software. (For example, a graphic that looks great on the
screen and on someone else's printer may turn out so poorly on your printer that it is not acceptable.)
Consult your instructor if you run into a problem, and listen to your instructor for directions on to handle
problems that you and others may run into.
Tasks 1
1. a) Type the command lines below into Maple in the order in which they are listed; they produce a
graphic of a plane.
> # Project 13.5b: 3-D Graphics, Lines and Planes
> # Task 1a
> restart: with(plots):
> implicitplot3d(x/2+y/3+z/4=1,x=-2..2,y=-3..3,z=0..4,style=hidden,shading=none,
axes=normal,projection=normal,scaling=constrained,orientation=[10,60]);
Note the options to implicitplot3d.
b) Continue by typing the command lines below into Maple in the order in which they are listed:
> # Task 1b
> implicitplot3d(x/2+y/3+z/4=1,x=-2..2,y=-3..3,z=0..4);
Note the absence of options to implicitplot3d.
c) Now click on the graphic you created in part (b), and use the tools that appear at the top of the
screen to get exactly the same graphic you got in part (a). Note that the orientation is specified by the
angles  and  in the menu bar, and that you can change  and  by retyping their values, by using the
up- and down-indicator arrows, or by clicking on the graphic and dragging the image.
2. a) Type the command lines below into Maple in the order in which they are listed.
> # Task 2
> setoptions3d(axes=normal,scaling=constrained,color=blue,orientation=[-6,45]);
1Since some parts of the code you will use in this course require large amounts of RAM, you may need to consult your local
computer guru to find out how to boost the available RAM on your computer.
The affect of the setoptions3d command is to set certain options so that they do not have to be
repeatedly typed in a Maple session.
b) Continue by typing the command lines below into Maple in the order in which they are listed.
They illustrate a line segment and the projection planes whose intersection is the line segment. (The
projection planes of a line or line segment in 3-space are the planes parallel to the coordinate axes whose
intersection is the line or line segment.)
> plot0 := spacecurve([2*t,3*t,4*t],t=0..1,shading=none,color=red,thickness=3):
> display(plot0,axes=normal);
> plot1 := implicitplot3d(y=1.5*x,x=0..2,y=0..3,z=0..4,color=blue,shading=none):
> display({plot0,plot1},axes=normal);
> plot2 := implicitplot3d(z=2*x,x=0..2,y=0..3,z=0..4,color=green,shading=none):
> plot3 := implicitplot3d(z=4*y/3,x=0..2,y=0..3,z=0..4,color=yellow,shading=none):
> display({plot0,plot1,plot2,plot3},axes=normal);
At this time, make a hard-copy of your typed input and Maple's responses. Then, ...
3. a) Label by hand the positive x-, y-, and z-coordinate axes on the first graphic you drew in Task 1.
b) On the graphic you created in part (b), label (by hand) each projection plane with its equation, and
highlight (by hand) the line segment.
Comments
In general, you can specify certain options before you draw a graphic or after you draw a graphic; in part
(a) of Task 1, you specified the options before you drew the graphic, and in part (c) you selected the options
after you drew the graphic. The importance of knowing how to specify options after you have drawn a
graphic is that you will not always know how to specify the options you want before you draw a graphic;
and at those times you will need to specify them interactively after you have drawn the graphic. Also, in
future projects, although a default set of display options may at times specified, you may (depending on the
hardware you're using) need to modify them to get an acceptable hard-copy.