Overview of the geom3d Package

geom3d[ command ]( arguments )

command ( arguments )

• The commands in the geom3d  package enable you to work in three-dimensional Euclidean geometry. Note that the package does not support the extended space, that is, it does not handle points at infinity and lines at infinity.
• Each command in the geom3d  package can be accessed by using either the long form  or the short form  of the command name in the command calling sequence.
• The geometric objects  supported in this package are: point, segment, directed segment, line, plane, triangle, sphere, and polyhedra. To create the basic geometric objects, use the following commands.
• For basic geometric objects, the following commands are supported.
• Point:
• Segment/Directed Segment:
• Line:
• Plane:
• Triangle:
• Sphere:
• The study of polyhedra has been one of the most enduring, fascinating topics of geometry. The geom3d  package supports various types of polyhedra.
• Regular Polyhedra:
• Quasi-regular Polyhedra:
• General Polyhedra:
• Archimedean Solids:
• Duality:
• The two processes to construct new polyhedra from given polyhedra are also supported.
• Various types of geom3d[transformation]  are supported.
• The geom3d[draw]  command provides the graphical visualization of all objects supported in the package.
• Other commands are also implemented.
• To display the help page for a particular geom3d  command, see Getting Help with a Function in a Package .
• When an object is defined using its algebraic representation (that is, an equation or a polynomial), you can use any name for the x-axis, the y-axis, and the z-axis. In general, the names of the axes must be included when you define an object. A simple way to set the names without being prompted is to set the environment variables _EnvXName , _EnvYName , and _EnvZName  to the axis names (or _EnvTName  for the case of line ) that you prefer.
• For commands in the package that create a geometric object, or a list of geometric objects, the calling sequence is of the form command_call(obj,...)  where obj  is either a name of the geometric object to be created, or a list of geometric objects to be created.
• Note that you must make explicit assumptions for the symbolic names in an object (such as, real, positive, ...) when you want to apply a test (for example, AreOnObject) to an object. In this case, the power of the geom3d  package is dependent on the power of the Maple assume  command.
• For commands where output is a boolean value ( true , false , FAIL ), the calling sequence is of the form command_call(..., cond) , where cond  is a an optional name. If the output is FAIL , and this optional argument is given, then the condition that makes the output true is assigned to cond . The value of cond  might be a Maple expression (use assume(cond) ), or of the form cond = &or(expr_1,...,expr_n)  or cond = &and(expr_1,...,expr_n)  (use assume(op(i,cond))  for the former case where i  is from 1 to n; and assume(op(cond))  for the latter case.

geom3d[objects] , geom3d[transformation] , geom3d[draw] , UsingPackages