Building a Simple Ball and Stick Molecule Graphic
from Graphics Primitives
Often the visualization of data can be performed most conveniently
by making use of Mathematica's graphics programming language
directly. One organizes various points, lines, textual elements,
3-dimensional primitives, and so on, in graphics objects such as
and then displays them using the function Show.
The standard reference for all of this (in addition to "The
Mathematica Book") is Tom Wickham-Jones's book, "Mathematica
Here we do a rather simple exercise: produce a "ball and
stick" graphic of a molecule. The molecule is specified in
terms of the atoms that it is composed of, their coordinates in
a Cartesian coordinate system, and the bonds between them.
Here is the atomic data. It is a list of lists, each of the form
the latter three quantities specifying the cartesian coordinates
of the atom.
And here is the bond data. Each sublist is of the form ,
where the bond extends from atom1 to atom2
(The integers that specify atom1 and atom2 are just
the positions in the list of the atoms in AtomData.)
The list of atom coordinates, AtomCoordinates,
and their respective types, AtomTypes,
can be easily extracted from AtomData
Similarly the bond information can be extracted.
The graphics primitives for the atoms will be built up in two
steps. For each atom's coordinates we create a Point
object with a size specification. These are both placed in a list
along with the atom type. The latter is not a graphics directive,
but we will use it later, via a replacement rule, to insert a color
directive chosen differently for each atom type. We use the function
MapIndexed to do
all of this at once since the part specification that MapIndexed
provides to the function is just the integer that specifies the
|MapIndexed[f, expr] applies f to the
elements of expr, giving the part specification of each element
as a second argument to f. MapIndexed[f, expr, levspec] applies
f to all parts of expr on levels specified by levspec.
|Usage message for MapIndexed
In a similar way we build up the bonds with line primitives (the
creates the pairs of starting and ending points for the bond lines).
Now we define some colors to use.
Finally we replace the atom types and the bond types with the
color directives. Replacement rules do this easily.
Now we can show the graphic.
You can get a better sense of the three dimensional structure
of this molecule by animating it. This is simplified by using the
from the standard add-on package Graphics`Animation`.
First load the package.
Now generate the animation. To view the animation select the cell
and choose the menu item,
or use its keyboard equivalent.