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I will also provide exercises for you to complete on your own at the end of most of the modules. Those exercises will concentrate on the material that youhave learned in that module and previous modules.

Viewing tip

II recommend that you open another copy of this module in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.


  • Figure 1 . Graphics illustration of four points and two lines.
  • Figure 2 . First of three views in the construction of a 3D human figure.
  • Figure 3 . Second of three views in the construction of a 3D human figure.
  • Figure 4 . Third of three views in the construction of a 3D human figure.
  • Figure 5 . Screen output from the program named PointLine02.
  • Figure 6 . Sample output from updated programming-math library.
  • Figure 7 . Graphic output from Exercise 1.
  • Figure 8 . Text output from Exercise 2.
  • Figure 9 . Text output from Exercise 3.


  • Listing 1 . The controlling class named PointLine01.
  • Listing 2 . Beginning of the class named GUI.
  • Listing 3 . Beginning of the inner class named MyCanvas.
  • Listing 4 . Define two points as two locations in space.
  • Listing 5 . Construct a line segment.
  • Listing 6 . Construct an object that represents a vertical line segment.
  • Listing 7 . Draw the two lines on the screen.
  • Listing 8 . Beginning of the class named PointLine02.
  • Listing 9 . Beginning of the class named GM2D01.
  • Listing 10 . Exercising the Point class.
  • Listing 11 . The static top-level class named Point.
  • Listing 12 . The static top-level class named Vector.
  • Listing 13 . The static top-level class named Line.
  • Listing 14 . Source code for the program named PointLine01.
  • Listing 15 . Source code for the program named PointLine02.
  • Listing 16 . Source code for the game-programming math library named GM2D01.


In this module, I will introduce you to an excellent interactive tutorial titled Vector Math for 3D Computer Graphics written by Dr. Bradley P. Kjell, (which you can also download in zip-file format from a link in the first module in this collection) . Then I will present and explain two sample programs and a sample game-programming math library intended to implement concepts from Dr.Kjell's tutorial in Java code.

Discussion and sample code

Points, lines, and vectors

Your homework assignment from the previous module was to study CHAPTER 0 -- Points and Lines and also to study CHAPTER 1 -- Vectors, Points, and Column Matrices down through the topic titled Variables as Elements in Kjell's tutorial.

You may have previously believed that you already knew all there was to know about points and lines. However, I suspect that you found explanations of some subtleissues that you never thought about before when studying those tutorials. In addition, Kjell begins the discussion of vectors and establishes the relationship between a vector and acolumn matrix in this material.

Represent a point with a column matrix

Hopefully you understand what Kjell means by a column matrix and you understand that a column matrix can be used torepresent a point in a given coordinate frame. The same point will have different representations in different coordinate frames. (You must know which coordinate frame is being used to represent a point with a column matrix.)

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Game 2302 - mathematical applications for game development. OpenStax CNX. Jan 09, 2016 Download for free at https://legacy.cnx.org/content/col11450/1.33
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