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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

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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
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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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