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Learn how to use the dot product to compute nine different angles of interest that a vector makes with various elements in 3D space. Also learn how to use the dot product to find six of the infinite set of vectors that are perpendicular to a given vector, and how to use the dot product to perform back-face culling of an image.

Table of contents

Preface

This module is one in a collection of modules designed for teaching GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX.

What you have learned

In the previous module, which was the first part of a two-part miniseries on the vector dot product, you learned the fundamentals of the vector dot productin both 2D and 3D. You learned how to update the game-math library to support various aspects of the vector dot product, and you learned how to write 2D and3D programs that use the vector dot product methods in the game-math library.

What you will learn

In this module, you will learn how to apply the vector dot product to three different applications. You will learn

  • how to use the dot product to compute nine different angles of interest that a vector makes with various elements in 3D space,
  • how to use the dot product to find six somewhat unique vectors of the infinite set of vectors that are perpendicular to a given vector as shown in Figure 4 , and
  • how to use the dot product to perform back-face culling to convert the image shown in Figure 1 to the image shown in Figure 2 .

Figure 1 - A 3D image before back-face culling.

Missing image.

Figure 2 - The 3D image after back-face culling.

Missing image.

Viewing tip

I 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.

Figures

  • Figure 1 . A 3D image before back-face culling.
  • Figure 2 . The 3D image after back-face culling.
  • Figure 3 . Screen shot of the output from the program named DotProd3D05.
  • Figure 4 . Six (magenta) vectors that are perpendicular to a given (black) vector.
  • Figure 5 . Screen output when one coordinate has a value of zero.
  • Figure 6 . A general formulation of 3D vector perpendicularity.
  • Figure 7 . Output from Exercise 1.
  • Figure 8 . Output from Exercise 2.

Listings

  • Listing 1 . Beginning of the actionPerformed method in the program named DotProd3D05.
  • Listing 2 . Create ColMatrix3D objects that represent projections.
  • Listing 3 . Create and draw vectors.
  • Listing 4 . Compute and display the nine angles.
  • Listing 5 . Beginning of the actionPerformed method for the program named DotProd3D06.
  • Listing 6 . Remainder of the actionPerformed method.
  • Listing 7 . The method named drawTheCylinder in DotProd3D04.
  • Listing 8 . The method named drawTheCylinder in DotProd3D03.
  • Listing 9 . Source code for the game-math library named GM02.
  • Listing 10 . Source code for the program named DotProd3D05.
  • Listing 11 . Source code for the program named DotProd3D06.
  • Listing 12 . Source code for the program named DotProb3D04.
  • Listing 13 . Source code for the program named DotProb3D03.

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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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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