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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

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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