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The new code in Listing 8 is highlighted by a long explanatory comment near the middle of Listing 8 . I will leave it as an exercise for the student to think about the rationale that was used to decide which lines to draw and which linesto suppress depending on the algebraic sign of the dot product between the two vectors.

Otherwise, no explanation of the code should be necessary beyond the embedded comments.

Homework assignment

The homework assignment for this module was to study the Kjell tutorial through Chapter 10, Angle between 3D Vectors.

The homework assignment for the next module is to study the Kjell tutorial through Chapter 11, Projections.

In addition to studying the Kjell material, you should read at least the next two modules in this collection and bring your questions about that material tothe next classroom session.

Finally, you should have begun studying the physics material at the beginning of the semester and you should continue studying one physics moduleper week thereafter. You should also feel free to bring your questions about that material to the classroom for discussion.

Run the program

I encourage you to copy the code from Listing 9 through Listing 13 . Compile the code and execute it in conjunction with the game-math library named GM02 in Listing 9 . Experiment with the code, making changes, and observing the results of your changes. Make certain that youcan explain why your changes behave as they do.

Summary

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

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

What's next?

In the next module, you will learn about first-person computer games in general, and how to use the game-math library to write a first-person game in a3D world using the game math library.

Miscellaneous

This section contains a variety of miscellaneous information.

Housekeeping material
  • Module name: GAME 2302-0150: Applications of the Vector Dot Product
  • File: Game0150.htm
  • Published: 10/23/12
  • Revised: 02/01/16
Disclaimers:

Financial : Although the Connexions site makes it possible for you to download a PDF file for thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.

I also want you to know that, I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.

In the past, unknown individuals have copied my modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing me as the author. Ineither receive compensation for those sales nor do I know who does receive compensation. If you purchase such a book, please beaware that it is a copy of a module that is freely available on cnx.org and that it was made and published withoutmy prior knowledge.

Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir 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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