1.16 Game 2302-0150: applications of the vector dot product  (Page 9/14)

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.