# 1.9 Game 2302-0125: vector addition

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Learn how to add two or more vectors. Also learn about the head-to-tail rule in vector addition, about the vector addition parallelogram, about the relationship between the length of the sum of vectors and the lengths of the individual vectors in the sum, how to add a vector to a point, how to get the length of a vector, and how to represent an object in different coordinate frames.

## 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 couple of modules, you learned:

• How to compare column matrices for equality
• How to compare two points for equality
• How to compare two vectors for equality
• How to add one column matrix to another
• How to subtract one column matrix from another
• How to get a displacement vector from one point to another

What you will learn

In this module you will learn:

• How to add two or more vectors
• About the relationship between the length of the sum of vectors and the lengths of the individual vectors in the sum
• How to add a vector to a point
• How to get the length of a vector
• How to represent an object in different coordinate frames

## 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 . Screen output from the program named VectorAdd01.
• Figure 2 . Screen output from CoordinateFrame01 at startup.
• Figure 3 . Screen output from CoordinateFrame01 after changes to the coordinate frame.
• Figure 4 . Screen output from the program named VectorAdd02.
• Figure 5 . Graphic screen output from the program named VectorAdd03.
• Figure 6 . Command-line output from the program named VectorAdd03.
• Figure 7 . Screen output from the program named VectorAdd04.
• Figure 8 . Screen output from Exercise 1.
• Figure 9 . Screen output from Exercise 2.

## Listings

• Listing 1 . The add method of the GM2D04.Vector class.
• Listing 2 . The getLength method of the GM2D04.Vector class.
• Listing 3 . The addVectorToPoint method of the GM2D04 class.
• Listing 4 . Beginning of the program named VectorAdd01.
• Listing 5 . Beginning of the method named drawOffScreen.
• Listing 6 . The method named setCoordinateFrame.
• Listing 7 . Adding two vectors.
• Listing 8 . Draw vecA in RED with its tail at the origin.
• Listing 9 . Draw vecB in GREEN head-to-tail with vecA.
• Listing 10 . Draw sumOf2 in MAGENTA with its tail at the origin.
• Listing 11 . Extending the example to three vectors.
• Listing 12 . The actionPerformed method.
• Listing 13 . The setCoordinateFrame method.
• Listing 14 . Beginning of the drawOffScreen method.
• Listing 15 . Define a point to position the vectors.
• Listing 16 . Remaining code in the drawOffScreen method.
• Listing 17 . Beginning of the method named drawOffScreen of the program named VectorAdd02.
• Listing 18 . Do the same operations in a different order.
• Listing 19 . Source code for the game-math library named GM2D04.
• Listing 20 . Source code for the program named VectorAdd01.
• Listing 21 . Source code for the program named CoordinateFrame01.
• Listing 22 . Source code for the program named VectorAdd02.
• Listing 23 . Source code for the program named VectorAdd03.
• Listing 24 . Source code for the program named VectorAdd04.

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