lab3

Lab 3 - Transformation Matrices

You should work individually on this assignment. To receive credit, demonstrate your completed program during lab or create a tag called lab03 push your code (and tag) up to Bitbucket and submit the hash to D2L prior to class on the due date.

In this lab, you’ll learn how to combine transformation matrices to move objects around in 2D space. A unit square, centered at the origin, is provided with its vertices set to red, green, blue, and yellow. You’ll transform the square using translation, rotation and scaling matrices. All three matrices will be combined in your vertex shader to transform the points in your scene. You may NOT use a linear algebra library for this lab.

Recommended Reading

Uniform Variables

• GL Chapter 2: Storage qualifiers
• Uniform variables (Uniforms section)

Transformations

• FoCG Section 6.1,.3
• Wikipdeia: Translation Matrix
• Wikipedia: Scale Matrix
• Wikipedia: Rotation Matrix

Part 1 - Transformation matrices

Use the translation, rotation and scale values to construct a transformation matrix that will be passed to your vertex shader to adjust the square’s transform. You must implement the matrices and their operations. Update your vertex shader to accept a uniform variable for the transformation and use it correctly to transform your vertex data.

Part 2 - Modes

Show off your work! Use your transformation matrices to implement 4 modes.

• static: image is non-changing
• rotate center: rotate the square around the center of the window
• rotate off center: rotate the square around a point that is not at the center of the window.
• scale: scale the square
• impress me: combine multiple matrix transformations to move your square however you like.

The user should change modes on spacebar release.

Some helpful tricks for simple periodic animation is to use sin and cos of the time. You can control speed by scaling the time. Get the time with glfwGetTime().

Here is an example in a (very low quality) animated gif.

Things to notice

Now that you have your transformations implemented make sure to spend some time understanding how the order of the matrix multiplications effects the resulting transformation. Also pay attention to how the range of the values effect the result. For example, what is the result of a negative scaling?