mini tutorial





In this tutorial I want to focus on two things:
  • The equality of the transform module to the application of a translate, rotate and scale module in exactly this order
  • The importance of the order of matrix modules in general.

I won't explain the creation of the project step by step. It's a good exercise to recreate the project from the screenshots.

The basic setup of the project is shown below:

A camera displays a red cube and a blue sphere, both located at the origin. The cube will be transformed by a transform matrix module. The transformation consists of a translation along the y-axis (up), a rotation around the z-axis (pointing out of the screen) and a scaling along the x-axis (to the right).

The next step shows one of many ways to display the equality of the tranform module and the application of a translate, a rotate and a scale matrix module:

Instead of copying the cube and the sphere modules with their color attributes, I inserted two label modules below them and linked these in the additional hierarchy with goto modules.

The result of this test is shown below (with the clear frame of the global modulator switched of, to display the movement of the cube):

As expected, the two structures behave equal.

In the final project we test the result of the six possible different orders of the transformations:

Every matrix stack got an additional text module describing the order of the matrix application. The original transform module was deactivated by inserting another label.

The following images show the result at an intermediate point of the animation cycle:

This screenshot displays one feature of transformation orders very nicely:

A scale transformation followed by a rotation 'distorts' objects.

The next screen displays the different movements of the cubes in a full animation cycle:

The [scale translate rotate] and [translate scale rotate] order result in the same movement, also the [rotate scale translate] and [rotate translate scale] orders. So we come to the conclusion of this minitutorial:

Different transformation orders have different results
(only exception: translation/scale equals scale/translation).

Project File

matrices.kds Logo