Linear Algebra Exercises

General notes on architecture

This is a JavaFX application which is split up into two major packages: The Application-Package and the Exercises-Package.

Application-Package

This package contains the main entry point of the application (class Main). The Main class loads the main window that will contain all exercises in a TabPane so that each Tab represents and loads one exercise. The ApplicationController class is assigned as controller to the application via the application.fxml user interface.

The ApplicationController is responsible for loading the individual exercises dynamically into the tabs of the TabPane. After the main window has successfully loaded, the Main class calls the controller to initialize the tabs and load the first exercise.

All exercises must implement the ifExercise interface.

Exercises-Package

Since many of the exercises are going to use common components, it is a good idea to only implement them once and make them available to the individual exercises. Here’s a short description on the common parts:

ifCanvasDrawable interface

This interface must be implemented by all objects that need to be drawn onto a JavaFX Canvas. Drawables will be iteratively called by the main render routine using the draw method which is passed a GraphicsContext reference. Thus, the actual process of drawing is delegated to the individual drawables themselves since they know best how to do it. The only thing that is decided by the class rendering the scene is where (which GraphicsContext) and when the objects are drawn.

AbstractExercise class

Implements an exercise container in its very basic functionalities. All it does is store a reference to the main exercise container (i.e. the Tab’s contents) and calling the onExerciseInitialized hook.

AbstractCanvasExercise class

Basic implementation of a JavaFX-Canvas-based exercise. This class extends the AbstractExercise class and implements all steps required to set up a JavaFX-Canvas element. A reference to the GraphicsContext of the Canvas is stored as protected so that it is available to all sub-classes.

Matrix class

This class represents a model of a matrix and provides methods to get and set values and to perform simple mathematical operations. The dimensions of the matrix are set on initialization and are immutable.

Vector2D class

As vectors are a specialized form of matrices, the Vector2D class inherits from the Matrix class. It implements methods for vector-specific operations such as calculating its length (i.e. magnitude) or its scalar product, for example.

Exercises

Exercise 1: «Wohin klickt die Maus?»

Using linear algebra to determine if a given set of coordinates lies on a specific line segment or not. Goto Exercise 1 Docs

Exercise 2: «Affine Transformationen»

Transforming geometry using matrices. Goto Exercise 2 Docs

Exercise 3: «Rotation 3D-Cube»

Rotating a 3D cube. Goto Exercise 3 Docs

Exercise 4: «Page Rank Algorithm»

A brief overview over Google’s Page Rank Algorithm. Goto Exercise 4 Docs