LAB3: Applying Math

This lab is to some extent based on Chapter 4 in the textbook, in particular sections 4.2.1 “Points and Cartesian Coordinates” and 4.2.4 “Vector Operations”.

The main focus here is to learn how we can use other coordinate systems to help us generate effects or behaviour that would be unintuitive to do with Cartesian coordinates.

Discussion thread for this lab is here: Lab 3 Discussion Thread

There are two main parts to this lab. In the first part, which has you thinking about coordinate systems, you create an animation effect that spins an object along a cylindrical path. In the second part, which focuses on vector operations, you use a simple dot product to find which direction you are facing relative to another object.

1. Create a new Project with the instructions from lab 1 or 2.
2. Make sure you have the completed Lab2 project (the optional steps are not necessary)
3. OgreMath.h included in your source file to access the Ogre::Math::Cos() and Ogre::Math::Sin() functions

Follow these steps to complete the lab project:

1. Attach an Object to the Ogre You should create a new movable entity that will be attached to the Ogre entity (from Lab2) wherever it goes. Essentially this new entity, that we will call “The Cube”, will exist in the coordinate system of the Ogre model. To do this, you need to create a new SceneNode as a child of the Ogre's scene node, and attach the Cube to that node. This means that all transformations applied to the Ogre's scene node will be passed down into the Cube's scene node as well. So, do the following:
   1. Add a member variable to your application class to hold the old Ogre entity (e.g. “_myOgre”) and assign the entity to it when you create it in createScene
   2. Add a member variable to your application class to hold the new Cube entity (e.g. “_myCube”).
   3. In the createScene method, add the following (after you create the Ogre entity):

      _myCube = _sceneManager->createEntity("Cube.mesh");
      Ogre::SceneNode* cubenode =_myOgre->getParentSceneNode()->createChildSceneNode();
      cubenode->attachObject(_myCube);

   4. You need to scale and then translate (position) the new Cube so that you can see it next to the Ogre:

      cubenode->scale(0.01, 0.01, 0.01);    //Try different values
      cubenode->setPosition(2.0, 0.0, 0.0); //Notice that this is relative to the Ogre's model origin

2. Attach a Light to the Cube You can make it look like the Cube is a source of light that lights up the Ogre and casts a shadow on the ground. Simply attach a point light source to the Cube's scene node:

   Ogre::Light* plight = _sceneManager->createLight("Light2");
   plight->setType(Ogre::Light::LT_POINT);
   cubenode->attachObject(plight);

3. Create a Cylindrical Effect Class This is the meat of the project. You should create a new class called CylindricalEffect that moves an entity along a cylindric path at a given velocity. The class has the following constructor:

   CylindricalEffect(Ogre::Entity* entity, Ogre::Vector3 position, Ogre::Vector3 velocity)

4. You should store each of the arguments as a private member variable in the class. The first argument entity is any movable entity in the scene that you want to apply the animation effect to. The second argument position is that entity's position (relative to it's parent) in Cylindrical Coordinates, that is, the vector consists of three numbers:
   1. First number is the height of the cylindrical position
   2. Second number is the radius of the cylindrical position
   3. Third is the angle (in radians) of the cylindrical position
      The third argument velocity is the velocity of the object along the three axes of the cylindrical coordinates, i.e. along the height axis, along the radius and the angular velocity along the circle.
5. Add a GetCartesian() Method If the class operates on cylindrical coordinates, you will always want to retrieve the corresponding cartesian coordinates for updating positions in the Ogre3D default cartesian coordinate system. Therefore you should add the following method which should return the class's position member variable converted to Cartesian coordinates Ogre::Vector3 getCartesian()
   
   Looking at this artistically gorgeous picture (Only constructive criticism accepted, I am an aspiring artist), you can get an idea on what cylindrical coordinates are and how you could convert them to Cartesian coordinates. Lets say:

    (height,radius,angle) = (h, r, α)
   X coordinate = cosine of the angle times the radius
   Y coordinate = height
   Z Coordinate = sin(angle) times the radius

6. Add an Update Method The heart of this effect is a calculation of a new position for the entity based on linear movement along the three axes of the cylindrical coordinate system (height, radius and angle). Since we are already representing the position cylindrically, all we have to do is to update the position by adding the velocity vector times the time that has passed since the last update:

   void update(float dt) {
       _position = _position + dt*_velocity;
       _entity->getParentSceneNode()->setPosition(getCartesian());	
   }

7. Instantiate Effect and Update from FrameListener Now you have to create an instance of your effect, passing the Cube entity into it's constructor, giving it initial position and velocity values, and finally make sure to call this effect's update function in every frame, e.g. inside the FrameListener's frameStarted method (note that you'll have to pass a pointer to this effect into the FrameListener constructor so that it knows about it). Don't forget to delete your effect instance in the destructor of your application!

The finished results should look somewhat like this picture here unless you implemented the bonus steps!

Upload your commented source files into Lab3 in MySchool (zip them up if more than one).