Examples:

1. Vector Components:
   • Right-ThumbStick: Move the block
   • Left-ThumbStick: Move the soccer
   • Right Trigger: rotate the block
   • A-Button: Show vector
      
2. Reflect A Vector:
• A-Button: to shoot the ball
• X-Button: to pause everything
• Left ThumbStick-Y: Speed of ball
• Right ThumbStick: direction for the ball
• Right Trigger: rotate the blocker
• Shoots the ball towards the blocker and shows velocity decomposition at collision
• Notice: the 4-5 lines of interesting code in VectorComponent::Update() function.
• This solution works for circle/rectangle intersection.
• Difference between FrontDirection and VelocityDirection:
  • FrontDirection: the front of the primitive.
  • VelocityDireciton: the direction the primitive velocity.
     
3. Elasticity and Friction:
• Almost exactly the same as above, only difference ...
• Right ThumbStick: direction and size of Ball
• Left ThumbStick.X: elasticity of Block (what does this mean?)
• Left ThumbStick.Y: friction of Block (what does this mean?)
• Do we see now why we want to have the different components? Cool?
   
4. Home in to target:
• Right ThumbStick: move the target dot
• Left ThumbStick.X: turn rate
• watch that soccer home into the target!!
• 3-5 lines of code in MySoccer::Update()!! Cool?
   
5. Gradual Turning:
Almost identical to Example-4 from week1, except, at the last stage of the road, if user change the road-end-point, the car moves/rotates gradually towards the endpoint rather than rotate to face the end point immediately.
• Left Thumb-Stick-Y: Change current road segment length
• Left Thumb-Stick-X: Change the turn approaching rate!?
• Right Thumb-Stick: Change current road segment direction
• A-Button: Add in new road segment
• Car rotates and follows current segment of road it is on
• MyCar class: UpdateCarDirAndSpeed()!!
   
6. Plotting and Following a Sine Function:
   • Left-Thumb-Stick Up/Down: to change number per periods that  will be fitted in the entire WorldDimension.X,
   • Left-Thumb-Stick-Left/Right to change the Amplitude
   • Only point interesting is to recognized we need to fit (2*PI*mPeriod) into WorldDimension.X:
   • Use mFrequeicyScale to help in converting x coordinate position into angular value.
   • Note: x-displacement is constant, speed is NOT constant.
   • Now to make speed a constant? (Type the A-Button)
   • Notice: use of PrimitiveSet for showing/hiding entire set (plotted out sine curves)
   • Notice: moving an object by ourselves (instead of setting ShouldTravel to true)
      
7. Boxed Sine Function:
   • Left-Thumb-Stick Up/Down: to change number per periods that  will be fitted in the box-Width
   • Left-Thumb-Stick-Left/Right to change the Amplitude
   • Right-Thumb-Stick: to move the location of the box to contain the Sine plot
   • Left-Trigger/Left-Button: to increase/decrease the width of box
   • Right-Trigger/Right-Button: to increase/decrease the height box
   • Class to check out: PlotBox:
     • Is a Rectangle: must set Center/Width/Height to be seen!
     • ComputePosition: uses the center position and width to compute LeftCenterPos.
     • Update(): changes box position (Center), and Width/Height. Triggers the ComputePosition to recompute leftCenterPos.
     • GetBoxPosition(): with this class, function computation can assume beginning from x=0, and evaluate the Y-value. When (x,y) values are computed, we can now call "GetBoxPosition()" to compute the relative position with respect to the leftCenterPos.
   • Interestingly: now, we do not need to factor in sine offsets wrt to the plotting area (taken care of by the PlotBox::GetBoxPosition()) function. So,
     • useX = currentX - mPlotBox.PlotOriginX is not needed anymore!
     • GetYValue(x): do not need to worry about: the mPolotBox Y-offset
   Constant Velocity: Notice the much more elaborate steps in computing constant velocity, where we convert into boxPlot position only in the very last steps. This clear separation of Function Position [mTheta, GetYValue(mTheta)] from the plotBox position is important in general when e.g., if we want to rotate the plotBox!

    

8. The FunctionPath class:
   • Identical to the above, except the new FunctionPlot class
   • except: B-Button: hide the plot area and plot positions
   • Class to check out: FunctionPlot:
     • Abstract the area upon which to plot the function as: PlotBox
     • Abstract x/y coverage of function to plot (mFunctionXCoverage and mFunctionYCoverage).
     • Notice: we can implement PlotFunction() even though we have no idea what is the function!!
     • GetYValue(x): is a virtual function, subclass can implement any function!
   • Check out the SineFunctionPath: implements a sine function.
   • So, we have a identical behavior system as the above example!

      

9. Boxed Parabola Function:
   • Identical to the above, except the new ParabolaFunctionPath class
   • ButtonX/Y: to change the control between the sine and the parabola plots
   • Class to check out: ParabolaFunctionPath:
     • GetUseX(x):
       • must translate x by PlotBox.Width/2 (to see the negative side of the x values)
       • Scale the x values to cover the entire width of the PlotBox.
       • Notice that in UI, when you change the xCoverage, the plot does not change! (because we compensate the by the above scale).
       • This is done to show the curve stretching/squeezing with the PlotBox scale.
     • GetYValue(x):
       • Must call GetUseX(x) to offset and properly scale the x value
       • Scale the y-value such that, yCoverage value touches the upper corners of the plot area.
       • This means, when yCoverage is larger than plotBox.height, the traveling circle will go outside of bounds.

    

10. General Boxed Function:
    • Almost identical to above, except, now, we separate out the PlotBox x/y directions into Front/Normal directions!
    • DPad Up/Down: Rotates the plotting area
    • Class to check out: FunctionPath:
      • the update function now accepts a rotDelta (delta rotate) parameter.
      • causes the PlotBox to rotate.
    • Class to check out: PlotBox
      • New instance variable: NormalDir: this variable is always 90-degrees of FrontDirection
      • With FrontDirection and NormalDir, we have the x (FrontDirection) and y (NormalDir) directions.
      • In GetBoxPosition(x, y): we compute the actual position in the box by offsets to the x-direction vector (FrontDirectoin) and y-direction vector (NormalDir).

       

11. Many Function Plots:
    • With proper abstraction, it is trivial to support large instances
    • XButton: cycles through all the plots
    • Try cycle through the plots and press-B button to see the PlotBox.
    • Bunch of random plots, interesting? May be yes? no? looks interestingly complex/chaotic, and yet we have absolute control!!
    • Cool?