In this assignment, you will use splines to create a roller coaster simulation. The simulation will run in a first-person view, allowing the user to “ride” the coaster in an immersive environment. After completing this assignment, you should have a solid understanding of:

• Designing smooth geometric curves using splines
• Arc-length reparameterization of polynomial splines
• Defining coordinate frames along splines
• Camera manipulation to create first-person movement

Specification

[5 point] Build your own virtual roller coaster using splines

• To design the rail trajectory, you may use any type of spline, including Catmull-Rom, natural, or B-splines.
• Make the spline closed so that the coaster can run continuously in a loop..

[5 points] Define the moving coordinate frame along the spline.

• Make sure that the coordinate frame moves smoothly along the spline by updating tangent, normal, and binormal vectors coherently.
• Make your track look like a track, by rendering roller coaster rails. The rail rendering would visualize the moving coordinate frame along the spline.

[5 points] Simulate the coaster to create physically correct motion along the spline.

• Implement arc-length reparameterization to remove side effects introduced by the original parameterization.
• Calculate the exact velocity at any u.
• Move the coaster along the spline by integrating time steps and updating arc-length parameter s.
• Use the timer callback so that the simulation runs in sync with real time.

[5 points] Render the simulating in a first-person view.

• Place the camera on the coaster facing forward.