CSE 694A: Lab 2
Due Wednesday, Oct. 8

LAB 2: Path following with ease-in/ease-out

Use the main routine and support routines from lab 1.

Write a program to animate a cube that follows a curved path through a given set of points starting from a stopped position, accelerating to some maximum speed and then decelerating to a stop at the initial position. The coordinates of the points to be interpolated can be hardcoded in your lab. Use at least 8 non-coplanar points.

The initialization part of this lab will:

1. set coefficient matrices for beginning segment, interior segments, and end segment.
2. For each segment, loop through points, summing linear distances to create a table of parametric value and summed linear distance to approximate arc length and the computed point. Compute at least 200 points per segment.

The simulation part of this lab will:

1. increment a time value, t, that goes from zero to one as the curve is traversed
2. apply an ease function, s = ease(t), using constant acceleration assumption
3. search the table created by the initialization routine for the entries s is between
4. compute the fraction that s is between the two entries.
5. use the computed fraction to interpolate between the points recorded in the table, u = table(s)
6. evaluate the interpolation function to produce a point along the curve, p = P(u)

Display the interpolated points using small cubes

• You can use any cubic interpolation method discussed in class. Catmul-Rom or Blended Parabolas are recommended because these interpolate (as opposed to approximate) the given points and don't require any additional information (such as tangents) to control the interpolation.
• you need to control the speed of the cube somehow. This can be done by setting an appropriate delta-t. Another way to do it is to fix the delta-t and use a delay variable that gets updated first and only when it flips back to zero does t get incremented; speed is controlled by setting the value at which the delay variable flips to zero.

• get one interior segment working, then add the beginning and then the ending segments
• get interpolation working first, then constant speed (equal-distance increments), then ease-in
• write your program so it's easy to set the number of interpolated positions per segment; start with a low number to test your code