CSE 683: Lab 2
Due Wednesday, Oct. 6

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

Use the main routine and support routines from lab 1.

Write a program to move an object 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 - and then repeat:

• the object does not change orientation - changing orientation to orient the animated object along the path of the curve will be the focus of Lab #3.
• draw a groundplane - because it helps to have a large stable visual reference when viewing the animation while moving the camera
• display the points to be interpolated using small cubes.
• For the moving object, You can use a simple cube or be more creative.
• The coordinates of the points to be interpolated can be hardcoded in your lab; use at least 8 non-coplanar points.

Initialization

1. set coefficient matrices for beginning segment, interior segments, and end segment - Use the Blended Parabolas or Catmull-Rom spline formulation.
2. For each segment, loop through points, summing linear distances to create a table of parametric values and summed linear distances to approximate arc length. Because we are using multiple segments, the table might look like:

   segment # u- value length 0 0.0 0.0 0 0.01 0.12 ... ... ... 0 0.99 5.35 0 1.0 5.4 1 0.01 5.45 ... ... ... 1 1.0 7.3 ... ... ... 7 0.01 12.0 ... ... ... 7 1.0 12.5

   OR

   point length x,y,z 0.0 x,y,z, 0.12 ... ... x,y,z 5.35 x,y,z 5.4 x,y,z 5.45 ... ... x,y,z 7.3 ... ... x,y,z 12.0 ... ... x,y,z 12.5

   Compute at least 200 points per segment. If you normalize the lengths in the table so the total length is 1.0 and if the ease-in/ease-out function i/o is also normalized to go from 0.0 to 1.0, then the code is easier to reuse with other ease-in/ease-out procedures.

Simulation

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)

Note that, because 't' monitonically increases, so does 's' and, therefore, so do the indices of the entries retrieved from the table. This should make your search more efficient since you can start the next search from the point of the previous search.

• 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.

• 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