Overview:
In this assignment, you'll implement several interpolation schemes to interpolate human motion data obtained from an optical mocap system. The human model (skeleton) is represented using a hierarchy, composed of a root node and several children nodes, corresponding to the various joints. The optical mocap system generates two data files: ASF file, which encodes the skeleton kinematics (length of various links, degrees of freedom, etc.) and AMC files, which stores the motion (translation, joint angles) over the sequence. We read the joint angles (for the various joints, in euler angles) and translation (of the root node) of the hierarchy from these files and store them in a data structure. We provide a player that draws a skeleton (with parameters specified by the ASF file) and plays back the motion from an AMC file. You will be given one ASF file and several AMC files for two different motion sequences (walking and story telling) of the character. For each type of motion (e.g.: walking), you will be provided with an AMC file corresponding to the original sequence, and several smaller AMC files that are sub-sampled from the original sequence. We're going to consider these sub-sampled sequences to be key frames, which you will use to create an interpolated sequence of the original length. We provide you code to perform linear interpolation of the key frames; your task is to implement Catmull-Rom or Bezier interpolation. We represent the orientations as Euler angles, you will also be required to represent the joint angles using quaternions and perform the same interpolations in quaternion space.

Requirements:
We are providing you with starter code to read, display and animate skeletons from the ASF and AMC files (motion capture data files). Our code uses euler angles to represent joint rotations. You will be given data for two sequences: (1) walking (in the data/walk_turn directory) and (2) story telling (in the data/tea_pot_small directory). For each of these sequences, we will give you the original sequence and sampled sequences (key frames). Some of the sampled sequences are uniformly sampled from the original, others are sampled at non-uniform intervals. We also give you information about the sampling rate (for uniform case) or the spacing between samples (for non-uniform case). Your task is to do the following for the two sequences:

• Implement Catmull-Rom or Bezier interpolation techniques for euler angle representation. You should use the data from the sampled sequences as the key frames.
• Represent the joint angles in the hierarchy using quaternions. Implement (i) Spherical Linear and (ii) Catmull-Rom or Bezier interpolation for quaternions. For the details on how to implement Bezier interpolation for quaternions see Rick Parent's "Computer Animation" book, pages 99-102 and Ken Shoemaker's "Animating Rotation with Quaternion Curves" paper.

• Your code and documentation of how to run it.
• Three resulting AMC files for walk_turn.AMC_samp20.AMC, and three for tea_pot_small_sampNonunif.AMC. These are the results for doing the three kinds of interpolation of each file:
• Catmull-Rom or Bezier for euler angle representation.
• Catmull-Rom or Bezier for quaternion angle representation.
• Spherical Linear interpolation for quaternion angle representation.
• A report comparing the linear and spline-based interpolation schemes and the two angle representations.
• Four graphs (use any program you want - matlab for example):
• Graphs #1 and #2 compare linear interpolation to Catmull-Rom or Bezier interpolation. One graph for each angle representation (see example below). Plot these graphs for lfemur joint, rotation around X axis, frames 600-800 of the interpolated motion, for walk_turn.AMC_samp20.AMC input file. X axis of the graph should be the frame number and Y axis the angle in degrees.
  
  
  
  
• Graphs#3 and #4 compare quaternion angle representation to euler angle representation. One graph for each interpolation scheme (linear and spline-based). Plot these graphs for root joint, rotation around Z axis, frames 200-500 of the interpolated motion, for walk_turn.AMC_samp20.AMC input file. X axis of the graph should be the frame number and Y axis the angle in degrees.
  
• You can also include other graphs to demonstrate the points you made in your report.

Starter Code Overview