In which, we take our first steps making our characters step

Due Friday, Oct 29, before midnight

The goals of this lab are to

On Github, do a Fetch Upstream to synchronize your forked repository with the class repository.

Then update the source on your local machine and rebuild.

Implement Quaternion::Slerp() in libsrc/atkmath/quaternion-basecode.cpp

To run the unit tests from the build directory, type

Here is sample output:

To run the class teapot demo from the build directory, type

The atk::Transform class represents a 4x4 homogeneous transform as a 2x2 block matrix. The transform’s rotation \(R_j^i\) and translation \(d_j^i\) are member variables. Because the bottom row of such matrices are always known, we do not store them. Instead, we store the top left block as a rotation (Quaternion) and the top right column as a vector.

For this question, you will use the transform class to position several boxes. Look at the code in assignments/a6-transform/boxes.cpp. You will need to modify it.

A room has three boxes in it. Each box has a local coordinate system attached to it. The lengths of all three boxes in the x,y, and z directions of their local coordinate frames are (3,2,1) respectively. The origin of each box is in the lower left-hand corner. The z-axis of each box is aligned with the global Z axis.

In your lab for this week, you will manually solve for the transforms corresponding to the above picture. In this part of the assignment, you will implement the solutions in assignments/a6-transform/boxes.cpp. You have already been given code corresponding the worksheet. You need to fill in values and define additional transforms.

To run the demo from the build directory, type

Transforms to implement:

After completing each part, your scene should look like the following:

In this question, you will learn about the atk::Skeleton and atk::Joint classes in your basecode.

First, read the header files for Skeleton and Joint in libsrc/atk/skeleton.h and libsrc/atk/joint.h.

Second, complete the program in assignments/a6-transform/skeleton.cpp This program loads a BVH file and prints information about the character in it. For more details, read below.

To run the demo from the build directory, type

The Skeleton class implements a hierarchy of joints using a tree data structure. Using the skeleton class, users can iterate over joints and navigate through the joint hierarchy using depth- or breadth- first searches.

The Joint class stores two transforms: one that converts from the local frame of the joint to its parent (called local2parent); and one that converts from the local frame to the global frame (called local2global). When a skeleton is created, each joint must be initialized with its local to parent transform. A joint’s local to global transform is only computed later, when the user calls Skeleton::fk(). Joints also store an ID, name, parent pointer, and list of children pointers. The root joint always has an ID of zero and a NULL parent pointer.

This program reads in the skeleton from a BVH file. The channels for each joint represent the degrees of freedom that are animated in the file. Rotations are specified as euler angles, based on the channel order.

After modifying the program, you should see output like this.

Forward kinematics (FK) is an algorithm that allows us to efficiently compute the global positions of the end effectors of a character, given the local2parent transforms at each joint. A by-product of this process is that we also get the local2global transforms for every joint in the skeleton, meaning we also get the global positions of every joint.

Create and animate your own character (or characters) consisting of multiple body parts. Try setting keyframes or defining procedural motions using functions like sine or the rose curves. Feel free to also add particle effects for extra flare!