qabot-zh / qpose

A templated C++ library for manipulating pose data through dual quaternions

QPose

What is QPose?

A templated C++ library for manipulating pose data through dual quaternions

What (the heck) is a Dual Quaternion?

We can think of a dual quaternion as simply two quaternions that go together, where the individual quaternions are named the real and the dual component. A defined set of mathematical properties come with working with dual quaternions, including some semblance of

• dual-quaternion addition
• dual-quaetnion subtraction
• dual-quaternion scalar multiplication (scalar times a Dual Quaternion)
• dual-quaternion products (Dual Quaternion times a Dual Quaternion)

Dual Quaternions play a vital role in manipulating objects in 3D. Traditionally, homogeneous transformation matrices and linear algebra are used to encode and manipulate an object's position and orientation. Dual Quaternions are less operation-intensive (they require less calculations) and avoid some singularities that occur when encoding 3D position and orientation with Matrices. They can also be smoothly interpolated from one Dual Quaternion to another, a quality that is excellent for animation or kinematics and very cumbersome with homogeneous transformation matrices.

Ok, Can I do math with this library?

Yes! Dual Quaternion addition, subtraction, scalar multiplication, and quaternion multiplication have been implemented. Since Dual Quaternions are commonly used for encoding objects with 6 degrees of freedom (position and orientation), member functions have also been implemented to set and get this information.

Dual-Quaternion Addition

QPose<float> myPose;    // default quaternion.
QPose<float> myOtherPose;    // default quaternion.

QPose<float> myNewPose = myPose + myOtherPose;   // OK!

Dual-Quaternion Subtraction

QPose<float> myPose;    // default quaternion.
QPose<float> myOtherPose;    // default quaternion.

QPose<float> myNewPose = myPose - myOtherPose;   // OK!

Dual-Quaternion Scalar Multiplication

QPose<float> myPose;    // default quaternion.
int scalar = 10;

QPose<float> myNewPose = scalar * myPose;   // OK!

Dual-Quaternion Product

QPose<float> myPose;    // default quaternion.
QPose<float> myOtherPose;    // default quaternion.

QPose<float> myNewPose = myPose * myOtherPose;   // OK!

Setting a Pose

float x, y, z, roll, pitch, yaw;

... //Assign values to above variables.

QPose<float> myPose(x, y, z, roll, pitch, yaw);

Getting a Pose

QPose<float> myPose;

... // myPose gets a pose assigned to it.

float x, y, z, roll, pitch, yaw;

myPose.get6DOF(x, y, z, roll, pitch, yaw);

// x, y, z, roll, pitch, yaw now have values from myPose.

Great, any caveats?

A few. Here they are:

Left-Scalar Multiplication Only

Only left scalar multiplication has been implemented. In other words:

QPose<float> myPose;    // default quaternion.
int scalar = 10;

QPose<float> myNewPose = scalar * myPose;   // OK!
QPose<float> myNewPose = myPose * scalar;   // NOT OK!

Luckily, the Compiler will complain about this practice and refuse to compile it.

Compiling requires C++11

QPose must be compiled with the -std=c++11 or -std=g++11 flag.