In this thesis we will focus on methods that are useful in computer aided geometric design. We will take a closer look at the motion of a rigid body in Euclidean three-dimensional space, which is generally determined by describing the location of the center of the rigid body and orientation as a function of time. In the description of these curves, we will get to know spatial Pythagorean-hodograph curves, which play an important role in computer aided geometric design, as their polynomial formulation allows a rational representation of the unit tangent vector, orthonormal frame, arc length, etc. Rational forms are important since they allow efficient and accurate calculations. Thus, we will get to know the rational Euler-Rodrigues frame, which is naturally defined on the quaternion representation of spatial Pythagorean-hodograph curves. We will see that this frame generally performs unnecessary rotations that cause image distortion in computer modeling. Frames that do not perform such rotations are called rotation minimizing frames. Although in general the Euler-Rodrigues frame is not rotation minimizing, we will derive the conditions on the spatial Pythagorean-hodograph curves where this applies.
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