QUATERNION FRAME APPROACH TO STREAMLINE VISUALIZATION

Curves in space are difficult to perceive and analyze, especially when they form dense sets as in typical 3D flow and volume deformation app lications. We propose a technique that exposes essential properties of space curves by attaching an appropriate moving coordinate frame to e ach point, reexpressing that moving frame as a unit quaternion, and su pporting interaction with the resulting quaternion field. The original curves in three-space are associated with piecewise continuous four-v ector quaternion fields, which map into new cut-yes lying in the unit three-sphere in four-space. Since four-space dusters of curves with si milar moving frames occur independently of the curves' original proxim ity in three-space, a powerful analysis tool results. We treat two sep arate moving-frame formalisms, the Frenet frame and the parallel-trans port frame, and compare their properties. We describe several flexible approaches for interacting with and exploiting the properties of the four-dimensional quaternion fields.