Quaternion frame approach to streamline visualization

摘要

Curves in space are difficult to perceive and analyze, especiallynwhen they form dense sets as in typical 3D flow and volume deformationnapplications. We propose a technique that exposes essential propertiesnof space curves by attaching an appropriate moving coordinate frame toneach point, reexpressing that moving frame as a unit quaternion, andnsupporting interaction with the resulting quaternion field. The originalncurves in 3-space are associated with piecewise continuous 4-vectornquaternion fields, which map into new curves lying in the unit 3-spherenin 4-space. Since 4-space clusters of curves with similar moving framesnoccur independently of the curves' original proximity in 3-space, anpowerful analysis tool results. We treat two separate moving-framenformalisms, the Frenet frame and the parallel-transport frame, andncompare their properties. We describe several flexible approaches forninteracting with and exploiting the properties of the 4D quaternionnfields