In this paper, we describe methods for constructing shape priors using orientation information to model white matter tracts from magnetic resonance diffusion tensor images (DTI). Shape Normalization is needed for the construction of a shape prior using statistical methods. Moving beyond shape normalization using boundary-only or orientation-only information, our method combines the idea of sweeping and inverse-skeletonization to parameterize 3D volumetric shape, which provides point correspondence and orientations over the whole volume in a continuous fashion. Tangents from this continuous model can be treated as a de-noised reconstruction of the original structural orientation inside a shape. We demonstrate the accuracy of this technique by reconstructing synthetic data and the 3D cingulum tract from brain DTI data and manually drawn 2D contours for each tract. Our output can also serve as the input for subsequent boundary finding or shape analysis.