Last update: July 14, 2002

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3D Shape Representation based on Shocks - Transitions

Frederic F. Leymarie and Benjamin B. Kimia, Brown

Peter J. Giblin, Liverpool

A_1^5 Transition:

  • Piece of cheese

    • A_1^5 - Transition - Block cut

    A_1^5 Transition
    (after Bogaevski)

    Illustration

    We illustrate this transition by shortening a rectangular block on one of its side, as shown in the sketch below.

    The five planes' (piece of cheese) version is available afterward.

    Sketch of A_1^5 transition (occuring on RHS of block).

    Input

    We illustrate, in greater detail, the final stage of the transition. We run this expriment on uniformly sampled dataset for the six faces of this block.

    Input

    Complete set: 8264 pts.  

    Recovered Surface

    The "surface scaffold" (i.e., the less significant part of the shock scaffold) gives us back a meshing of the input data. Thus, we can re-build connectivity on the input samples automatically.

    Surface Mesh (1 view)

    Recovered surface mesh (shown as a transparent wireframe).
    Recovered surface ridges are shown as green triangles.

     

    Recovered "Internal" Medial Axis description

    Internal MA (3 views)

    Recovered Medial Axis: Distance from generators (white dots) color coded (blue is near, red is far).

    Same MA data shown as a transparent wire-mesh;

    Recovered principal shock curves: A_3 in blue (ridge-like), A_1^3 in pink (axial-like).
    Note the A_1^5 transition point where the two triangular patches bounded by pink shock curves meet.

    A_1^5 - Transition - Five planes (piece of cheese ;)

    A_1^5 Transition
    (after Bogaevski)

    Illustration

    Before transition.

    At transition.

    Past transition.

    Last updated: July 14, 2002

    F.F.Leymarie

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