# Annex JJ Surface Mesh Representation (Informative)

For a general introduction into the underlying principles used in the Surface Mesh Module see:

Foley & van Dam [et al], Computer Graphics: Principles and Practice, Second Edition , Addison-Wesley, 1990.

## JJ.1 MULTIDIMENSIONAL VECTORS

The dimensionality of the Vectors Macro (PS 3.3, C.27.7.3) is not restricted to accommodate broader use of this macro in the future. Usage beyond 3-dimensional Euclidian geometry is possible The Vectors Macro may be used to represent any multi-dimensional numerical entity, like a set of parameters that are assigned to a voxel in an image or a primitive in a surface mesh.

Examples:

In electro anatomical mapping, one or more tracked catheters are used to sample the electrophysiological parameters of the inner surface of the heart. Using magnetic tracking information, a set of vertices is generated according to the positions the catheter was moved to during the examination. In addition to its 3D spatial position each vertex is loaded with a 7D-Vector containing the time it was measured at, the direction the catheter pointed to, the maximal potential measured in that point, the duration of that potential and the point in time (relative to the heart cycle) the potential was measured.

For biomechanical simulation the mechanical properties of a vertex or voxel can be represented with a n-dimensional vector.

## JJ.2 ENcoding Examples

The following example demonstrates the usage of the Surface Mesh Module for a tetrahedron.

[pic]

Figure JJ.2-1 – Surface Mesh Tetrahedron

 Tag Name Value (Note: When the actual values are binary a text string is shown.) Comment (0066,0001) Number of Surfaces 1 (0066,0002) Surface Sequence (0066,0003) Surface Number 1 (0066,0004) Surface Comments Test Surface (0066,0009) Surface Processing YES (0066,000A) Surface Processing Ratio 1.0 (0066,000B) Surface Processing Description Moved Object (0066,0035) Surface Processing Algorithm Identification Sequence (0066,002F) Algorithm Family Code Sequence (0008,0100) Code Value 1231009 (0008,0100) Code Value AA01 (0066,0031) Algorithm Version “V1.0” (0066,0032) Algorithm Parameters “x = 5 y = 1 z = 0” (0062,000C) Recommended Display Grayscale Value FFFFH (0062,000D) Recommended Display CIELab Value FFFF\8080\8080 (0066,000C) Recommended Presentation Opacity 1.0 (0066,000D) Recommended Presentation Type SURFACE (0066,000E) Finite Volume YES (0066,0010) Manifold YES (0066,0011) Surface Points Sequence (0066,0015) Number Of Surface Points 4 (0066,0016) Point Coordinates Data -5.\-3.727\-4.757\ 5.\-3.707\-4.757\ 0.\7.454\-4.757\ 0.\0.\8.315 4 triplets. The points are marked a,b,c,d in the sketch. (0066,0017) Point Position Accuracy 0.001\0.001\0.001 (0066,0018) Mean Point Distance 10.0 (0066,0019) Maximum Point Distance 10.0 (0066,001A) Points Bounding Box Coordinates -5.\-3.727\-4.757\ 5.\7.454\8.315 2 triplets (0066,001B) Axis of Rotation 0.0\0.0\1.0 (0066,001C) Center of Rotation 0.0\0.0\0.0 (0066,0012) Surface Points Normals Sequence (0066,0013) Surface Mesh Primitives Sequence (0066,0025) Vertex Point Index List (0066,0024) Edge Point Index List (0066,0023) Triangle Point Index List 1\3\2\1\2\4\2\3\4\3\1\4 The second triangle is the one marked green in the sketch. (0066,0026) Triangle Strip Sequence (0066,0027) Triangle Fan Sequence (0066,0028) Line Sequence (0066,0034) Facet Sequence