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Octree-to-BRep conversion for volumetric NC simulation

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Abstract

User-friendliness such as ease of creation and modification and system-friendliness such as space and time complexities, accuracy etc. are two important criteria for the selection of a solid representation scheme. No single solid representation scheme fully meets all the requirements of user-friendliness and system-friendliness. Hence, any practical CAD/CAM system maintains the geometry of the objects in more than one solid representation scheme simultaneously. Therefore, it is often required to convert one solid representation scheme to the other. The authors have developed a volumetric NC simulation system in which the instantaneous blank is represented as an octree as its space and time complexities are independent of the number of NC blocks. However, since octree does not lend itself readily for operations such as arbitrary transformations, rendered display etc., it is not directly usable for downstream applications such as animated display, verification and optimization. Boundary representation is suitable for these downstream applications. Therefore, it is required to convert octree of the instantaneous blank into BRep. An efficient algorithm for this conversion is presented in this paper. This algorithm essentially splits the octree into three quadtrees that store the geometry along the three principal directions. This algorithm is fast as it involves only tree-traversals.

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Abbreviations

root:

Root node of the octree of the object

quad_proj[0]:

Root node of the quadtree for storing the boundary faces of FULL cubes that are perpendicular to Z axis (i.e, parallel to XY plane)

quad_proj[1]:

Root node of the quadtree for storing the boundary faces of FULL cubes that are perpendicular to X axis (i.e, parallel to YZ plane)

quad_proj[2]:

Root node of the quadtree for storing the boundary faces of FULL cubes that are perpendicular to Y axis (i.e, parallel to ZX plane)

fill_status:

Array of 4 bytes or 32 bits to store fill status of siblings. 4 bits are assigned for each sibling of the octree/ quadtree

sons:

Array of PARTIAL nodes of the octree/quadtree node

U:

Size of universe

s:

Size of the node

[x0 y0 z0]:

Point in the octree

[xq yq zq]:

Point in the quadtree

[xoffset yoffset zoffset]:

Boolen offset values of 0 or 1 used to identify the reference of any sibling

[nx ny nz]:

Normal of a face

fill_flag:

The field that stores the fill status of a node as either EMPTY, FULL or PARTIAL

prev_fill_flag:

Fill status of the parent node

ZList:

The array that stores the elevation values of the faces at any FULL node of the quadtree

Prev_ZList:

ZList of the parent node of the quadtree

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Authors and Affiliations

  1. Computer Graphics Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    K. P. Karunakaran & R. Shringi

Authors
  1. K. P. Karunakaran
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  2. R. Shringi
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Correspondence to R. Shringi.

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Karunakaran, K.P., Shringi, R. Octree-to-BRep conversion for volumetric NC simulation. Int J Adv Manuf Technol 32, 116–131 (2007). https://doi.org/10.1007/s00170-005-0310-8

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  • DOI: https://doi.org/10.1007/s00170-005-0310-8

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