1 Using Voxelization and Ray-Tracing to Identify Wall Thinness of ...

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$Henry T. Schatz Math or Science Education Fellowship Application$

28Figure 15: A two-dimensional example of voxel classificationsFigure 16: Another two-dimensional example of voxel classificationsAfter studying the initial results stemming from these voxel classifications, wedetermined that an additional distinction needed to be made to classify unsafe voxels accordingto depth. The term we chose was 'distance-k'. To clarify, a distance-1 voxel is an unsafe voxelthat has one voxel-unit of separation from a safe voxel. It is in the 26-neighborhood of a safe-byproxyvoxel, which is in turn in the 26-neighborhood of a safe voxel. Correspondingly, adistance-2 unsafe voxel has two voxel-units of separation from a safe voxel: it is in the 26-neighborhood of a distance-1 voxel. The choice of flooding, though far and away the mostcomputationally expensive part of our algorithm, made it easy to characterize voxels accordingto any chosen depth, providing very customizable output.
Use of the flooding technique to classify voxels was made easier by converting the octreeSubCube into a three-dimensional array. Though it would be possible to do a 26-neighborhoodflood within an octree structure, at the time we felt more comfortable tackling the floodingalgorithm within the familiar array. This array of voxel information was fundamental to theflooding operations: we could easily index into any voxel's 26-neighborhood to 'push'information outward, and so on and so on, to the edges of the SubCube. Perhaps moreimportantly, converting the short octree SubCube into a 3D array made conceptualization of theevolving voxel classification an easy task. However, this later proved to be a verycomputationally expensive sequence of operations. A more efficent approach would be to trustthe octree implementation and stick with it, to avoid memory churn and unnecessary datacopying.Aside from producing visualizations (examples of which are just ahead), output alsoincludes a count of the number of voxels considered SAFE, SAFE_BY_PROXY,BORDERLINE_SAFE, and UNSAFE. It also prints out other volumetric information about theinput triangle mesh, shown below. Twelve numbers are recorded, representing, in order:1. volume of the model (float). Volume will be in cubic centimeters, assuming that all modelmeasurements are in true size and each unit of the model coordinate system corresponds to theX3D convention of 1 meter in size.2. min bounds x-axis of the input model (float).3. max bounds x-axis (float).4. min bounds y-axis (float).5. max bounds y-axis (float).6. min bounds z-axis (float).7. max bounds z-axis (float).8. total number of assessed volume voxels (integer).9. number of safe voxels (integer).10. number of voxels that are safe due to proximity of other safe voxels (integer).11. number of distance-1 unsafe voxels and borderline voxels that may be unsafe for printing(integer).12. number of distance-2 and distance ≥2 voxels that are decidedly unsafe for printing (integer).29
Page 2 and 3: 2Table of Contents1. Introduction2.
Page 4: for printing. This technique can be
Page 8 and 9: y the curve and the exterior is unb
Page 10 and 11: The advantage of using XML-based X3
Page 12 and 13: 12Figure 7: X3D file containing a s
Page 14 and 15: and less 'boxy' the more polygons a
Page 16 and 17: 16Child 3 contains points where x i
Page 18 and 19: An algorithm that processes the inp
Page 20 and 21: The algorithm we used for the trian
Page 22 and 23: 22Figure 11: An odd number of inter
Page 24 and 25: 24Figure 13: Example of a model fai
Page 26 and 27: grid point is a zero dimensional ob
Page 30 and 31: 7. ResultsFive values are calculate
Page 32 and 33: 32Figure 19: Many voxels are flagge
Page 34 and 35: 34Figure 21: Closeup of two columns
Page 36 and 37: 36Figure 24: Unshaded mesh geometry
Page 38 and 39: Table 2 Simple Sphere results with
Page 40 and 41: dimensions. Note that the current s
Page 42 and 43: 42Figure 28: Default visualization:
Page 44 and 45: At the original one millimeter reso
Page 46: Despite these successes, I predict

1 Using Voxelization and Ray-Tracing to Identify Wall Thinness of ...

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