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

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

22Figure 11: An odd number of intersections causing interior/exterior identification issuesImagine that the solid black line represents the surface of the model defined by thetriangle mesh. The upper ray, cast from the left to the right, begins in the exterior since there isan even number (zero) of ray-triangle intersections at the origin of the ray. However, the lowerray, cast from the right to the left, defines this same region of space as interior to the model,since it has encountered one ray-triangle intersection along its voyage.To prevent this problematic issue, our current software specification accepts twomanifoldobjects only. This is done by carefully examining each triangle described by thecoordinates in the mesh. We proceed through the set of triangles, cataloging every edge thatappears. The results are placed into a collection of edges. The assumption of two-manifold isdetermined if the same edge is placed into the collection twice and only twice. Two-manifold isthe case of an edge being attached to only two triangles.See Figure 12 for more information:
23Figure 12: Visualization of the 'manifold' propertyManifold detection consists of the following test:If an edge between two vertices A and B is placed in the collection of edges twice, thatedge is considered two-manifold, meaning it is shared by two and only two triangles. If any edgeis placed in the collection with a different number of edges, it is outside specifications and the3D input model is not processed by our algorithm. For example, if an edge appears in the edgecontainer three times, it is three-manifold, meaning the same edge is shared by three triangles. Ak-manifold object with k greater than two is highly likely to contain self-intersecting loops. Anexample of this is shown in the following figure:
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 24 and 25: 24Figure 13: Example of a model fai
Page 26 and 27: grid point is a zero dimensional ob
Page 28 and 29: 28Figure 15: A two-dimensional exam
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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