nested sphere packing surface rationalization Since the master design surface could not be modified GT used a surface rationalization technique that adjusted to the curvature of the surface. Nested sphere packing is a simple technique that can be applied in many conditions with different results depending on the curvature of the surface. 1 The packing algorithm needs a path along the surface to follow, a start point on the path, a sphere radius, and a direction to travel [1]. One sphere is constructed at the start point and then intersects the surface creating a circle. The 2 second sphere center point along the path is created at the intersection of the circle and the path in the predetermined direction of travel [2]. When the second sphere is generated and intersected with the surface and path the third point is created along with the first point for the second row [3]. This process is repeated until the surface is populated with 3 spheres and intersection points [4]. Finally the intersection points are connected into triangles [5]. On a flat surface with zero curvature the resulting triangles will be equal. However, when the surface is convex or concave the resulting triangles are deformed. This type of rationalization process follows the natural topology of the surface creating a non-uniform pattern ideal for irrational geometry.
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Zero Curvature