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In this section we demonstrate the use of the curvature computation on images of surfaces that have been mapped onto a regular 2D (3D) grid of square (cubic) pixel elements. Each pixel in the grid can be assigned a phase corresponding to those in the image, and any pixel containing phase α, for example, is then an α − β surface pixel if it is in contact along an edge (face) with a β-pixel. The area (volume) calculations described in the previous section therefore reduce to counting pixels within a digitized circular (spherical) template. Discrete mapping of an interface therefore allows a simple computation of mean curvature for every interface element in the grid.
As with any other method that uses digital images, this procedure can be memory intensive, especially when applied in sintering simulations of porous powder compacts. Accurate curvature computation on a single particle surface usually requires that the particle contain at least 100 pixels in 2D, or 1000 pixels in 3D. Simulating the sintering of a portion of a compact containing, say, 1000 particles therefore requires a lattice composed of 2 106 pixels, or about 1 megabyte of memory. In addition, the curvature computation method itself requires some memory allocation, since the position and pixel count of each interfacial pixel must be stored. But if the position and pixel count each use 4 bytes of memory for each interfacial pixel, and if the number of interfacial pixels is about 5% of the total number of pixels (typical for a powder compact with approximately 1 micrometer-diameter particles), then the curvature method requires only around 10% extra memory allocation. Typical workstations can accommodate this memory requirement, although much larger-scale simulations may require the memory capacity of a supercomputer.