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# 3D calculations of volume, surface area, centroid

On Programmer » Matlab

1,911 words with 0 Comments; publish: Wed, 07 May 2008 09:43:00 GMT; (200125.00, « »)

Problem: Have a 3D shape, generated from a rotated profile

about 1 of 3 axis. Can break the shape into sub-volumes of

more simple homogeneous shapes, cylinders, frustrum, sector

of a sphere, sphere, etc... The composite shape is placed

into the water such that some volume is above and some is

below the water line. Eventually the waterline may be

represented by another function representing a wave, but

that is another post. Now to determine the still waterline

at a rotated angle of the composite shape, all volume below

the waterline * density of water will equal the weight of

the total shape. Rotational moments may also exist, as a

function of the wet volumes distance from the CG of the

composite shape. At present, knowledge of all points u, v,

w in the shape reference frame are a function of i,j with i

being the height, and j being the radial angles which

divide the mesh to create the 3D shape. Using simpler

shapes, from a point along the waterline(origin for the

main shape) a tetrahedoron to each mesh grid can be

computed for volume, centroid, and surface area in the

water (outside surface only) and all pieces(mesh grids)

with a Z (Height Axis) value of negative are "below the

waterline" and all could be summed and translated into the

equavalent volume below the waterline with a composite

centroid (center of buoyancy). I can state this problem

well, but I have a hard time coding it, does anyone have

some code snippits that might help with this integration

effort?

An alternative perspective is that the composite shape is

subjected to a "cut plane", and the total volume is divided

into above and below the cut plane, and the finding of the

geometric properties (external surface area, centroid,

volume) for each of the cuts of the total shape. sort of

Bolean Geometry in the agregate from.

*http://matlab.todaysummary.com/q_matlab_1125.html*

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