Region Moments

Support of polynomial moments of a region in Version 11 provides powerful and flexible tools to compare, classify, and compute properties over regions.

Symbolically calculate moments of regions.

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RegionMoment[Disk[], {0, 0}]

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RegionMoment[CapsuleShape[], {2, 0, 0}]

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RegionMoment[Cone[{{0, 0, 0}, {0, 0, 1}}, r], {2, 0, 0}]

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Suppose a region with unknown parameters is provided, along with the knowledge that all zero-order and first-order moments are 1. Find the numerical values of each parameter.

Define the region and the assumptions on its parameters.

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$Assumptions = r > 0 && x > 0 && y > 0 && z > 0;

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cyl = Cylinder[{{0, 0, 0}, {x, y, z}}, r];

Calculate its zero-order and first-order moments.

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cfs = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}};

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{m0, m100, m010, m001} = Table[RegionMoment[cyl, c], {c, cfs}]

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Solve for the parameters, given that all zero-order and first-order moments are 1.

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sol = Solve[{m0 == 1, m100 == 1, m010 == 1, m001 == 1, $Assumptions}]

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Obtain the region.

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cyl /. sol

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Approximate its radius.

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N[cyl /. sol]

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