Mass Properties

Measures the mass, volume, centre of mass and principal moments of inertia of a Solid or a closed mesh. A Solid's density may vary through space; a mesh uses one constant density.

  • A Solid is measured to Relative error: its box is cut into cubes, those the surface crosses cut finer where the surface bends, a wall is thinner than the cube or the density changes, at least to 1/128 of the longest side, until the estimated error is small enough or a budget of 40 million field samples is spent. Every surface cube is cut again while one in twenty or more shows a wall or gap thinner than itself; a single thin wall that no sample falls into can still be missed. The Error row shows the estimated error reached, and ErrorMet whether it is within Relative error; when the budget ends first, a warning on the block says so.
  • A mesh is measured exactly, from its triangles.

Inputs

Input Solid or Mesh

The Solid or closed mesh to measure.

Takes: any block that gives Solid (116 blocks)
Density Number

Material density. A Solid's may vary through space (wire a field); a mesh takes one value.

Takes: any block that gives Number (102 blocks)
Relative error Number

How close the result must be, as a fraction of it (0.01 = 1 %; over a surface, of the integrand's size summed over it). The Solid is measured more finely where its surface needs it until the estimated error is this small, within a budget of 40 million field samples.

Output

Mass Properties

Properties

Values the block gives besides its output. The editor lists them under Properties, and an input can read one by reference.

Mass Number

Total mass: the density field integrated over the Solid.

Volume Number

How much space the Solid fills.

CenterOfGravity Point

The mass-weighted average position.

PrincipalMoments Vector

The three principal moments of inertia, taken about the center of gravity.

PrincipalFrame Frame

A frame at the center of gravity whose axes are the principal axes of inertia.

Error Number

The estimated relative error of Mass and Volume (0.01 = 1 %); 0 for a mesh, which is measured exactly.

ErrorMet Yes/No

Whether Error is within the Relative error asked for. False when the measuring budget ran out before it was: the numbers are then only as close as Error says.

In the demos

What implicit modeling is

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