Systems and methods for determining mass properties of a modeled object
View Patent ↗Methods for product design and corresponding systems and computer-readable mediums. A method includes receiving a modeled object having a surface and a non-homogeneous density distribution. The method includes tessellating the surface of the object into a set of triangles defined by triangle vertices. The method includes selecting a reference point for the object. The method includes, for each triangle in the tessellation, constructing a tetrahedron, the tetrahedron defined by tetrahedron vertices that include the vertices of the corresponding triangle and the reference point, determining a material density at each of the tetrahedron vertices, and computing mass properties for the tetrahedron using the material density at each of the tetrahedron vertices. The method includes aggregating the mass properties of the tetrahedrons. The method includes storing the aggregated mass properties of the tetrahedrons as the mass properties of the object.
1. A method comprising:
by a data processing system:
receiving a modeled object with a surface and a non-homogeneous density distribution;
tessellating the surface of the modeled object into a set of triangles, each triangle defined by triangle vertices;
selecting a reference point for the modeled object;
constructing a tetrahedron set from the set of triangles, including by, for a given triangle of the set of triangles:
constructing a given tetrahedron, the given tetrahedron defined by tetrahedron vertices that include the triangle vertices of given triangle and the reference point; and
responsive to a determination that a percentage difference between an average density of the given tetrahedron and a density at a centroid of the given tetrahedron exceeds a density threshold:
further splitting the given tetrahedron into multiple smaller tetrahedrons; and
computing a mass property for each tetrahedron of the tetrahedron set using material densities of the tetrahedron vertices of the tetrahedrons of the tetrahedron set;
aggregating the mass properties computed for tetrahedrons of the tetrahedron set;
storing the aggregated mass properties of the tetrahedron set as a computed mass property of the modeled object; and
providing the computed mass property of the modeled object for use in manufacturing a physical object by an additive manufacturing process according to the modeled object.
2. The method of claim 1 , comprising splitting the given tetrahedron eight smaller tetrahedrons along edges of the given tetrahedron that connect the tetrahedron vertices of the given tetrahedron.
3. The method of claim 1 , wherein the mass property comprises volume, mass, center of mass, or moments of inertia.
4. The method of claim 1 , wherein the reference point comprises an origin of a coordinate system that the modeled object is modeled in.
5. The method of claim 1 , comprising computing the mass property of each tetrahedron using a closed-form formula for the mass property with integrals with a linearly-varying density function.
6. A system comprising:
a processor; and
a non-transitory machine-readable medium comprising instructions that, when executed, cause the system to:
receive a modeled object with a surface and a non-homogeneous density distribution;
tessellate the surface of the modeled object into a set of triangles, each triangle defined by triangle vertices;
select a reference point for the modeled object;
construct a tetrahedron set from the set of triangles, including by, for a given triangle of the set of triangles:
construct a given tetrahedron, the given tetrahedron defined by tetrahedron vertices that include the triangle vertices of given triangle and the reference point; and
responsive to a determination that a percentage difference between an average density of the given tetrahedron and a density at a centroid of the given tetrahedron exceeds a density threshold:
further split the given tetrahedron into multiple smaller tetrahedrons; and
compute a mass property for each tetrahedron of the tetrahedron set using material densities of the tetrahedron vertices of the tetrahedrons of the tetrahedron set;
aggregate the mass properties computed for tetrahedrons of the tetrahedron set;
store the aggregated mass properties of the tetrahedron set as a computed mass property of the modeled object; and
provide the computed mass property of the modeled object for use in manufacturing a physical object by an additive manufacturing process according to the modeled object.
7. The system of claim 6 , wherein the instructions, when executed, cause the system to split the given tetrahedron eight smaller tetrahedrons along edges of the given tetrahedron that connect the tetrahedron vertices of the given tetrahedron.
8. The system of claim 6 , wherein the mass property comprises volume, mass, center of mass, or moments of inertia.
9. The system of claim 6 , wherein the reference point comprises an origin of a coordinate system that the modeled object is modeled in.
10. The system of claim 6 , wherein the instructions, when executed, cause the system to compute the mass property of each tetrahedron using a closed-form formula for the mass property with integrals with a linearly-varying density function.
11. A non-transitory machine-readable medium comprising instructions that, when executed by a processor, cause a computing system to:
receive a modeled object with a surface and a non-homogeneous density distribution;
tessellate the surface of the modeled object into a set of triangles, each triangle defined by triangle vertices;
select a reference point for the modeled object;
construct a tetrahedron set from the set of triangles, including by, for a given triangle of the set of triangles:
construct a given tetrahedron, the given tetrahedron defined by tetrahedron vertices that include the triangle vertices of given triangle and the reference point; and
responsive to a determination that a length of an edge of the given tetrahedron that connects two vertices of the given tetrahedron exceeds a length threshold:
further split the given tetrahedron into multiple smaller tetrahedrons; and
compute a mass property for each tetrahedron of the tetrahedron set using material densities of the tetrahedron vertices of the tetrahedrons of the tetrahedron set;
aggregate the mass properties computed for tetrahedrons of the tetrahedron set;
store the aggregated mass properties of the tetrahedron set as a computed mass property of the modeled object; and
provide the computed mass property of the modeled object for use in manufacturing a physical object by an additive manufacturing process according to the modeled object.
12. The system of claim 6 , wherein the instructions, when executed, cause the computing system to split the given tetrahedron eight smaller tetrahedrons along edges of the given tetrahedron that connect the tetrahedron vertices of the given tetrahedron.
13. The system of claim 6 , wherein the mass property comprises volume, mass, center of mass, or moments of inertia.
14. The system of claim 6 , wherein the reference point comprises an origin of a coordinate system that the modeled object is modeled in.
15. The system of claim 6 , wherein the instructions, when executed, cause the computing system to compute the mass property of each tetrahedron using a closed-form formula for the mass property with integrals with a linearly-varying density function.