Surface mapping apparatuses and methods

1. A method for performing simulation of a model of a physical object, the method comprising:

mapping mesh simulation results obtained from a finite element simulation of a finite element mesh of the model to a surface representation of the model by:

determining the mesh simulation results corresponding to nodes or integration points of the finite element mesh by performing the finite element simulation using the finite element mesh, the mesh simulation results comprising numerical results; and

after determining the mesh simulation results, determining arbitrary results with respect to the surface representation based on the mesh simulation results by translating the mesh simulation results corresponding to the nodes or the integration points of the finite element mesh to arbitrary results corresponding to points that define the surface representation; and

displaying the arbitrary results with respect to the surface representation, wherein the finite element mesh is defined independently of the surface representation, wherein

the surface representation of the model comprises one or more Non-Uniform Rational Basis Spline (NURBS) surfaces;

each of the one or more NURBS surfaces is defined by one or more control points and one or more knot vectors associated with the one or more control points;

each of the one or more control points has an initial control point position;

each initial control point position is associated with an idealized point;

the idealized point is a point within a volume of or on a surface of the finite element mesh;

the idealized point is defined by isoparametric coordinates;

performing the finite element simulation using the finite element mesh to obtain the mesh simulation results comprises determining the mesh simulation results with respect to the nodes or the integration points of the finite element mesh;

determining the arbitrary results with respect to the surface representation based on the mesh simulation results comprises mapping the mesh simulation results with respect to the nodes or the integration points to the idealized points using a mapping function;

each of the idealized points is at a same physical location as a corresponding control point; and

each of the control points inherit displacement and all other arbitrary quantities of the corresponding idealized point.

2. The method of claim 1 , wherein:

the model is a 3-dimensional solid;

performing the finite element simulation using the finite element mesh comprises performing the finite element simulation using Finite Element Method (FEM) or Finite Element Analysis (FEA).

3. The method of claim 1 , wherein:

each finite element of the finite element mesh is associated with a shape function or interpolation function; and

each finite element of the finite element mesh is one of a 4-node tetrahedron, 5-node pyramid, 6-node pentahedron, 8-node hexahedron, 10-node tetrahedron, 13-node pyramid, 15-node pentahedron, or 20-node hexahedron.

4. The method of claim 1 , wherein the mapping function is based on interpolation functions of elements of the finite element mesh or based on a weighted average of a collection of nearby nodes.

5. The method of claim 1 , wherein the mesh simulation results comprise deformation information for the nodes or the integration points of the finite element mesh.

6. A method for performing simulation of a model of a physical object, the method comprising:

mapping mesh simulation results obtained from a finite element simulation of a finite element mesh of the model to a surface representation of the model by:

determining the mesh simulation results corresponding to nodes or integration points of the finite element mesh by performing the finite element simulation using the finite element mesh, the mesh simulation results comprising numerical results; and

after determining the mesh simulation results, determining arbitrary results with respect to the surface representation based on the mesh simulation results by translating the mesh simulation results corresponding to the nodes or the integration points of the finite element mesh to arbitrary results corresponding to points that define the surface representation; and

displaying the arbitrary results with respect to the surface representation, wherein the finite element mesh is defined independently of the surface representation, wherein

the surface representation comprises discrete patches;

each of the discrete patches is defined by one or more discrete patch positions or surface points;

each of the one or more surface points has an initial surface point position;

each initial surface point position is associated with an idealized point;

the idealized point is a point within a volume of or on a surface of the finite element mesh;

the idealized point is defined by isoparametric coordinates;

performing the finite element simulation using the finite element mesh to obtain the mesh simulation results comprises determining the mesh simulation results with respect to the nodes or the integration points of the finite element mesh;

determining the arbitrary results with respect to the surface representation based on the mesh simulation results comprises mapping the mesh simulation results with respect to the nodes or the integration points of the finite element mesh to the idealized points using a mapping function;

each of the idealized points is at a same physical location as a corresponding surface point; and

each of the surface points inherit displacement and all other arbitrary quantities of the corresponding idealized point.

7. The method of claim 6 , wherein the mapping function is based on interpolation functions of elements of the finite element mesh or based on a weighted average of a collection of nearby nodes.

8. A non-transitory computer-readable medium having computer-readable instructions such that, when executed by a processor, causes the processor to perform the method of claim 6 .

9. An apparatus capable of performing simulation of a model of a physical object, the apparatus comprises:

a memory; and

a processor configured to perform the method of claim 6 .

10. A non-transitory computer-readable medium having computer-readable instructions such that, when executed by a processor, causes the processor to perform simulation of a model of a physical object by:

mapping mesh simulation results obtained from a finite element simulation of a finite element mesh of the model to a surface representation of the model by:

determining the mesh simulation results corresponding to nodes or integration points of the finite element mesh by performing the finite element simulation using the finite element mesh, the mesh simulation results comprising numerical results; and

after determining the mesh simulation results, determining arbitrary results with respect to the surface representation based on the mesh simulation results by translating the mesh simulation results corresponding to the nodes or the integration points of the finite element mesh to arbitrary results corresponding to points that define the surface representation; and

displaying the arbitrary results with respect to the surface representation, wherein the finite element mesh is defined independently of the surface representation, wherein

the surface representation of the model comprises one or more Non-Uniform Rational Basis Spline (NURBS) surfaces;

each of the one or more NURBS surfaces is defined by one or more control points and one or more knot vectors associated with the one or more control points;

each of the one or more control points has an initial control point position;

each initial control point position is associated with an idealized point;

the idealized point is a point within a volume of or on a surface of the finite element mesh;

the idealized point is defined by isoparametric coordinates;

performing the finite element simulation using the finite element mesh to obtain the mesh simulation results comprises determining the mesh simulation results with respect to the nodes or the integration points of the finite element mesh;

determining the arbitrary results with respect to the surface representation based on the mesh simulation results comprises mapping the mesh simulation results with respect to the nodes or the integration points to the idealized points using a mapping function;

each of the idealized points is at a same physical location as a corresponding control point; and

each of the control points inherit displacement and all other arbitrary quantities of the corresponding idealized point.

11. An apparatus capable of performing simulation of a model of a physical object, the apparatus comprises:

a memory;

a processor configured to:

map mesh simulation results obtained from a finite element simulation of a finite element mesh of the model to a surface representation of the model by:

determining the mesh simulation results corresponding to nodes or integration points of the finite element mesh by performing the finite element simulation using the finite element mesh to obtain the mesh simulation results; and

after determining the mesh simulation results, determining arbitrary results with respect to the surface representation based on the mesh simulation results by translating the mesh simulation results corresponding to the nodes or the integration points of the finite element mesh to arbitrary results corresponding to points that define the surface representation; and

a user interface configured to display the arbitrary results with respect to the surface representation, wherein the finite element mesh is defined independently of the surface representation, wherein

the surface representation of the model comprises one or more Non-Uniform Rational Basis Spline (NURBS) surfaces;

each of the one or more NURBS surfaces is defined by one or more control points and one or more knot vectors associated with the one or more control points;

each of the one or more control points has an initial control point position;

each initial control point position is associated with an idealized point;

the idealized point is a point within a volume of or on a surface of the finite element mesh;

the idealized point is defined by isoparametric coordinates;

performing the finite element simulation using the finite element mesh to obtain the mesh simulation results comprises determining the mesh simulation results with respect to the nodes or the integration points of the finite element mesh;

determining the arbitrary results with respect to the surface representation based on the mesh simulation results comprises mapping the mesh simulation results with respect to the nodes or the integration points to the idealized points using a mapping function;

each of the idealized points is at a same physical location as a corresponding control point; and

each of the control points inherit displacement and all other arbitrary quantities of the corresponding idealized point.