Mesh formation for multi-element volumes

A method of forming mesh data for three-dimensional data, the method comprising:

• generating, by a computing device, inside/outside (IO) functions based on indicator functions to identify element interfaces between a plurality of elements identified in three-dimensional (3-D) data, wherein an indicator function of the indicator functions is defined to represent a volume identified for an element of the plurality of elements identified in the 3-D data;
• defining, by a computing device, a cell indicator function for each element interface of the identified element interfaces based on the generated IO functions to identify a plurality of types of element interfaces, wherein the cell indicator function identifies points in the 3-D data where a plurality of the generated IO functions evaluate to approximately zero, and further wherein a type of element interface is identified based on a number of the generated IO functions that evaluate to approximately zero at a point in the 3-D data;
• distributing, by a computing device, 3-D point locations on the identified element interfaces based on the identified plurality of types of element interfaces and the generated IO functions;
• and
• generating, by a computing device, surface mesh data for the 3-D data based on the distributed 3-D point locations.

A non-transitory computer-readable medium including computer-readable instructions stored therein, wherein, when executed by a processor, the computer-readable instructions cause a computing device to:

• generate inside/outside (IO) functions based on indicator functions to identify element interfaces between a plurality of elements identified in three-dimensional (3-D) data, wherein an indicator function of the indicator functions is defined to represent a volume identified for an element of the plurality of elements identified in the 3-D data;
• define a cell indicator function for each element interface of the identified element interfaces based on the generated IO functions to identify a plurality of types of element interfaces, wherein the cell indicator function identifies points in the 3-D data where a plurality of the generated IO functions evaluate to approximately zero, and further wherein a type of element interface is identified based on a number of the generated IO functions that evaluate to approximately zero at a point in the 3-D data;
• distribute 3-D point locations on the identified element interfaces based on the identified plurality of types of element interfaces and the generated IO functions;
• and
• generate surface mesh data for the 3-D data based on the distributed 3-D point locations.