US 2022/0028164 A1Published application

Determination of vertices of triangular grids for three-dimensional object representations

AssigneesHewlett-Packard Development Company, L.P., Universidade Federal de Pernambuco

InventorsDiogo Henriques, Francisco Simoes, Silvio Melo, Andre Silva, Thiago Chaves, Gustavo Charamba, Joao Teixeira, Veronica Teichrieb, Gutenberg Barros, Walter Correia, Thiago Domingues, Vinicius Castilho, Marcelo Riss, Scott A. White

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Abstract

An example of a non-transitory computer-readable medium storing machine-readable instructions. The instructions may cause the processor to receive a three-dimensional (3D) object representation and subdivide it into a triangular grid. Curved triangles may be calculated for triangles in the triangular grid. The triangles may be subdivided and differences calculated between corresponding sections of the curved triangles and the received 3D object representation.

Claims15

Dependent claims

A non-transitory computer-readable medium to store machine-readable instructions that, when executed by a processor, cause the processor to:

receive a three-dimensional (3D) object representation;
subdivide a parametric space of the 3D object representation into a first triangular grid, the first triangular grid comprising a first set of grid lines and a first set of vertices where grid lines in the first set of grid lines intersect;
calculate a first curved triangle for a triangle in the first triangular grid, the first curved triangle corresponding to the 3D object representation for the triangle;
subdivide the triangle into a first subdivision and a second subdivision;
calculate a difference between a point on the 3D object representation and a corresponding point on the first curved triangle, the point on the 3D object representation corresponding to a point within the first subdivision;
and
based on the difference exceeding a predetermined error threshold:
combine the point within the first subdivision with the first set of vertices to create a second set of vertices;
subdivide the parametric space into a second triangular grid, the second triangular grid comprising a second set of grid lines between the second set of vertices;
and
calculate a second curved triangle for a second triangle in the second triangular grid, the first triangle comprising a first area and a second area, and the second triangle comprising the first area and a third area, the third area being distinct from the second area.

8 more elements

A non-transitory computer-readable medium to store machine-readable instructions that, when executed by a processor, cause the processor to:

partition a parametric space of a 3D object representation into a uniform triangular grid;
create a first curved triangle for a first triangle in the uniform triangular grid, the first curved triangle corresponding to the 3D object representation for the first triangle;
partition the first triangle into a set of shapes, the set of shapes including a first shape and a second shape;
calculate a first difference between a first section of the first curved triangle corresponding to the first shape and a first section of the 3D object representation corresponding to the first shape;
determine that the first difference is greater than a first predetermined error threshold;
in response to the determination that the first difference is greater than the first predetermined error threshold, partition the first shape into a set of sub-shapes, the set of sub-shapes including a first sub-shape and a second sub-shape;
calculate a second difference between a second section of the first curved triangle corresponding to the first sub-shape and a second section of the 3D object representation corresponding to the first sub-shape;
determine that the second difference is greater than a second predetermined error threshold;
in response to the determination that the second difference is greater than the second predetermined error threshold, partition the parametric space into a non-uniform triangular grid, the non-uniform triangular grid including a vertex based on the calculation of the second difference;
and
create a second curved triangle for a second triangle in the non-uniform triangular grid, the second curved triangle corresponding to the 3D object representation for the second triangle.

8 more elements

Dependencies are inferred from the claim text.