Google Inc.

Adobe, Inc.

Ondrej Stava

Michael Hemmer

Byungmoon Kim

Peter F Falco, Jr

Frank William Galligan

Igor Vytyaz

Xiaoxu Meng

Lauren Denaut

Frank Galligan

Techniques of compressing triangular mesh data involve generating a neighborhood table (i.e., a table) of fixed size that represents a neighborhood of a predicted vertex of a triangle within a triangular mesh for input into a machine-learning (ML) engine. For example, such a neighborhood table as input into a ML engine can output a prediction for a value (e.g., a position) of a vertex. The residual between the prediction and the actual value of the vertex is stored in an array. The data in the array representing the residuals may be compressed and transmitted over a network. Upon receipt by a computer, the array may be decompressed by the computer. Obtaining the actual value involves the receiving computer generating the same neighborhood table, inputting that neighborhood table into the same ML engine to produce the predicted value, and adding the predicted value to the residual from the decompressed file.

Efficient compression of data representing triangular mesh attributes

Techniques of compressing triangular mesh data involve encoding a bitstream that defines a traversal order for vertices in a triangular mesh. The encoded bitstream defining the traversal order is in addition to an encoded bitstream of prediction errors and is an explicit, rather than implicit, traversal. One example of a bitstream that defines a traversal order is an array in which a bit signifies whether a step in an implicit, deterministic scheme such as a depth-first traversal. Upon decoding, the usual deterministic steps are used to find the vertices of the triangular mesh unless specified by the traversal bitstream. Such an encoded bitstream, when occupying less memory than that saved from the compression efficiencies gained in defining the traversal order defined in the bitstream, offers a simple, efficient compression without requiring that the triangular mesh be connected.

Guided traversal in compression of triangular meshes

In one general aspect, a method can include receiving, by processing circuitry of a computer configured to represent information related to a three-dimensional object, a plurality of vertices of a triangular mesh representing the three-dimensional object, the triangular mesh including a plurality of faces, each if the plurality of faces including three vertices of the plurality of vertices; generating a traversal order for the vertices of the triangular mesh based on valences of the plurality of vertices; producing an array of errors between predicted vertices and vertices of the plurality of vertices, the array of errors being arranged in a sequence based on the traversal order; and performing a compression operation on the array of differences to produce a compressed error array, the compressed error array producing the plurality of vertices of the triangular mesh in response to a decompression operation.

Valence based implicit traversal for improved compression of triangular meshes

An encoder includes a processor, a buffer, and a memory. The memory includes code as instructions that cause the processor to perform a number of steps. The steps include quantizing geometric data associated with a geometric construct, partitioning the geometric construct, determining a number of points in the partition, generating a deviation value based on the number of points in the partition, storing the deviation value in the buffer, and entropy encoding the deviation value.

K-D tree encoding for point clouds using deviations

An encoder includes a processor, a buffer, and a memory. The memory includes code as instructions that cause the processor to perform a number of steps. The steps include partitioning a geometric construct within an axis of the geometric construct based on a point differential between two partitions, the geometric construct including geometric data, determining a number of points in the partition, storing a value indicating the number of points in the buffer, and entropy encoding the value stored in the buffer.

Advanced k-D tree encoding for point clouds by most significant axis selection

Methods and apparatus to encode and decode normals of geometric representations of surfaces are disclosed herein. An example method includes defining a tile having regions, each of the regions of the tile corresponding with a surface of a geometric shape, arranging an edge of a first instance of the tile to abut an edge of a second instance of the tile to define a composite tile, determining a first vector between a first point on the composite tile in the first instance of the tile, and a second point on the composite tile in the second instance of the tile, and encoding the first vector to determine an approximation of the location of the second point relative to the first point.

Methods and apparatus to encode and/or decode normals of geometric representations of surfaces

This document describes techniques and apparatuses for 3D printing for colored models on multi-head fused-deposition modeling (FDM) printers. These techniques are capable of enabling FDM printers to create 3D objects based on colored models, in some cases by determining printer instructions for multiple printer heads based on a 3D model and color data for the surface of the 3D model. These techniques can also tailor printer instructions to characteristics of a particular type or individual FDM 3D printer.

3D printing of colored models on multi-head printers

Techniques are provided for repairing a polygon mesh that represents a three-dimensional surface, the repaired mesh comprising explicit regions that are preserved from the original mesh and implicit regions that are modified from the mesh repair operation. The explicit and implicit regions that comprise the hybrid surface meet along a 'cut path' which can be located by identifying the elements of the volumetric grid where the implicit and explicit surfaces diverge. These elements comprise a path of marching cubes having faces that intersect the polygon elements of the explicit surface along the cut path. In certain embodiments the path between these intersections is selected so as to reduce deviation from the marching cube face and the path length. Once a preferred cut path is selected, the polygons that comprise the explicit surface are subdivided to conform to the cut path.

Hybrid surfaces for mesh repair

Techniques of data compression involve ordering the points of a point cloud according to distance along a space-filling curve. Advantageously, a space-filling curve has the property that points close in distance along the curve are close together in Euclidean space. Thus, differences between points ordered by distance along such a curve, e.g., a Hilbert curve, will be close. When the curve is fractal, i.e., self-similar at all levels, the differences will be small even when the points are very unevenly clustered throughout the point cloud. Such small differences will provide greatly improved compression to the resulting delta-encoded set of points.

Point cloud data compression using a space-filling curve

Methods and systems are disclosed for preserving thin components for three dimensional (3D) printing. An exemplary method generates a medial axis of a 3D shape and identifies components of the 3D shape that need to be preserved by applying a transform to the medial axis. The method creates an output model based at least in part on the components and an insetted shape corresponding to the 3D shape. A system includes a computing device with a processor and a memory having instructions that, if executed, cause the processor to perform operations. The operations comprise generating a medial axis of a 3D shape and applying a transform to the medial axis to identify one or more components of the shape to be preserved. The operations further comprise creating an output model based at least in part on the one or more components and an insetted shape corresponding to the 3D shape.

Preserving thin components for 3D printing

This document describes techniques and apparatuses for a three-dimensional (3D) cleaning object for multi-print-head 3D printing. These techniques are capable of cleaning leftover material from an active or inactive print head using a 3D cleaning object. This cleaning object is printed along with the desired 3D object, with the cleaning object retaining leftover material that may otherwise become an undesirable artifact of the desired 3D object.

3D cleaning object for multi-print-head 3D printing

Methods and systems for defining adaptive support structures for three dimensional (3D) printing are disclosed. An exemplary method detects an area of a 3D model needing support and generates contact points for the area. The method creates a set of virtual supports that extend downward from respective contact points and then identifies connections between the virtual supports in the set, the connections satisfying connection constraints. Next, a virtual support in the set is selected to be a trunk based on comparing connectivity levels of virtual supports in the set, the connectivity level of each of the virtual supports determined by a number of connections between the respective virtual support and other virtual supports. The method then defines a support structure originating from the contact points and including the trunk, at least one virtual support connected to the trunk, and connections between the trunk and the at least one virtual support.

Adaptive supports for 3D printing

Techniques of data compression involve performing a separate compression operation on each set of corresponding bits of a sequence of bit strings in which each bit string represents a number having an upper bound. Advantageously, compressing the sets of corresponding bits produces an improved compression ratio over compressing each number in the sequence. Further, decompression is straightforward as long as sequence order is preserved and the upper bound of each number in the sequence is known.

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San Jose, CA, United States of America

Ondrej Stava