Bezier volume representation of point cloud attributes

A method comprising:

• accessing, by one or more processors of a decoder machine, a data structure that represents a volumetric function, the volumetric function representing a signal on a finite set of points specified by a point cloud in three-dimensional space;
• recovering, by one or more processors of the decoder machine, the point cloud within a predetermined approximation threshold by evaluating the volumetric function represented by the accessed data structure;
• and
• causing, by one or more processors of the decoder machine, rendering and display of the recovered point cloud based on results of the evaluating of the volumetric function represented by the accessed data structure.

An encoder system comprising:

• one or more processors;
• and
• a memory storing instructions that, when executed by at least one processor among the one or more processors, cause the system to perform operations comprising:
• accessing a point cloud that specifies a finite set of points in three-dimensional space;
• and
• generating a data structure that represents a volumetric function, the volumetric function representing a signal defined on the finite set of points of the accessed point cloud.

A decoder system comprising:

• one or more processors;
• and
• a memory storing instructions that, when executed by at least one processor among the one or more processors, cause the system to perform operations comprising:
• accessing a data structure that represents a volumetric function, the volumetric function representing a signal on a finite set of points specified by a point cloud in three-dimensional space;
• recovering the point cloud within a predetermined approximation threshold by evaluating the volumetric function represented by the accessed data structure;
• and
• causing rendering and display of the recovered point cloud based on results of the evaluating of the volumetric function represented by the accessed data structure.

A non-transitory machine-readable storage medium comprising instructions that, when executed by one or more processors of a decoder machine, cause the decoder machine to perform operations comprising:

• accessing a data structure that represents a volumetric function, the volumetric function representing a signal on a finite set of points specified by a point cloud in three-dimensional space;
• recovering the point cloud within a predetermined approximation threshold by evaluating the volumetric function represented by the accessed data structure;
• and
• causing rendering and display of the recovered point cloud based on results of the evaluating of the volumetric function represented by the accessed data structure.