Volumetric kernel representation of three dimensional models

A non-transitory computer-readable medium encoding instructions operable to cause data processing apparatus to perform operations that store a representation of a three dimensional (3D) model, and enable user manipulation of the 3D model, the operations comprising:

• modeling a three dimensional object using a volumetric representation of volumetric properties including material mixing and porosity within a three dimensional space of the three dimensional object, the volumetric representation comprising fields that determine the volumetric properties, each of the fields is parameterized by an input and output tensor structure, and at least one of the fields maps tensor output of a first of the fields to tensor input of a second of the fields to provide a unified framework for geometry manipulation and composition that encompasses both discrete and continuous representations of materials in the three dimensional space of the three dimensional object;
• evaluating the fields of the volumetric representation, including evaluating the at least one of the fields using coverage values that determine compositing behavior when mapping the tensor output of the first of the fields to the tensor input of the second of the fields, to generate output data corresponding to the volumetric properties, wherein the fields of the volumetric representation do not have an intrinsic resolution and so are evaluated differently depending on context during the evaluating;
• and
• providing the output data for the three dimensional object, wherein the three dimensional object has physical characteristics that vary from point to point within a volume of the three dimensional object in accordance with the volumetric properties.

A system comprising:

• a non-transitory storage medium having instructions of a computer aided design program stored thereon;
• and
• one or more data processing apparatus able to run the instructions of the computer aided design program to perform operations that store a representation of a three dimensional (3D) model, and enable user manipulation of the 3D model, the instructions of the computer aided design program being configured to cause the one or more data processing apparatus to
• model a three dimensional object using a volumetric representation of volumetric properties including material mixing and porosity within a three dimensional space of the three dimensional object, the volumetric representation comprising fields that determine the volumetric properties, each of the fields being parameterized by an input and output tensor structure, and at least one of the fields mapping tensor output of a first of the fields to tensor input of a second of the fields to provide a unified framework for geometry manipulation and composition that encompasses both discrete and continuous representations of materials in the three dimensional space of the three dimensional object,
• evaluate the fields of the volumetric representation, including the at least one of the fields using coverage values that determine compositing behavior when mapping the tensor output of the first of the fields to the tensor input of the second of the fields, to generate output data corresponding to the volumetric properties, wherein the fields of the volumetric representation do not have an intrinsic resolution and so are evaluated differently depending on context, and
• provide the output data for the three dimensional object, wherein the three dimensional object has physical characteristics that vary from point to point within a volume of the three dimensional object in accordance with the volumetric properties.