Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for volumetric kernel representation of three dimensional models include: modeling a three dimensional object using a volumetric representation including fields that determine 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; evaluating the fields including using coverage values that determine compositing behavior to generate output data corresponding to the volumetric properties; and providing the output data for the three dimensional object having physical characteristics that vary from point to point within a volume of the three dimensional object in accordance with the volume

Abstract: A 3D modeling workflow system is disclosed that allows the user to create multiple 2D planes or paint canvases in the 3D scene each having a position and orientation. These 2D planes can be arbitrarily positioned in the 3D scene and can contain a combination of paint and model construction geometry. The construction geometry can span multiple 2D planes. The user is allowed to sketch on the planes using paint and create curve geometry in and between the planes using the sketches as a reference. Collectively the 2D planes allow a 3D object to be represented with different types of input where portions of the object are drawn in by paint and other or the same portions are composed of geometry. The user can swap between painting on the 2D planes and creating model geometry as needed.

Abstract: A 3D modeling workflow system is disclosed that allows the user to create multiple 2D planes or paint canvases in the 3D scene each having a position and orientation. These 2D planes can be arbitrarily positioned in the 3D scene and can contain a combination of paint and model construction geometry. The construction geometry can span multiple 2D planes. The user is allowed to sketch on the planes using paint and create curve geometry in and between the planes using the sketches as a reference. Collectively the 2D planes allow a 3D object to be represented with different types of input where portions of the object are drawn in by paint and other or the same portions are composed of geometry. The user can swap between painting on the 2D planes and creating model geometry as needed.

Abstract: A method of modeling complex surface models using a network of intersecting non-uniform rational B-spline curves. Topological information of the curve network and interpolating surfaces to the network of curves are automatically generated. Different levels of continuity between surface patches are enforced. Surface patches of three and four sides and positional, tangent or curvature continuity between the patches are provided. Using a constrained minimization process, arbitrary, non-uniform B-spline curves may be used to manipulate the shape of the surfaces interpolating the curve network without violating the continuity conditions enforced during the generation of the surface patches allowing for very complex three-dimensional shapes to be modeled using the method.