Abstract: Small objects causing aliasing are enlarged so that they are likely to be sampled by image sampling points. The opacity of the enlarged object is reduced in proportion to the enlargement. To efficiently render partially transparent objects, such as enlarged objects, objects are sampled using sigma buffer samples instead of image sample points. For each sigma buffer sample, a corresponding portion of the object is set to either completely transparent or completely opaque. The proportion of transparent to opaque portions of the object matches or approximates the partial transparency of the object as a whole. The completely opaque portions of one or more objects are sampled with the corresponding sigma buffer samples. Aggregate values of the sigma buffer samples are determined and can be combined with the attribute values of other objects sampled with image sampling points associated with the same region as the set of sigma buffer samples.

Abstract: Method and system for determining a scalar field on a subdivision surface. The method includes providing a surface mesh including an edge. The edge connects a plurality of vertices, and is adjacent to a plurality of faces. The plurality of vertices correspond to a plurality of values for a scalar field. Additionally, the method includes processing information associated with the surface mesh, and determining a geometric location for an edge point on a subdivision surface. The edge point corresponds to the edge. Moreover, the method includes determining whether the edge is a face-varying boundary, processing information associated with whether the edge is a face-varying boundary, and determining a first value for the scalar field corresponding to the edge point based on at least information associated with whether the edge is a face-varying boundary.

Abstract: A method and apparatus for visibility determination and processing. The method includes receiving at least information associated with a plurality of objects, generating a first plurality of geometric primitives based on at least information associated with the plurality of objects, generating a first plurality of grids based on at least information associated with the first plurality of geometric primitives, and shading the first plurality of grids. The generating a first plurality of grids includes generating a second plurality of grids associated with the first plurality of geometric primitives, selecting a third plurality of grids from the second plurality of grids, and selecting the first plurality of grids from the third plurality of grids.

Abstract: A method and apparatus for rendering a plurality of objects. The method includes receiving ray differential information associated with a ray, determining a first resolution associated with a first surface patch based on at least information associated with the ray and the first surface patch, processing information associated with the first resolution and a database, and determining whether a first geometry representation associated with the first surface patch tessellated at the first resolution is present in the database. The database is associated with a plurality of predetermined resolutions, and the first resolution is equal to one of the plurality of predetermined resolutions. At least one of the plurality of predetermined resolutions includes a first tessellation rate associated with a first dimension and a second tessellation rate associated with a second dimension. The first tessellation rate is different from the second tessellation rate.

Abstract: A method and apparatus for rendering a plurality of objects. The method includes receiving ray differential information associated with a ray, determining a first ray differential based on at least information associated with the ray and a first surface patch, processing information associated with the first ray differential and the first surface patch, determining a first resolution based on at least information associated with the first ray differential and the first surface patch, and selecting a second resolution from the plurality of predetermined resolutions. Additionally, the method includes obtaining a first geometry representation associated with the second resolution.

Abstract: A method and apparatus for rendering a plurality of objects. The method includes receiving ray differential information associated with a ray, determining a first ray differential based on at least information associated with the ray and a first surface patch, and determining a first resolution based on at least information associated with the first ray differential and the first surface patch. Additionally, the method includes obtaining a first geometry representation based on at least information associated with the first surface patch and the first resolution, and obtaining a second geometry representation associated with a second surface patch tessellated at a second resolution. Moreover, the method includes determining whether there is at least one patch crack between the first geometry representation and the second geometry representation, and if there is the at least one patch crack, performing a stitching process to the first geometry representation and the second geometry representation.

Abstract: A method and apparatus for visibility determination and processing. The method includes receiving at least information associated with a plurality of objects, generating a first plurality of geometric primitives based on at least information associated with the plurality of objects, generating a first plurality of grids based on at least information associated with the first plurality of geometric primitives, and shading the first plurality of grids. The generating a first plurality of grids includes generating a second plurality of grids associated with the first plurality of geometric primitives, selecting a third plurality of grids from the second plurality of grids, and selecting the first plurality of grids from the third plurality of grids.

Abstract: A method and apparatus for rendering a plurality of objects. The method includes receiving ray differential information associated with a ray, determining a first ray differential based on at least information associated with the ray and a first surface patch, processing information associated with the first ray differential and the first surface patch, determining a first resolution based on at least information associated with the first ray differential and the first surface patch, and selecting a second resolution from the plurality of predetermined resolutions. Additionally, the method includes obtaining a first geometry representation associated with the second resolution.

Abstract: A method and apparatus for rendering a plurality of objects. The method includes receiving ray differential information associated with a ray, determining a first ray differential based on at least information associated with the ray and a first surface patch, and determining a first resolution based on at least information associated with the first ray differential and the first surface patch. Additionally, the method includes obtaining a first geometry representation based on at least information associated with the first surface patch and the first resolution, and obtaining a second geometry representation associated with a second surface patch tessellated at a second resolution. Moreover, the method includes determining whether there is at least one patch crack between the first geometry representation and the second geometry representation, and if there is the at least one patch crack, performing a stitching process to the first geometry representation and the second geometry representation.

Abstract: Method and system for determining a scalar field on a subdivision surface. The method includes providing a surface mesh including an edge. The edge connects a plurality of vertices, and is adjacent to a plurality of faces. The plurality of vertices correspond to a plurality of values for a scalar field. Additionally, the method includes processing information associated with the surface mesh, and determining a geometric location for an edge point on a subdivision surface. The edge point corresponds to the edge. Moreover, the method includes determining whether the edge is a face-varying boundary, processing information associated with whether the edge is a face-varying boundary, and determining a first value for the scalar field corresponding to the edge point based on at least information associated with whether the edge is a face-varying boundary.

Abstract: A method and apparatus for rendering a plurality of objects. The method includes receiving ray differential information associated with a ray, determining a first resolution associated with a first surface patch based on at least information associated with the ray and the first surface patch, processing information associated with the first resolution and a database, and determining whether a first geometry representation associated with the first surface patch tessellated at the first resolution is present in the database. The database is associated with a plurality of predetermined resolutions, and the first resolution is equal to one of the plurality of predetermined resolutions. At least one of the plurality of predetermined resolutions includes a first tessellation rate associated with a first dimension and a second tessellation rate associated with a second dimension. The first tessellation rate is different from the second tessellation rate.