Abstract: Techniques and tools for mesh processing are described. For example, a multi-chart geometry image represents arbitrary surfaces on object models. The multi-chart geometry image is created by resampling a surface onto a regular 2D grid, using a flexible atlas construction to map the surface piecewise onto charts of arbitrary shape. This added flexibility reduces parameterization distortion and thus provides greater geometric fidelity, particularly for shapes with long extremities, high genus, or disconnected components. As another example, zippering creates a watertight surface on reconstructed triangle meshes. The zippering unifies discrete paths of samples along chart boundaries to form the watertight mesh.

Abstract: Systems and methods are provided for providing a fine-to-coarse look ahead in connection with parametrization in a graphics system. The use of a variety of parametrization metrics may be supplemented and improved by the fine-to-coarse look ahead techniques of the invention. First, the metric of a parametrization is minimized using a coarse-to-fine hierarchical solver, and then accelerated with a fine-to-coarse propagation. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail at all levels of detail in the progressive mesh sequence.

Abstract: Systems and methods are provided for optimizing a parametrization scheme in accordance with information about the surface signal. A surface parametrization is created to store a given surface signal into a texture image. The signal-specialized metric of the invention minimizes signal approximation error, i.e., the difference between the original surface signal and its reconstruction from the sampled texture. A signal-stretch parametrization metric is derived based on a Taylor expansion of signal error. For fast evaluation, the metric of the invention is pre-integrated over the surface as a metric tensor. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail. Compared to traditional geometric parametrizations, the number of texture samples can often be reduced by a significant factor for a desired signal accuracy.

Abstract: Techniques and tools for mesh processing are described. For example, a multi-chart geometry image represents arbitrary surfaces on object models. The multi-chart geometry image is created by resampling a surface onto a regular 2D grid, using a flexible atlas construction to map the surface piecewise onto charts of arbitrary shape. This added flexibility reduces parameterization distortion and thus provides greater geometric fidelity, particularly for shapes with long extremities, high genus, or disconnected components. As another example, zippering creates a watertight surface on reconstructed triangle meshes. The zippering unifies discrete paths of samples along chart boundaries to form the watertight mesh.

Abstract: Systems and methods for discontinuity edge overdraw are described. In one aspect, a polygonal mesh is rendered to produce a computer-generated image. The image exhibits aliasing at its discontinuity edges. The discontinuity edges are sorted prior to overdrawing. The discontinuity edges are overdrawn as anti-aliased lines to reduce the aliasing.

Abstract: Systems and methods are provided for optimizing the geometric stretch of a parametrization scheme. Given an arbitrary mesh, the systems and methods construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. The systems and methods minimize geometric stretch, i.e., small texture distances mapped onto large surface distances, to balance sampling rates over all locations and directions on the surface. The systems and methods also minimize texture deviation, i.e., “slippage” error based on parametric correspondence, to obtain accurate textured mesh approximations. The technique(s) begin by partitioning the mesh into charts using planarity and compactness heuristics. Then, the technique(s) proceed by creating a stretch-minimizing parametrization within each chart, and by resizing the charts based on the resulting stretch. Then, the technique(s) simplify the mesh while respecting the chart boundaries.

Abstract: Systems and methods are provided for optimizing the geometric stretch of a parametrization scheme. Given an arbitrary mesh, the systems and methods construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. The systems and methods minimize geometric stretch, i.e., small texture distances mapped onto large surface distances, to balance sampling rates over all locations and directions on the surface. The systems and methods also minimize texture deviation, i.e., “slippage” error based on parametric correspondence, to obtain accurate textured mesh approximations. The technique(s) begin by partitioning the mesh into charts using planarity and compactness heuristics. Then, the technique(s) proceed by creating a stretch-minimizing parametrization within each chart, and by resizing the charts based on the resulting stretch. Then, the technique(s) simplify the mesh while respecting the chart boundaries.

Abstract: Systems and methods are provided for optimizing the geometric stretch of a parametrization scheme. Given an arbitrary mesh, the systems and methods construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. The systems and methods minimize geometric stretch, i.e., small texture distances mapped onto large surface distances, to balance sampling rates over all locations and directions on the surface. The systems and methods also minimize texture deviation, i.e., “slippage” error based on parametric correspondence, to obtain accurate textured mesh approximations. The technique(s) begin by partitioning the mesh into charts using planarity and compactness heuristics. Then, the technique(s) proceed by creating a stretch-minimizing parametrization within each chart, and by resizing the charts based on the resulting stretch. Then, the technique(s) simplify the mesh while respecting the chart boundaries.

Abstract: Systems and methods are provided for optimizing the geometric stretch of a parametrization scheme. Given an arbitrary mesh, the systems and methods construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. The systems and methods minimize geometric stretch, i.e., small texture distances mapped onto large surface distances, to balance sampling rates over all locations and directions on the surface. The systems and methods also minimize texture deviation, i.e., “slippage” error based on parametric correspondence, to obtain accurate textured mesh approximations. The technique(s) begin by partitioning the mesh into charts using planarity and compactness heuristics. Then, the technique(s) proceed by creating a stretch-minimizing parametrization within each chart, and by resizing the charts based on the resulting stretch. Then, the technique(s) simplify the mesh while respecting the chart boundaries.