Brigham Young University

Shell Oil Comapny

Autodesk, Inc.

S-splines, LLC

T-splines, Inc.

Thomas W Sederberg

Xin Li

Nazim S Nathoo

Martin Cvetanov Marinov

Gordon Thomas Finnigan

William Barrett

Adam Michael Helps

Prashant D Parikh

Douglas J Kennard

Techniques of refining a model of a complex surface can include refining, upon insertion of a new control point, only those blending functions corresponding to the control points adjacent to the control point being inserted. The resulting curves cannot be considered as B-splines because the relationship between blending functions corresponding to adjacent control points no longer has a fixed relationship. Rather, the resulting blending functions, denoted herein as 'S-splines,' sacrifice this fixed relationship in exchange for the ability to specify how many blending functions corresponding to adjacent control points are refined when performing exact local refinement. S-splines do not produce excess control points and have a simple representation. While the resulting functions representing the surface are not B-splines, they allow for exact refinement without affecting the blending functions corresponding to control points not neighboring the new control point. Such a representation uses fewer computing resources and improves the user experience.

Isogeometric analysis and computer-aided design using S-splines

Techniques of refining a model of a complex surface can include deriving a set of refinement rules based on eigen polyhedra in a plane. Such rules reduce the refinement of a mesh in the plane to a scale and translation of the eigen polyhedron. Such refinement rules may then be applied to a non-uniform mesh in three-dimensional space having an extraordinary point in place of conventional refinement rules used in Catmull-Clark surfaces or NURBS surfaces. When these refinement rules are applied to a non-uniform mesh having an extraordinary point, the limiting surface is Gat the extraordinary point, i.e., the tangent surfaces of the limiting mesh are continuous at the extraordinary point.

Physical object production using a refined model

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for constructing a trim-free T-spline surface and control mesh for a NURBS surface control grid of a B-rep face; modifying the trim-free T-spline control mesh to align the trim-free T-spline surface boundary with a functional trimming curve; and redefining one or more faces in the modified trim-free T-spline control mesh that is adjacent to the trimming curve as a variable knot spline face.

Conversion of T-spline models to trim-free T-spline models: functional case

Performing word recognition operations to determine what an image of a word represents. The method includes accessing a first image. The first image represents an image version of a word. The method further includes accessing a second image. The second image also represents an image version of a word. Using a warp mesh, the method includes warping the second image to cause the second image to approximately match the first image by applying a mesh to the second image and moving vertices of the mesh to warp the second image. The difference between the warped second image and the unwarped first image are determined.

Word warping for offline handwriting recognition

A system and method is provided for defining a bi-cubic spline surface in a computing environment. One operation in the method is creating a control mesh with a substantially rectangular structure. A further operation is inferring from the control mesh the tensor product B-spline basis functions for each control point. The surface can then be computed based on the basis functions and the control mesh.

System and method for defining T-spline and T-NURCC surfaces using local refinements

A method of using a computer graphic system for free-form deformation of geometric models. The method is based on the use of a control-point grid which is imposed on the model and which can then be moved by a system designer to specify a deformation to a particular region of the model. Displacement of control points on the grid provides the designer with an intuitive appreciation for the resulting affect in terms of deformation on the specified region of the geometric model. The free-form deformation of the model is accomplished through the use of a trivariate vector rational polynomial in which the displaced control points represent coefficients of the polynomial. The method provides a powerful and highly flexible technique that can be adapted and used in the environment of virtually any presently known solid modeling system, such as CSG or B-rep. The method can be used to deform surface primitives of any type or degree, such as planes, quadrics, parametric surface patches or implicitly defined surfaces. Single or successive deformations can be applied both globally and locally, and local deformations can be imposed using the method of the present invention with any desired degree of derivative continuity. It is also possible to use the method of the present invention to deform a solid geometric model in such a way that its volume is preserved.

Computer graphics method for changing the shape of a geometric model

A method is disclosed for the determination of the shape of a flat section of fabric prior to application of the fabric to a curved surface.

Growing community of inventors

Orem, UT, United States of America

Thomas W Sederberg