Abstract: A system and methods for weak spot analysis. A mesh shape is preprocessed to approximate an input model for an object. The mesh shape is analyzed with modal analysis to identify weak regions. A method and system for determining weak spots in an object. The method and system uses an optimization problem which is solved to determine a pressure distribution on the object maximizing maximal principal stress by solving a set of optimization problems maximizing stress for each point of the object.

Abstract: A system and methods for weak spot analysis. A mesh shape is preprocessed to approximate an input model for an object. The mesh shape is analyzed with modal analysis to identify weak regions. A method and system for determining weak spots in an object. The method and system uses an optimization problem which is solved to determine a pressure distribution on the object maximizing maximal principal stress by solving a set of optimization problems maximizing stress for each point of the object.

Abstract: A system, method, and program product for re-parameterizing one or more three-dimensional Catmull-Clark models is disclosed. Each of the models has one or more surfaces and one or more extraordinary vertices. One or more adjacent iso-parameter lines of the model have a spacing between them that increases as the iso-parameter lines approach the extraordinary vertex. A re-parameterization process that re-parameterizes the model so that one or more of the extraordinary vertices have adjacent iso-parameter lines with spacing that does not increase as the lines approach the extraordinary vertex.

Abstract: A system, method, and program product for re-parameterizing one or more three-dimensional Catmull-Clark models is disclosed. Each of the models has one or more surfaces and one or more extraordinary vertices. One or more adjacent iso-parameter lines of the model have a spacing between them that increases as the iso-parameter lines approach the extraordinary vertex. A re-parameterization process that re-parameterizes the model so that one or more of the extraordinary vertices have adjacent iso-parameter lines with spacing that does not increase as the lines approach the extraordinary vertex.

Abstract: A system, method, and program product for re-parameterizing one or more three-dimensional Catmull-Clark models is disclosed. Each of the models has one or more surfaces and one or more extraordinary vertices. One or more adjacent iso-parameter lines of the model have a spacing between them that increases as the iso-parameter lines approach the extraordinary vertex. A re-parameterization process that re-parameterizes the model so that one or more of the extraordinary vertices have adjacent iso-parameter lines with spacing that does not increase as the lines approach the extraordinary vertex.

Abstract: In this invention there are described a set of algorithms based on multiresolution subdivision surfaces that perform at interactive rates and enable intuitive surface cut-and-paste operations. The method includes separating a source region of interest of a source surface into a source base surface and a source detail surface; separating a target region of interest of a target surface into a target base surface and a target detail surface; and pasting the source detail surface onto the target base surface in accordance with a mapping. The step of pasting includes parameterizing and mapping the parameterized regions of interest of the source and target surfaces into an intermediate plane, and aligning the parameterizations using a linear transformation that compensates for first order distortions.

Abstract: A system, method, and program product for re-parameterizing one or more three-dimensional Catmull-Clark models is disclosed. Each of the models has one or more surfaces and one or more extraordinary vertices. One or more adjacent iso-parameter lines of the model have a spacing between them that increases as the iso-parameter lines approach the extraordinary vertex. A re-parameterization process that re-parameterizes the model so that one or more of the extraordinary vertices have adjacent iso-parameter lines with spacing that does not increase as the lines approach the extraordinary vertex.

Abstract: A method for representing a sharp feature on a surface of a model comprises the steps of defining at least one feature curve on the surface; reparameterizing the surface; and creating the feature on the reparameterized surface so as to be generally coincident with the feature curve, where the feature lies along boundaries between piecewise-smooth patch surfaces where patch surfaces with distinct tangent planes are joined. The surface is reparameterized by moving a control mesh relative to the surface to sample the feature curve with vertices of the control mesh, and creating the feature includes a subdivision step where edges and diagonals are treated as creases in the control mesh, and piecewise-smooth subdivision rules are applied to obtain a sharp feature on the surface. The surface may be defined in a Catmull-Clark multiresolution subdivision surface representation.

Abstract: A method for representing a sharp feature on a surface of a model comprises the steps of defining at least one feature curve on the surface; reparameterizing the surface; and creating the feature on the reparameterized surface so as to be generally coincident with the feature curve, where the feature lies along boundaries between piecewise-smooth patch surfaces where patch surfaces with distinct tangent planes are joined. The surface is reparameterized by moving a control mesh relative to the surface to sample the feature curve with vertices of the control mesh, and creating the feature includes a subdivision step where edges and diagonals are treated as creases in the control mesh, and piecewise-smooth subdivision rules are applied to obtain a sharp feature on the surface. The surface may be defined in a Catmull-Clark multiresolution subdivision surface representation.

Abstract: In this invention there are described a set of algorithms based on multiresolution subdivision surfaces that perform at interactive rates and enable intuitive surface cut-and-paste operations. The method includes separating a source region of interest of a source surface into a source base surface and a source detail surface; separating a target region of interest of a target surface into a target base surface and a target detail surface; and pasting the source detail surface onto the target base surface in accordance with a mapping. The step of pasting includes parameterizing and mapping the parameterized regions of interest of the source and target surfaces into an intermediate plane, and aligning the parameterizations using a linear transformation that compensates for first order distortions.

Abstract: An imaging system which corrects perceptual distortion in wide angle picture balances between direct view distortion and linear perspective distortion. The two kinds of distortion are balanced according to a transformation ratio. The balancing can be expressed as: and .phi.=.o slashed.where .rho. and .phi. are the transformed polar coordinates corresponding to the original polar coordinates r and .o slashed., .lambda. is the transformation ratio defining the amount of each transform to be used, and R is the size of the new image. This can also be effected by a lens having the transfer characteristic whereby B=tan .beta./K; where K is between 1 and 2.