Abstract: A method for smoothing a graphic model includes forming a loop from a plurality of parametrically defined curves and creating a ribbon along each parametrically defined base curve between preceding and subsequent parametrically defined curves of the loop. The ribbons are blended to form a multi-sided surface patch between the parametrically defined curves. A system for smoothing a graphic model includes a curve network module, a lofting module and a blending module. The curve network module, the lofting module and the blending module, are configured to cause a processor to form a loop from a plurality of parametrically defined curves, create a ribbon along each parametrically defined curve between a preceding parametrically defined curve of the loop and a subsequent parametrically defined curve of the loop and blend the ribbons to form a multi-sided surface patch between the parametrically defined curves.

Abstract: A method for smoothing a graphic model includes forming a loop from a plurality of parametrically defined curves and creating a ribbon along each parametrically defined base curve between preceding and subsequent parametrically defined curves of the loop. The ribbons are blended to form a multi-sided surface patch between the parametrically defined curves. A system for smoothing a graphic model includes a curve network module, a lofting module and a blending module. The curve network module, the lofting module and the blending module, are configured to cause a processor to form a loop from a plurality of parametrically defined curves, create a ribbon along each parametrically defined curve between a preceding parametrically defined curve of the loop and a subsequent parametrically defined curve of the loop and blend the ribbons to form a multi-sided surface patch between the parametrically defined curves.

Abstract: An apparatus, system, and method for creating, viewing and manipulating 3D patch compressed images.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft.

Abstract: A method models an object composed of one or more components. Data are input to a memory of a computer system for each component of the object. The data include Cartesian coordinates expressed in Euclidean space of a plurality of points x of each component. Each component point x is encoded as a vector x in a general homogeneous space by x=(x+½x2e+e*)E=xE?½x2e+e*, where e and e* are basis null vectors of a Minkowski space E. General homogeneous operators are associated with each data point to generate a model of the object. The general homogeneous operators are applied to each encoded point of the associated component for each component to manipulate the model of the object.

Abstract: A method regularizes a distance field of a graphics model or object. The distance field includes variable scalar values and a set of fixed zero values. The zero values define a boundary or surface of the object. The distance field is evaluated by a cost function, optimized according predetermined parameters, to determine a cost of the distance field. The variable scalar values are then randomly perturbed while holding the zero values fixed. The evaluating, determining, perturbing steps are repeated until the cost is less than a predetermined threshold. The distance field can be in the form of a non-differentiable implicial field. A surface of the graphics model can be textured or stenciled by following streamlines along the gradients of the regularized distance field.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft.

Abstract: A method regularizes a distance field of a graphics model or object. The distance field includes variable scalar values and a set of fixed zero values. The zero values define a boundary or surface of the object. The distance field is evaluated by a cost function, optimized according predetermined parameters, to determine a cost of the distance field. The variable scalar values are then randomly perturbed while holding the zero values fixed. The evaluating, determining, perturbing steps are repeated until the cost is less than a predetermined threshold. The distance field can be in the form of a non-differentiable implicial field. A surface of the graphics model can be textured or stenciled by following streamlines along the gradients of the regularized distance field.