Abstract: An interactive development environment for design and placement of tiered geometrical objects, such as objects used in pop-up card designs. Relations between objects are represented mathematically, allowing computerized modeling and enforcement of design constraints. For example, in the context of pop-up cards, a card that cannot close will not be allowed. A dependency hierarchy is used to track different objects of a card. Card objects are instantiated as related to other card objects so that changes to one card object can be appropriately propagated to related objects. If all card objects are defined with respect to a base card, an entire card design can be animated by only adjusting, e.g., “opening” and “closing,” the base card. A graphical interface provides drag-and-drop and manual forms of placing card parts. For drag-and-drop, design constraints can be used to automatically determine proper positioning of card pieces.

Abstract: Methods for modifying shapes for display, represented as non-self-intersecting, simply connected, triangulated polyhedron of genus-O, defined as a plurality of triangular faces, each triangular face defined as a set of three coordinate points, eliminate concave edges in the shapes by performing pop or slide procedures on the concave edges. These procedures result in a visually smooth transformation of the concave shape to its convex hull, or to other shapes located therebetween.

Abstract: A method of rendering a color image on a designated output medium is disclosed which maps colors to the gamut of the designated output medium while preserving the semantic consistency of the object color and illumination information in the image. The method performs gamut mapping earlier in the image synthesis process than current gamut method methods, at the point where information about object primitives and their spectral attributes in a scene description is available, but after the fixed scene geometry has been determined by the rendering system. The method makes use of the output of a symbolic rendering system which produces symbolic pixel expressions, having basis spectra variables which represent the interplay of light and object primitives in the scene description, and spectral data having color information about the light and object primitives in the scene, and which is indexed to the basis spectra variables.

Abstract: Methods for modifying shapes represented as non-self-intersecting, simply connected, triangulated polyhedra of genus-0, defined as a plurality of triangular faces, each triangular face defined as a set of three coordinate points, determine an ordering of concave edge elimination procedures which are required to smoothly convert a concave shape to its convex hull. The ordering technique attempts to avoid self-intersections and degeneracies in the metamorphs produced between the starting concave shape and its convex hull.

Abstract: A method for constructing object-local sampling histories for efficient path tracing. The present invention provides a technique for efficiently producing computer generated two-dimensional synthetic images of three-dimensional scenes. Objects within in the scene (10) are assigned packs (30,36) containing one or more elements (32,38). For light reflective objects (19,O1), each element (32) of the object's pack (30) represents a region of the object's reflection hemisphere (30) through which incident light is equally likely to be reflected. For light transmissive objects (19,O1), the elements (32) represent analogous regions of equal transmission. For light emitting objects (L1), each element (38) of the object's pack (36) represents a region of equal light emission probability.