Methods for designing pop-up cards, and cards produced thereby

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. Graphics can be associated with card parts, and such graphics are automatically adjusted, e.g., adjusting perspective, for proper viewing of the image on a particular card piece.