Abstract: A method includes providing a three-dimensional representation of a doubly curved surface as a smooth function or triangulated mesh. The three-dimensional surface is cut into one or more panels representing each panel by a triangulated mesh. A two-dimensional approximation of the set of panels is created by representing the two-dimensional pattern as a triangulated mesh that is topologically equivalent to the three-dimensional meshes representing the panels.

Abstract: A graphic, includes a substrate and a printed pattern disposed over the substrate. The substrate is configured to attach to a mounting surface, and is transparent. The printed pattern exposes a nonprinted pattern. The printed pattern is a geometric projection of a graphic design on the mounting surface from a first viewpoint, and the nonprinted pattern is a geometric projection of a transparency design on the mounting surface from a second viewpoint.

Abstract: A method includes providing a three-dimensional representation of a doubly curved surface as a smooth function or triangulated mesh. The three-dimensional surface is cut into one or more panels representing each panel by a triangulated mesh. A two-dimensional approximation of the set of panels is created by representing the two-dimensional pattern as a triangulated mesh that is topologically equivalent to the three-dimensional meshes representing the panels.

Abstract: A method includes providing a three-dimensional representation of a doubly curved surface as a smooth function or triangulated mesh. The three-dimensional surface is cut into one or more panels representing each panel by a triangulated mesh. A two-dimensional approximation of the set of panels is created by representing the two-dimensional pattern as a triangulated mesh that is topologically equivalent to the three-dimensional meshes representing the panels.

Abstract: An apparatus, system, and method for applying a graphic or decal to a car window or other three-dimensional surface using a stretchable film and associated mounting frame is described. In some embodiments, a frame is mounted to the edge of a car window (or other target surface). The frame, which can be flexible or bendable, includes attachment points at various locations to facilitate attachment of a stretchable and/or shrinkable film to the frame. The film can include corresponding holes or other attachment openings, which generally align with the attachment points of the frame when the film is stretched (and/or shrunk) to conform to the shape of the frame (and, thus, the window).

Abstract: A method includes providing a three-dimensional representation of a doubly curved surface as a smooth function or triangulated mesh. The three-dimensional surface is cut into one or more panels representing each panel by a triangulated mesh. A two-dimensional approximation of the set of panels is created by representing the two-dimensional pattern as a triangulated mesh that is topologically equivalent to the three-dimensional meshes representing the panels.

Abstract: A graphic, includes a substrate and a printed pattern disposed over the substrate. The substrate is configured to attach to a mounting surface, and is transparent. The printed pattern exposes a nonprinted pattern. The printed pattern is a geometric projection of a graphic design on the mounting surface from a first viewpoint, and the nonprinted pattern is a geometric projection of a transparency design on the mounting surface from a second viewpoint.

Abstract: A graphic, includes a substrate and a printed pattern disposed over the substrate. The substrate is configured to attach to a mounting surface, and is transparent. The printed pattern exposes a nonprinted pattern. The printed pattern is a geometric projection of a graphic design on the mounting surface from a first viewpoint, and the nonprinted pattern is a geometric projection of a transparency design on the mounting surface from a second viewpoint.