Abstract: Triangle strip merging for length maximization of triangle strips representing a triangle mesh. In one embodiment, a computer-implemented method, for each strip, first including determining whether a defining face of the strip has a neighboring face that is a defining face of another strip. A defining face of a particular strip is either a front face, an end face, or an orphan face of the particular strip. Upon determining that a defining face of the strip has a neighboring face that is a defining face of another strip, then the two strips are joined to create a new, larger strip if they are joinable.

Abstract: A shadow for a three-dimensional model having an infrastructure that includes a bone is generated by projecting the bone onto a surface and generating the shadow on the surface based on a projection of the bone. Projecting the bone includes drawing lines from the virtual light source, through points on the bone, onto the surface and connecting points at which the lines intersect the surface.

Abstract: Modifying a three-dimensional model includes constructing a bones infrastructure for a polygon mesh, removing edges of polygons in the polygon mesh to reduce a resolution of the polygon mesh, receiving an instruction to reduce a number of bones in the bones infrastructure, reducing the number of bones in the bones infrastructure in response to the instruction, and associate the polygon mesh with the bones infrastructure having a reduced number of bones.

Abstract: Memorialization of commercial transactions via an electronic receipt including establishing a connection between a mobile device and an electronic receipt terminal, and transmitting an electronic receipt of a commercial transaction from the electronic receipt terminal to the mobile device.

Abstract: A method in a computer system includes identifying faces of a mesh which share an edge and identifying normals of vertices of the faces not included by the edge. The depth components of the normals are multiplied in camera space. When the product of multiplying the depth components of the normals has a first sign, the edge is identified as a silhouette edge.

Abstract: Processing a scene graph includes applying view frustrum culling to sort models of the scene graph into first and second lists of models, the first list comprising models at least one of within a view frustrum and intersecting with the view frustrum, the second list comprising models outside of the view frustrum, and applying a first selected collision detection process to pairs of models of the first list. The method further includes applying a second selected collision detection process to pairs of models of the second list. In some embodiments, the first collision detection process is more computationally intensive than the second collision detection process.

Abstract: An apparatus and method is provided for creating a neighbor mesh from a multi-resolution mesh (MRM) representation of a triangulated model. The apparatus and method include computing neighbor data for the neighbor mesh at the highest resolution of the MRM, and creating the neighbor mesh using the computed neighbor data. The apparatus and method further include changing the resolution of the MRM and re-computing the neighbor data at the changed resolution of the MRM, and computing an updated neighbor mesh from the re-computed neighbor data.

Abstract: Motion of a user is approximated by obtaining a three-dimensional model to represent the user, tracking the motion of the user, positioning the three-dimensional model to approximate the motion of the user, and rendering a two-dimensional image from the positioned three-dimensional model. The three-dimensional model includes one or more bones. Positioning the three-dimensional model includes adjusting a position of at least one of the bones.

Abstract: Rendering a three-dimensional model comprised of three-dimensional data defining a bone includes obtaining a point at which the bone intersects a collision surface, determining a correction factor for use in rotating the bone from the point to a position in front of the collision surface, and rendering the three-dimensional model, including the bone, using the correction factor.

Abstract: A shadow is generated in a virtual three-dimensional space by adjusting a resolution of a 3D model, projecting elements of the 3D model onto a surface in the virtual 3D space, and rendering a shadow having the adjusted resolution of the 3D model on the surface using the projected elements.

Abstract: Rendering a three-dimensional model comprised of three-dimensional data defining a bone and a polygon includes determining a location of a vertex of the polygon relative to the bone, transforming the vertex based on the location to produce a transformed vertex, and rendering the three-dimensional model using the transformed vertex. Determining the location of the vertex includes obtaining a plane that intersects the bone and determining a side of the plane on which the vertex is located.

Abstract: Shading a polygon includes identifying points on edges of the polygon using shading values for vertices of the polygon, connecting the points to form at least two areas within the polygon, and shading the at least two areas differently. Vertices are assigned to at least two different bins. The bins correspond to different shades. The points may be identified by identifying points on edges of the polygon having vertices assigned to different bins.

Abstract: Triangle strip length maximization. Embodiments of the invention provide an efficient mechanism to represent triangle meshes as series of one or more triangle strips. In one embodiment, a computer-implemented method first including determining an area of each of a plurality of triangles of a triangle mesh. A distance from the smallest area triangle to every other triangle on the list is determined. An available triangle on the list closest to the smallest area triangle is added to a triangle strip that beings with the smallest area triangle.

Abstract: A method of adding primitives in real time to a model to produce a non-photorealistic rendering (NPR) of a model includes storing attribute data for each one of the primitives. A ring buffer is provided, having at least one stage, for each vertex of the model which is to have a primitive. Within each ring buffer, data is stored representative of a direction of each one of the primitives. Information is retrieved from the ring buffer by using a pointer, wherein the pointer is incremented and iterated over each stage of the ring buffer.

Abstract: A silhouette edge is rendered in a display format that corresponds to a geometry of a three-dimensional model. An angle between the silhouette edge and an adjacent silhouette edge in the image is determined, and the display format for the silhouette edge is selected based on the angle. Texture mapping is used to generate the silhouette edge in the display format.