Application of bevel curves to splines

#Some computer aided design programs allow users to create custom geometries by extruding two-dimensional splines into three dimensions. An extruded geometry can be shaped by applying a bevel curve to the geometry. However, doing so can result in unwanted deformations such as bumps protruding from the geometry. In addition, bevel curves cannot typically be easily applied to self-intersecting splines.

#In general, one aspect of the subject matter described in this specification can be embodied in a method that includes a computer-implemented method, comprising applying a first spline to a second spline that is closed to create a third spline, where the third spline is closed and has the shape of the second spline as modified by the first spline. One or more points of self intersection are detected in the third spline and the third spline is divided into one or more sections at the points of self intersection. A first section is removed from the third spline where the first section includes two non-overlapping segments, a first segment having crossed a second segment as a result of the applying. Other embodiments of this aspect include corresponding systems, apparatus, and computer program products.

#These and other embodiments can optionally include one or more of the following features. The first segment has an normal that is outward pointing in the second spline and inward pointing in the third spline. The first spline is applied to one side of the second spline. The first spline is closed. The third spline is extruded to form a solid. The third spline is associated with a neighbor spline. The third spline and the neighbor spline each have a plurality of vertices, the method further comprising linking corresponding vertices on the third spline and the neighbor spline to create a geometry comprising a plurality of polygons. The geometry has an opening, the method further comprising filling the opening with one or more polygons.

#FIG. 1A illustrates an example spline.

#FIG. 1B illustrates an example extruded shape.

#FIG. 1C illustrates an example beveled shape.

#Like reference numbers and designations in the various drawings indicate like elements.

#FIG. 1A illustrates an example two-dimensional (2D) spline curve 102 (or “spline”). In various implementations, the spline 102 can be described by a function or a set of functions and by a set of tangents. In further implementations, the spline 102 can be manipulated through the set of tangents and/or a set of control points, for example. The spline 102 can be created, for example, using a CAD (Computer Aided Drafting) program.

#The spline 102 in this example is a closed spline. A closed spline is a spline that has an interior (i.e., a closed spline is connected end-to-end). The spline 102 is a self-intersecting spline. A self-intersecting spline includes line segments that cross each other. The spline 102 can be used as a basis for custom geometry. For an example, FIG. 1B illustrates an extruded shape 104 based off of the spline 102. The spline 102 can be extruded to create the three-dimensional (3D) extruded shape 104. For example, the extruded shape 104 has the same general shape as the spline 102 but has a depth (e.g., the extruded shape 104 is a 3D solid).