Browse Theses

Self-intersection is an ill-formed condition of a solid boundary. Very little research has been directed toward detecting solid self-intersections. The lack of effective solutions to the problem motivates us to develop a set of methods for solid self-intersection detection in various situations.

The first strategy of our approach is to transform the self-intersection detection problem to an edge-face intersection check problem. Then we develop a method for detecting the existed edge-face intersection without calculating intersection points. The method uses a convex decomposition method to decompose polygons derived from a test face. The method then builds a convex cone for each decomposed convex polygons. With these convex cones, intersections between the test edge and these convex cones can be easily checked. Using the results of these intersection checks, it can be determined whether the test edge and the test face intersect. The method has a time complexity of $O(n\sp3$) which is better than $O(n\sp3logn$) time complexity of the face-face intersection approach.

To enhance the general method, we develop a method based on layered convex hulls to reduce the number of required edge-face intersection checks. The idea is to build layered convex hulls from the input solid, then use the information from these layers to classify the faces of the solid into categories. With the face classification, screening rules are invoked to screen out identifiable unnecessary intersection checks. For the remaining intersection possibilities, the general method is used to determine if self-intersection does occur.

To avoid global check when only a portion of a solid is modified, a local self-intersection detection method is provided. The method takes advantages of spatial information of those entities being affected before and after modifications to minimize edge-face pairs to be checked for possible intersection. For these affected edge-face pairs, the general method is used to determine if self-intersection does occur.