This dissertation focuses on three new methods for calculating visibility and accessibility, which contribute directly to the precise planning of setup and toolpaths in a Computer Numerical Control (CNC) machining process. They include 1) an approximate visibility determination method; 2) an approximate accessibility determination method and 3) a hybrid visibility determination method with an innovative computation time reduction strategy. All three methods are intended for polyhedral models.

First, visibility defines the directions of rays from which a surface of a 3D model is visible. Such can be used to guide machine tools that reach part surfaces in material removal processes. In this work, we present a new method that calculates visibility based on 2D slices of a polyhedron. Then we show how visibility results determine a set of feasible axes of rotation for a part. This method effectively reduces a 3D problem to a 2D one and is embarrassingly parallelizable in nature. It is an approximate method with controllable accuracy and resolution. The method’s time complexity is linear to both the number of polyhedron’s facets and number of slices. Lastly, due to representing visibility as geodesics, this method enables a quick visible region identification technique which can be used to locate the rough boundary of true visibility.

Second, tool accessibility defines the directions of rays from which a surface of a 3D model is accessible by a machine tool (a tool’s body is included for collision avoidance). In this work, we present a method that computes a ball-end tool’s accessibility as visibility on the offset surface. The results contain all feasible orientations for a surface instead of a Boolean answer. Such visibility-to-accessibility conversion is also compatible with various kinds of facet-based visibility methods.

Third, we introduce a hybrid method for near-exact visibility. It incorporates an exact visibility method and an approximate visibility method aiming to balance computation time and accuracy. The approximate method is used to divide the visibility space into three subspaces; the visibility of two of them are fully determined. The exact method is then used to determine the exact visibility boundary in the subspace whose visibility is undetermined. Since the exact method can be used alone to determine visibility, this method can be viewed as an efficiency improvement for it. Essentially, this method reduces the processing time for exact computation at the cost of introducing approximate computation overhead. It also provides control over the ratio of exact-approximate computation.