| Feedback, such as an inspection of a part, is a key step in the design and manufacture of complex products. It determines where a product or manufacturing process should be re-evaluated to conform to design specifications. The inspection of a part is characteristically accomplished by comparing the CAD model to the measurements of a manufactured part. This is simple for parts that contain a commonality: central axis, plane on a flat side, center of a sphere, etc. When a part does not share a commonality---like free-form surfaces---the comparison analysis becomes complex.;This complexity occurs when determining the process for correspondence of every point on a manufactured part to every point on a design model. Whenever one coordinate system is shifted, the comparison can be lost and, then, has to be reevaluated, creating an iteration. The demand for substantial iterations protracts the process and thwarts optimization. It is, also, challenging to mathematically determine which points should be compared to another. Is the selected point optimal for comparison? Is a higher resolution of points needed? This problem of how the coordinate systems of the CAD model and the measured part can be aligned is termed as localization and is extensively researched [1]. Currently, most algorithms use a line or surface fitting technique that minimizes the sum of the square of the errors, drawing upon Gunnarsson and Prinz's original idea [2]. Such nonlinear approaches may result in local minima when minimized, resulting in false solutions. Additionally, a solution achieved may not be optimal due to averaging of outliers in the data.;This thesis proposes a methodology that automatically aligns the coordinate systems of free-form CAD models to collected manufactured measurements, with resiliency to outliers of the fit and false solutions given by local minima, by maximizing the shared extent depending on dimension. To perform this, data from the manufactured surface and design surface are polygonized and compared until geometrically similar. Then, the overlapping or intersecting extent is calculated depending on the dimension and maximized using a heuristic approach, particle swarm optimization. At the maximum shared extent, two coordinate systems should be aligned in the optimal position. In this work, only two dimensional free-form curves are used to determine if the maximization of the shared extent results in an optimal solution, reducing complexity from three dimensions. Results obtained validated the approach and that the manufactured curve was aligned to the design, as measured by the sum of the squared errors. Also, the method was discovered to resist outliers, demonstrated by the tight alignment of consistent sloped areas while not necessarily aligned to peaks and valley features. Error observed is mainly due to inaccurate polygon geometry between the curves rather than the maximization of shared area process. |
