Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Offset-polygon annulus placement problems
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
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Coordinate metrology aims to answer two questions: whether a manufactured part meets design tolerance specifications and how well the manufactured part meets the specifications. Existing methods for analyzing measured coordinate data are not adequate or effective for parts of complex tolerance zones. This paper presents a new approach to dimensional qualification of manufactured parts. In this paper, we view the part qualification problem as an issue of finding an admissible point in transformation space. Based on the concept of admissible point, we develop theories and algorithms for part geometric dimensioning and tolerancing (GD&T) conformance check. A formulation based on containment fit for tolerance check is developed. An admissible transformation volume (ATV) is used to quantitatively characterize the quality of manufactured parts with respect to design tolerance specifications. We examine our approach in three tolerance examples and conclude that admissible transformation volume is an effective metric for part dimensional quality gauging and it is especially useful for multi-tolerance zone check where traditional methods fail to address it effectively.