Abstract
Conventionally, geometric computing problems are treated as algebraic computing problems by representing a geometric object in a global reference coordinate system. This approach has two problems. The first problem is that the intuitive view of the interaction of objects is lost, and the second problem is that algebraic computing is prone to errors for degenerated cases related to the interaction of (e.g., notable case of “divided by zero”). In this paper, we propose a new approach to geometric computing especially to analyze the interaction of two objects (e.g., two triangles). The main idea behind this new approach is a specially-tailored local coordinate system for two interacting objects is defined, which makes the projection of the objects on this local coordinate system represent the true geometry of the objects. This idea significantly departs from the conventional approach which is primarily based on the concept of the global coordinate system. Three examples are provided to illustrate the effectiveness of the proposed approach. Among them, one example is related to the robustness of methods for analyzing the relations of two interacting objects, which is still an open issue in the field of geometric computing and suggests that the proposed approach could have some benefit to robustness in analysis.
Highlights
In product development, including both aesthetic products and functional products [21], manipulation of a set of geometric objects is an essential task
The first idea is to establish a local projection plane (LP for short) for the two interacting geometric entities by tailoring it to two concerned geometric objects such that they are in parallel, vertical, or symmetrical to the LP, and subsequently establishing a local coordinate system (LCS) based on the LP. The philosophy behind this idea is that the relation between two interacting objects can be captured and represented most effectively and efficiently by the local coordinate system, which is primarily based on the geometric feature of the two objects in interaction, rather than a general-purpose local coordinate system, which is the case in other geometric computing methods in literature [28], [29]
WITH FURTHER DISCUSSIONS This paper presented a new approach to geometric computing
Summary
In product development, including both aesthetic products (e.g., sculpture) and functional products [21], manipulation of a set of geometric objects is an essential task. The first idea is to establish a local projection plane (LP for short) for the two interacting geometric entities by tailoring it to two concerned geometric objects such that they are in parallel, vertical, or symmetrical to the LP, and subsequently establishing a local coordinate system (LCS) based on the LP The philosophy behind this idea is that the relation between two interacting objects can be captured and represented most effectively and efficiently by the local coordinate system, which is primarily based on the geometric feature of the two objects in interaction, rather than a general-purpose local coordinate system, which is the case in other geometric computing methods in literature [28], [29].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
