Vol. 12, No. 4, December 1980 | ARISTIDES A. G. REQUICHA
The paper "Representations for Rigid Solids: Theory, Methods, and Systems" by Aristides A. G. Requicha discusses the importance of computer-based systems for modeling the geometry of rigid solid objects in various fields such as mechanical and civil engineering, architecture, computer graphics, and computer vision. The author introduces a mathematical framework to characterize the key aspects of representations, including their semantic integrity. The paper is divided into three parts: the first part introduces the framework, the second part describes and compares major known schemes for representing solids, and the third part surveys existing geometric modeling systems and applies the concepts to the design of a high-level geometric modeling system.
The paper emphasizes the need for robust and versatile representations that can support a wide range of applications, such as calculating moments of inertia and generating hidden surface-free displays. It discusses the limitations of current systems, particularly in handling ambiguous representations and ensuring representational validity. The author proposes that future systems should be unambiguous and unique to ensure reliable and automatic processing.
The paper also explores various representation schemes, including ambiguous schemes like engineering drawings and wireframe representations, and unambiguous schemes like spatial occupancy enumeration, cell decompositions, constructive solid geometry (CSG), and sweep representations. Each scheme is evaluated based on properties such as validity, completeness, uniqueness, conciseness, ease of creation, and efficacy in specific applications.
The author concludes that general-purpose geometric modeling systems will likely contain multiple representations tailored to different classes of applications, with each representation optimized for specific tasks. The paper provides a comprehensive overview of the current state of solid representation theory and methods, offering insights into the design of advanced modeling systems.The paper "Representations for Rigid Solids: Theory, Methods, and Systems" by Aristides A. G. Requicha discusses the importance of computer-based systems for modeling the geometry of rigid solid objects in various fields such as mechanical and civil engineering, architecture, computer graphics, and computer vision. The author introduces a mathematical framework to characterize the key aspects of representations, including their semantic integrity. The paper is divided into three parts: the first part introduces the framework, the second part describes and compares major known schemes for representing solids, and the third part surveys existing geometric modeling systems and applies the concepts to the design of a high-level geometric modeling system.
The paper emphasizes the need for robust and versatile representations that can support a wide range of applications, such as calculating moments of inertia and generating hidden surface-free displays. It discusses the limitations of current systems, particularly in handling ambiguous representations and ensuring representational validity. The author proposes that future systems should be unambiguous and unique to ensure reliable and automatic processing.
The paper also explores various representation schemes, including ambiguous schemes like engineering drawings and wireframe representations, and unambiguous schemes like spatial occupancy enumeration, cell decompositions, constructive solid geometry (CSG), and sweep representations. Each scheme is evaluated based on properties such as validity, completeness, uniqueness, conciseness, ease of creation, and efficacy in specific applications.
The author concludes that general-purpose geometric modeling systems will likely contain multiple representations tailored to different classes of applications, with each representation optimized for specific tasks. The paper provides a comprehensive overview of the current state of solid representation theory and methods, offering insights into the design of advanced modeling systems.