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== Overview ==
The use of solid modeling techniques allows for the automation process of several difficult engineering calculations that are carried out as a part of the design process. Simulation, planning, and verification of processes such as [[machining]] and [[Assembly line|assembly]] were one of the main catalysts for the development of solid modeling. More recently, the range of supported manufacturing applications has been greatly expanded to include [[sheet metal]] [[manufacturing]], [[injection molding]], [[welding]], [[Piping|pipe]] routing, etc. Beyond traditional manufacturing, solid modeling techniques serve as the foundation for [[rapid prototyping]], digital data archival and [[reverse engineering]] by reconstructing solids from sampled points on physical objects, mechanical analysis using [[finite elements]], [[motion planning]] and NC path verification, [[Kinematics|kinematic]] and [[Dynamics (physics)|dynamic analysis]] of [[Mechanism (engineering)|mechanisms]], and so on. A central problem in all these applications is the ability to effectively represent and manipulate three-dimensional geometry in a fashion that is consistent with the physical behavior of real artifacts. Solid modeling research and development has effectively addressed many of these issues, and continues to be a central focus of [[computer-aided engineering]].
== Mathematical foundations ==
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