adminGEOMETRIC MODELS
Geometric models are mathematical representations of objects or systems using geometric shapes, such as points, lines, curves and surfaces.
There are two types of geometric models and they are as follows; parametric and non-parametric, geometric models.
Parametric geometric models are models defined by a set of parameters such as dimensions, angles and relationships that control the shape and behavior of the model. Parametric models are often used in computer aided design (CAD) and can be easily modified and updated by changing the parameters.
Non-parametric geometric models are models also known as explicit or direct models are defined by their geometric shape and topology without reference to a set of parameters. Non parametric models are often used in applications where exact shape and geometry are more important than the underlying parameters.
The advantages of geometric models are as follows; geometric models can accurately represent complex shapes and objects. Geometric models can be easily modified and analyzed using various algorithms and techniques. Geometric models can be used to optimize and automate various processes such as design and manufacturing. Geometric models can be used to create detailed and realistic visualizations of objects and systems.
The disadvantages of geometric models are as follows; geometric models can be complex and difficult to create and analyze especially for large and complex simulations and analysis. Geometric models require accurate and detailed data to create and validate which can be time consuming and expensive to obtain. Geometric models require expertize to interpret and analyze especially for complex systems.
Geometric models find widespread application in several industries and they are as follows; geometric models are used in various engineering fields such as mechanical, aerospace, automobile, manufacturing, architecture etc. to design and analyze machines, equipment, bridges, civil works, buildings and infrastructure etc. geometric models are used to design and analyze products such as consumer goods and house products, domestic and industrial equipment. Geometric models are used to analyze and visualize medical imaging data. Geometric models are used to create 3D graphics and animations.
The future of geometric models is based on the advances and development of the following technologies; advances in computer power, artificial intelligence, virtual and augmented reality and internet of things, will drive or enable more complex and detail geometric model allowing for more accurate simulations and analysis.
SOURCES:
- Geometric modeling by Michael E. Mortenson.
- Computational geometry: Algorithms and applications by Mark de Berg, Otfried Cheong and Marc van Kreveld.
- Geometric modeling for computer graphics by Gerald Farin and Dianne Hansford.
- Computer aided geometric design by Gerald Farin.
- Geometric modeling for engineering applications by Gerald Farin.
