Mathematical Representation of Solids
1)Explain Constructive Solid Geometry (CSG)
Definition: It is a system which allows the user to build the model out of the solid graphic primitives, such as rectangular blocks, spheres, cylinders, cones, wedges and torus.
It is also known as the Building Block approach.
This is one of the most popular methods of building and representing complex solids. A CSG model is based on the principle that any physical object can be divided into a set of bounded primitives which can be combined in a certain manner to form the physical object.
List of solid graphic primitives:
- Block
- Cylinder
- Torus
- Sphere
- Cone
- Wedge
These primitives are structured and combined by using the Boolean operations such as Combine, Intersect and Difference.
2)Limitations of a wireframe model
Following are the limitations of a wireframe model:
- Confusing Image
- Cannot get required information from this model
- Not suitable to represent complex solids
- Not possible to calculate volume and mass from the model
- Takes more time to create a wireframe model compared to a solid model
- Hard to understand
3)Difference between C-rep and B-rep modeling
| C-rep modeling | B-rep modeling |
|---|---|
| Also known as Constructive Solid Geometry (CSG) | Also known as Boundary representation |
| It is easy to create precise solid model out of primitives | Used to create object of unusual shape |
| Less storage space | More storage space |
| More compact file | Larger file |
| Requires more computations | Requires less computations |
| By using C-rep, we cannot easily convert solid file into a wireframe model | By using B-rep, a solid model can be easily converted into a wireframe model |
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