Geometric Modelling approaches
- 1. CAD Software CAD software can be divided based upon the technology used: 1. 2-D drawing. Its applications include, · mechanical part drawing · printed-circuit board design and layout · facilities layout · cartography 2. Basic 3-D drawing (such as wire-frame modelling) 3. Sculptured surfaces (such as surface modelling) 4. 3-D solid modelling 5. Engineering analysis
- 2. Geometric Modeling Geometric modelling refers to a set of techniques concerned mainly with developing efficient representations of geometric aspects of a design. Therefore, geometric modelling is a fundamental part of all CAD tools.
- 3. Geometric modeling is the basic of many applications such as: • Mass property calculations. • Mechanism analysis. • Finite-element modelling. • NC programming. Requirements of geometric modelling include: • Completeness of the part representation. • The modelling method should be easy to use by designers. • Rendering capabilities (which means how fast the entities can be accessed and displayed by the computer).
- 4. Geometric Modeling Approaches The basic geometric modelling approaches available to designers on CAD/CAM systems are: 1. Wire-frame modeling. 2. Surface modeling. 3. Solid modeling.
- 5. Wire-frame Modeling Wire-frame modelling uses points and curves (i.e. lines, circles, arcs), and so forth to define objects. The user uses edges and vertices of the part to form a 3-D object Wire-frame model part
- 6. Example
- 7. Surface Modeling Surface modeling is more sophisticated than wireframe modeling in that it defines not only the edges of a 3D object, but also its surfaces. In surface modeling, objects are defined by their bounding faces.
- 8. SURFACE ENTITIES Similar to wireframe entities, existing CAD/CAM systems provide designers with both analytic and synthetic surface entities. Analytic entities include : •Plane surface, •Ruled surface, •Surface of revolution, and •Tabulated cylinder. Synthetic entities include •The bicubic Hermite spline surface, •B-spline surface, •Rectangular and triangular Bezier patches, •Rectangular and triangular Coons patches, and •Gordon surface.
- 9. Plane surface. This is the simplest surface. It requires three noncoincident points to define an infinite plane.
- 10. Ruled (lofted) surface. This is a linear surface. It interpolates linearly between two boundary curves that define the surface (rails). Rails can be any wireframe entity. This entity is ideal to represent surfaces that do not have any twists or kinks.
- 11. Surface of revolution. This is an axisymmetric surface that can model axisymmetric objects. It is generated by rotating a planar wireframe entity in space about the axis of symmetry a certain angle.
- 12. Tabulated cylinder. This is a surface generated by translating a planar curve a certain distance along a specified direction (axis of the cylinder).
- 13. Bezier surface. This is a surface that approximates given input data. It is different from the previous surfaces in that it is a synthetic surface. Similarly to the Bezier curve, it does not pass through all given data points. It is a general surface that permits, twists, and kinks . The Bezier surface allows only global control of the surface.
- 14. B-spline surface. This is a surface that can approximate or interpolate given input data (Fig. 6-9). It is a synthetic surface. It is a general surface like the Bezier surface but with the advantage of permitting local control of the surface.
- 15. Solid Modeling Solid models give designers a complete descriptions of constructs, shape, surface, volume, and density.
- 16. In CAD systems there are a number of representation schemes for solid modeling include: •Primitive creation functions. •Constructive Solid Geometry (CSG) •Sweeping •Boundary Representation (B-rep)
- 17. Primitive creation functions: These functions retrieve a solid of a simple shape from among the primitive solids stored in the program in advance and create a solid of the same shape but of the size specified by the user.
- 18. Constructive Solid Geometry (CSG) CSG uses primitive shapes as building blocks and Boolean set operators (U union, difference, and ∩ intersection) to construct an object.
- 19. Sweeping Sweeping Sweeping is a modeling function in which a planar closed domain is translated or revolved to form a solid. When the planar domain is translated, the modeling activity is called translational sweeping; when the planar region is revolved, it is called swinging, or rotational sweeping.
- 20. Boundary Representation Objects are represented by their bounded faces.