Lecture three Geometric Modeling curve rep
- 2. Part #3-Outline • Introduction • Requirements of Geometric Modelling • Geometric Models • Geometric Construction Methods • Wireframe Modelling • Solid-Representation Methods • Solid modeling techniques - CSG, and - B-rep • Representation of curves - Hermite curve - Bezier curve- - B-spline curves- rational curves- • Techniques for surface modeling - Surface patch - Coons and bicubic patches - Bezier and B-spline surfaces.
- 3. Objectives: ➢ Understand the various requirements for the information that is generated during the geometric modelling stage ➢ Study various types of geometric models possible and their applications ➢ Understand the methods of representation of wireframe, surface, and solid modelling systems ➢ Develop various methodologies used for geometric construction such as sweep, surface models, solid models, etc. ➢ Recognise the various types of surfaces and their applications as used in geometric modelling ➢ Understand the solid construction methods including B-rep and CSG methods ➢ Understand the parametric representation of curves.
- 4. Geometric Modeling ❑ Geometric modeling is as important to CAD as governing equilibrium equations to classical engineering fields as mechanics and thermal fluids. ❑ What does geometric modelling mean? What is it expected to provide? ❑ Primarily, geometric models are used for representation of products to realize abstracted ideas in designer’s mind and to use for evaluation purposes. ❑ The functions that are expected of geometric modelling are: ▪ Geometric (3D) models are easier to interpret. ▪ Simulation under real-life conditions. ▪ Less expensive than building a physical model. ▪ 3 D models can be used to perform finite element analysis (stress, deflection, thermal) ▪ 3D models can be used directly in manufacturing, Computer Numerical Control (CNC), bill of materials. ▪ Can be used for presentations and marketing.
- 5. Geometric Modeling The Role of Geometric Modeling in a CAD System
- 7. Comments on Geometric Modeling
- 10. Types of CAD Models ❑ Objects and geometric models can be classified into three types from a geometric construction point of view: 1) 2½ D: ✓ An extrusion has a constant cross section and a thickness in a direction perpendicular to the plane of cross section:; ✓ An axisymmetric object has a constant cross section that is revolved about an axis of revolution through an angle 0 < 360o,and ✓ A composite 2½ D object is a combination of multiple 2½ D objects 2) 3D: that do not have any geometric uniformity in any direction 3) Combination of both: that has geometric uniformity and non- uniformity in different directions
- 11. Types of CAD Models ❑CAD models can be classified into four types from a construction point of view: ▪ Extrusion: This is a part with constant cross section along a given axis, with a uniform thickness along the axis ▪ Revolve: This is an axisymmetric part with a constant cross section through an angle of revolution about a given axis of revolution ▪ Composite: This combines both extrusion and revolves ▪ Free form: This has a shape that does not exhibit any uniform shape (example: Computer mouse, Auto body)
- 12. Types of CAD Models Axisymmetric model Composite model Non-uniform cross section Non-uniform thickness More than one sketch in different sketch plane Uniform thickness models 2 ½ D 3D
- 13. Planning Part Creation Part clue How to use in part creation on CAD system Part type • Extrusion: create a sketch and extrude it • Revolve: create a sketch and revolve it • Composite: use a combination of extrusions and/or revolves • Free form: use lofts, sweeps, surfaces, etc. Part symmetry • Split the part into two halves at the symmetry plane, construct one half and mirror it about the symmetry plane to finish the creation of the CAD model Part patterns If they exist, e.g. holes in a flange or phone buttons, use CAD patterns to create them Designated points Make use of end, mid, and/or intersection points of entities during construction to avoid unnecessary calculations. SolidWorks snaps to these points when you move the mouse close to them, or hover the mouse over them, during construction Geometric constraints These include parallelism, concentricity etc. SolidWorks has a library of them Relations These include proportions such as D1 = 2D2. SolidWorks allows you to create your own relations Center planes for features When you break the part into features to begin construction, always build features off center, i.e. use mid planes. When you extrude a sketch, extrude it on both sides of the sketch plane. This strategy is good for mirror; use the sketch plane to mirror (see Chapter 1 tutorials). It also makes changes and part evolution easy Miscellaneous • Avoid measuring from corners; measure form mid planes • If you do not have dimensions, sketch freely • Use “Trim Entities” to clean up construction and avoid calculations • Use transformations (move, rotate, copy, scale, offset) to speed up construction
- 14. Part Creation Planning (Example) • What is the best modeling plan to use to create the CAD model shown below
- 15. Geometric Modeling Objects: # Topology represents the relationships of the geometry of an object. # In addition to its shape, an engineering object also possesses some other attributes: dimensions, tolerances, and surface finish. # The model of an engineering object consists of geometry, topology and auxiliary information. # Geometry includes points, lines, circles, planes, cylinders and other surfaces. It defines the basic shape characteristics.
- 16. Cont’d… ❑ Many properties of products have to be modeled, including form, dimension, tolerance and structure. ❑ In all of these areas geometry, images and spatial manipulation are very important. For this reason, CAD is founded on computational geometry and computer graphics.
- 17. Part Topology (Anatomy) ◼A Solid Model is a geometric model of a part and represents most complete definition of a part ◼A Solid Model is also known as a body (B) ◼A Solid Model Consists of the following: ◼Faces (F): It is a surface that may be planar or non-planar ◼Edges (E): It is a curve that may be a line ◼Loops (L): It a set of contiguous edges on a face ◼Vertices (V): It is a point (Corner) ◼Genus (G): It is a hole in a solid
- 18. Part Topology • The description of a model in terms of F, E, V, L, G is known as model topology • The topology of a valid solid model must satisfy Euler equation • F-E+V-L = 2(B-G) • The figure shown here has the following topology: F=6, E=12,V=8, L=8, B=1, G=4 • Hence this model is a valid model • CAD/CAM systems create valid model
- 19. Parametric Modeling • CAD/CAM systems use parameters to define a model instead of specific explicit dimensions • In this type of modelling, often called parametric modelling or constraint-based modelling, most of the time the modelling starts with a sketch in 2D plane and then is swept along a specified direction, thereby producing the desired component. • The figure below shows the difference between parameters and dimensions
- 20. Benefits of Parametric Modeling • Parametric modeling offers three benefits • Sketching freely on a plane • Ability to create a family of parts in which all parts have identical shapes with different dimensions • Ability to create relations between parameters to control the geometry of the sketch • Gives the designer incredible flexibility and power during conceptual design stage without worrying about the dimensions
- 21. Form Features Modeling • A feature is a geometric shape specified by a parameter set which has special meaning for design or manufacturing engineers. • Features represent a collection of entities in an intelligent form (like ‘hole’, ‘slot’, ‘thread’, ‘groove’, etc.) and hence provide information at a higher conceptual level. • The use of such groups of geometry coupled with the necessary information needed for other applications such as process-planning functions is seen as a practical means of linking the design and manufacturing.
- 22. Defining the Model: Methods of defining elements in interactive computer graphics 1. Points Methods of defining points in computer graphics include: 1) Pointing to the location on the screen by means of cursor control. 2) Entering the coordinates via the alphanumeric keyboard. 3) The intersection of two lines.
- 23. Cont’d… 2. Lines Methods of defining lines include: 1) Using two previously defined points. 2) Using one point and specifying the angle of the line with the horizontal. 3) Using a point and making the line either normal or tangent to a curve. 4) Using a point and making the line either parallel or perpendicular to another line. 5) Making the line tangent to two curves. 6) Making the line tangent to a curve and parallel or perpendicular to a line.
- 24. Lines
- 25. Cont’d… 3. Arcs, Circles & Curves Methods of defining arcs and circles include: 1) Specifying the center and the radius. 2) Specifying the center and a point on the circle. 3) Making the curve pass through three previously defined points. 4) Making the curve tangent to two lines. 5) Specifying the radius and making the curve tangent to two lines or curves.
- 26. Circles
- 27. Arcs
- 28. 4. Surface Modeling A surface is a 2D space in an object that has breadth and width much like a piece of cloth. A surface has two degrees of freedom. This means that a point on surface can be moved in 2 independent directions. The x, y coordinates of any point on the surface are determined by these free variables or parameters( i.e. u & v).
- 29. Cont’d… > Surface is controlled by series of control points and boundaries. > Classification of surfaces: 1) Planar surfaces: a flat 2D surface. 2) Curved surfaces: > Single curved surfaces: It s a simple curved surface obtained by rotating straight lines around an axis Ex: Cylindrical, conical, pyramid surfaces, prisms > Conics: are double curved surfaces: They are complex surfaces generated by complex curved lines/surfaces. Ex: Spherical, Torous, Ellipsoid, Parabaloid, Fuselage, Automobiles, etc
- 30. Techniques in Geometric Modeling The various methods for representing the solids are: 1) Boundary representation method (B-rep) 2) Constructive solid geometry (CSG and C-rep) 3) Sweep representation 4) Analytical solid modeling (ASM).
- 31. Boundary Representation Method (B-rep) > In surface/solid modeling and computer-aided design, boundary representation often abbreviated as B-rep or BREP - is a method for representing shapes using the limits. > A solid is represented as a collection of connected surface elements, the boundary between solid and non-solid. > Boundary representation models are composed of two parts: Topology and Geometry (surfaces, curves and points).
- 32. The main topological items/ primitives of B-rep are: Vertex (V) : It is a unique point (an ordered triplet) in space. Edge (E): It is finite, non-self intersecting, directed space curve bounded by two vertices that are not necessarily distinct. Face (F): It is defined as a finite connected, non-self-intersecting, region of a closed oriented surface bounded by one or more loops Loop (L): It is an ordered alternating sequence of vertices and edges. Body/Shell(B) : It is a set of faces that bound a single connected closed volume. Cont’d…
- 33. Cont’d… > A minimum body is a point; topologically this body has one face, one vertex, and no edges. > Geometry: i. Open polyhedral objects
- 35. Modeling Surfaces: Ex1. Creating Extruded Surfaces
- 36. Ex. 2 - Creating Revolved Surfaces
- 37. Ex.3 - Creating Swept surfaces You can create a swept surface by sweeping out a profile in planes normal to a spine curve while taking other user-defined parameters (such as guide curves and reference elements) into account. 1. Click the Sweep icon 2. Select the planar profile to be swept out, that is the circle. 3. Select a guide curve. 4. If needed, select a spline. If no spline is selected, the guide curve is implicitly used as the spline. 5. If needed, select a second guide curve. 6. If you want to control the position of the profile during the sweep, you can select a reference surface. You can impose a reference angle on this surface. 7. Click OK to create the swept surface.
- 38. Creating Swept Surfaces Cont’d… Swept circle along a curvilinear guiding curve.
- 39. Ex. 4. Creating Fill Surfaces
- 40. Ex.5. Creating Blended Surfaces
- 41. Ex. 6. Creating Spherical Surfaces The spherical surface is based on a center point, an axis-system defining the meridian & parallel curves orientation, and angular limits. 1) Click the Sphere icon from the Extrude-Revolution toolbar. 2) Select the center point of the sphere. 3) Select an axis-system 4) Click Apply to preview the surface. 5) Modify the Sphere radius and the Angular Limits as required This axis-system determines the orientation of the meridian and parallel curves, and therefore of the sphere.
- 42. Ex. 7. Creating Cylindrical Surfaces 1) Click the Cylinder icon 2) Select the Point that gives the center of the circle to be extruded and specify the desired Direction of the cylinder axis 3) Select the Radius of the cylinder. 4) Enter values or use the graphic manipulators to define the start and end limits of the extrusion. 5) You can click the Reverse Direction button to display the direction of the cylinder on the other side of the selected point or click the arrow in the 3D geometry. 6) Click OK to create the surface
- 43. Ex. 8 Creating Offset Surfaces 1) Click the Offset icon 2) Select the Surface to be offset. 3) Specify the Offset by entering a value or using the graphic manipulator. An arrow indicates the proposed direction for the offset. 4) The offset surface is displayed normal to the reference surface. 5) Click Apply to preview the offset surface 6) Check the Both sides button to generate two offset surfaces, one on each side of the reference surface. 7) Click OK to create the surfaces.
- 44. Geometric Modeling ❑ 3D GM has the ability to provide all the information required for manufacturing applications. The basic 3D GM approaches available to designers on CAD systems are: ➢ The line model (Wireframe modeling). ➢ Surface modeling. ➢ Solid or Volume modeling.
- 46. Wireframe Modeling ❑ Wireframe Modelling: these modelling methods rely on the ability of the user to define the basic elements such as points, lines and circles to be defined in a number of ways. The user uses edges and vertices of the part to form a 3-Dobject
- 48. Wireframe Modeling ❑ Curves plays important role in generating a wire frame modelling Advantages : 1. Ease of creation. 2. Low level of hardware and software requirements. 3. Data storage requirement is low. Disadvantages: 1. It can very confusing to visualize. Example : A blind hole in a box may be look like a solid cylinder
- 62. Constructive Solid Geometry (CSG) • Boolean Operators and their effect on Model Construction
- 65. Constructive Solid Geometry (CSG)
- 85. Sweeping • Linear sweep between two cross sections
- 86. Sweeping • Component Model by Rotational Sweep