1. Three-Dimensional Modeling (A Brief Introduction)
MECH 100 – Graphics I
Technical Graphics Communication:
Three-Dimensional Modeling
(A Brief Introduction)

2. Three-Dimensional Modeling

3. Objectives Briefly Place 3-D Modeling in a Historical Perspective
Define the most Popular Types of 3-D Modeling Systems
Understand How Constraint- and Feature-based Modeling Alters 3-D Modeling Strategy

4. CAD History Beginnings: SKETCHPAD (1962) by Ivan Sutherland @ MIT
1960s and 1970s: Developed by large defense, aerospace, and auto companies
(Lockheed, Boeing, GM, etc.)
Powerful mainframes required to run 3-D CAD programs => Expensive, limited availability

5. CAD History
2-D CAD: Programs developed to be drafting tools, much like traditional manual drafting.
Objects represented in 2-D like traditional engineering drawings.
End product are drawings on paper.
3-D CAD: Computer model more like a real object, not a drawing object.
Considered a computer modeling tool, not just a drafting tool.

6. 3-D CAD Relatively newcomer to engineering & technical graphics
Demand a new way of thinking: How graphics integrates into the engineering process
Today’s Emphasis: Constraint-based modeling

7. Wireframe Modeling

8. Wireframe Modeling: Simplest 3-D modeler.
3-D CAD Types
Wireframe Modeling: Simplest 3-D modeler.
Straight or curved Edges (list), Vertices (x, y, z coordinates) & sometimes Faces (size, location, orientation) are defined and kept in the database to represent the objects
Integrity rules must be observed to avoid invalid models, e.g.,
Each vertex must have a unique coordinate location
Each vertex must be associated with at least three edges
Each edge can have only two vertices
Each face must contain at least three edges that form a closed loop.

9. 3-D CAD Types
Wireframe Modeling: Vertex & Edge List

10. 3-D CAD Types
Wireframe Modeling: Vertex, Edge, Face List

11. 3-D CAD Types
Wireframe Modeling: Linear & Circular Edges

12. 3-D CAD Types
Wireframe Modeling: Construction Stages

13. Wireframe model with ambigous orientation: the necker cube
3-D CAD Types
Wireframe Modeling: Have problems with uniqueness
Wireframe model with ambigous orientation: the necker cube

14. 3-D CAD Types
Wireframe Modeling: Have problems with uniqueness

15. Surface Modeling

16. 3-D CAD Types
Surface Modeling: Define surface features (as well as edges) of objects.
Bézier and/or NURBS (non-uniform rational B-splines) are used to mathematically define curves.
Surface Generation:
Sweeping – moving a directrix along a generatrix
Revolving – revolve the directrix about an axis
Lofting – uses a series of directrix curves to define multiple intermediate points along the generatrix path to create complex-shaped surfaces. Boundary curves can be used to create surface patches.
Directrix – typically a 2-D curve
Generatrix – can be a line, planar curve, or a 3-D curve

17. 3-D CAD Types
Surface Modeling: Define surface features (as well as edges) of objects. Swept Surfaces

18. Revolve the directrix about an axis
3-D CAD Types
Surface Modeling: Define surface features (as well as edges) of objects. Revolved Surface
Revolve the directrix about an axis
Axis of Revolution
Directrix

19. 3-D CAD Types
Surface Modeling: Define surface features (as well as edges) of objects. Lofted Surfaces
Lofting two or more directrix curves to define a surface
Directrix curves
More control with a defined generatrix curve
Generatrix curve

20. Surface patch created by 4 boundary curves & 12 control points
3-D CAD Types
Surface Modeling: Define surface features (as well as edges) of objects. Patch Surface
Surface patch created by 4 boundary curves & 12 control points

21. Surface Modeling: Trimming - Sphere trimmed by a circle.
3-D CAD Types
Surface Modeling: Trimming - Sphere trimmed by a circle.
Projecting curve onto surface to be trimmed
Trimmed surface

22. 3-D CAD Types
Surface Modeling: Continuity conditions when joining surfaces
Discontinuous: surfaces do not touch along their entire lengths
Positional continuity: edges of the two surfaces touch along their entire lengths. They share a common edge but not a common slope. There is a crease where the surfaces join.
Tangent continuity: smooth tangent transition between the two surfaces but can have different curvatures coming into the transition
Curvature continuity: the two surfaces merge without a noticeable transition

23. Surface Modeling: Continuity conditions when joining surfaces
3-D CAD Types
Surface Modeling: Continuity conditions when joining surfaces
Discontinuous
Positional continuity
Tangent continuity
Curvature continuity

24. Solid Modeling

25. 3-D CAD Types
Solid Modeling: Include volumetric information about the inside as well as the surface features of the 3-D model of objects.
3-D solid geometry defined by either Constructive Solid Geometry (CSG) or Boundary Representation (B-rep). Hybrid modeling uses both.
CSG modelers support a small set of geometric primitives (cubes, blocks, wedges, spheres, cones, tori, and cylinders)
Primitives are joined together to create more complex objects.
Relationships between primitives are defined with Boolean operations

26. 3-D CAD Types
Solid Modeling: Include volumetric information about the inside as well as the surface features of the 3-D model of objects.
CSG modelers support a small set of geometric primitives (cubes, blocks, wedges, spheres, cones, tori, and cylinders)
primitives are joined together to create more complex objects.
Relationships between primitives are defined with - Boolean operations:
Union:
Difference:
Intersection:

27. 3-D CAD Types
CSG Modeling: primitives are joined together to create more complex objects

28. CSG modeling: Boolean operations
3-D CAD Types
CSG modeling: Boolean operations
Union:
Difference:
Intersection:
Objects
Block A
Cylinder B
positioned as shown

29. CSG modeling: difference (order matters)
3-D CAD Types
CSG modeling: difference (order matters)
Objects
Block A
Cylinder B
positioned as shown
A  B
B  A

30. positioned as shown with NO overlap
3-D CAD Types
CSG modeling: boolean operations (on adjoining primitives)
Objects
Block A
Wedge B
positioned as shown with NO overlap
Union:
Difference:
Intersection:

31. 3-D CAD Types
CSG modeling: modeling a complex object with boolean operations

32. B-rep modeling: surfaces or faces are basis for defining the solid
3-D CAD Types
B-rep modeling: surfaces or faces are basis for defining the solid
faces are explicitly oriented surfaces (unlike wireframe models) There is an inside and an outside
faces can contain linear & curved edges (sometimes approx. by a series of planar ones) – faceted

33. 3-D CAD Types
B-rep modeling: surfaces or faces are basis for defining the solid
shapes are created similar to wireframe model construction except solid bounded by faces is created.
Hybrid modeling: modeler combines fully functional CSG and B-rep databases
Constraint-based modeling: model defined by a series of modifiable features. Each feature defined through operations that closely represented design or manufacturing features of the final product.
Feature geometry controlled through modifiable constraints.

34. 3-D CAD Types
Constraint-based modeling: model defined by a series of modifiable features. Each feature defined through operations that closely represented design or manufacturing features of the final product.
Feature geometry controlled through modifiable constraints. Planning the modeling process is critical with this method. When done properly, facilitates modification of design in the future.
Method pioneered by PTC – Pro/Engineer (1988)
SolidWorks® is a constraint-based solid modeler

35. 3-D CAD Types
Planning a constraint-based model:

36. Assignment Study: Chapter 10 Multiview Drawings
Note: Chapter 10 will be covered in two lectures
Answer Review Questions on Bb Learn