# Three-Dimensional Modeling (A Brief Introduction)

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

Three-Dimensional Modeling

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

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

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.

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

Wireframe Modeling

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.

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

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

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

3-D CAD Types Wireframe Modeling: Construction Stages

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

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

Surface Modeling

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

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

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

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

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

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

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

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

Solid Modeling

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

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:

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

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

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

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:

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

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

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.

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

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

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