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

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

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

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

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.

– Bezier 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 curveGeneratrix – 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

3-D CAD Types• Surface Modeling: Define surface features (as

well as edges) of objects. Revolved Surface

Revolve the directrix about an axis

Directrix

Axis of Revolution

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

Generatrix curve

More control with a defined

generatrix curve

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

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

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

3-D CAD Types• CSG modeling: Boolean operations

• Union: • Difference:• Intersection:

Objects

Block ACylinder B

positioned as shown

3-D CAD Types• CSG modeling: difference (order matters)

Objects

Block ACylinder B

positioned as shown

A B

B A

3-D CAD Types• CSG modeling: boolean operations (on adjoining

primitives) Objects

Block AWedge B

positioned as shown with NO overlap

Union:

Difference:

Intersection:

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

boolean operations

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