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

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Three-Dimensional Modeling

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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

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CAD History Beginnings: SKETCHPAD (1962) by Ivan 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

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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.End product are drawings on paper. 3-D CAD: Computer model more like a real object, not a drawing object. modeling draftingConsidered a computer modeling tool, not just a drafting tool.

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

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Wireframe Modeling

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3-D CAD Types SimplestWireframe 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.

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

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

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

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3-D CAD Types Wireframe Modeling : Construction Stages

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

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

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Surface Modeling

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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 Directrix – typically a 2-D curve Generatrix Generatrix – can be a line, planar curve, or a 3-D curve

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

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

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3-D CAD Types Lofted SurfacesSurface 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

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

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

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3-D CAD Types Continuity conditionsSurface Modeling : Continuity conditions when joining surfaces DiscontinuousDiscontinuous: surfaces do not touch along their entire lengths Positional continuityPositional 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 continuityTangent continuity: smooth tangent transition between the two surfaces but can have different curvatures coming into the transition Curvature continuityCurvature continuity: the two surfaces merge without a noticeable transition

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

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Solid Modeling

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

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3-D CAD Types insidesurfaceSolid 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. Boolean operations:Relationships between primitives are defined with - Boolean operations: –Union: –Difference: –Intersection:

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

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

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

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

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

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

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3-D CAD Types facesB-rep modeling: surfaces or faces are basis for defining the solid –shapes solidis created –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 modifiablefeaturesConstraint-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 geometrymodifiable constraints –Feature geometry controlled through modifiable constraints.

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3-D CAD Types modifiable featuresConstraint-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 modifiable constraints –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. PTC – Pro/Engineer –Method pioneered by PTC – Pro/Engineer (1988) –SolidWorks –SolidWorks ® is a constraint-based solid modeler

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

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

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