Lecture 8 and 9 ENGR3030U Zeid Ch 7

Lecture 8 and 9 ENGR3030U Zeid Ch 7 - Surfaces Ch 7...

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ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surfaces – Ch. 7 Objectives: Surfaces and solid modelling. Surface entities. Surface properties. Extending curves to surfaces and surface parametric equations. Analytic and parametric surfaces. Surface manipulations.

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ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 In design of complex objects such as car, ship, and airplane bodies, surfaces must be used precisely and accurately. In CAD/CAM, surface creation requires curves to start On computer screen, a user controlled mesh of m x n size displayed. Introduction
ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.1 Construction of improper and proper surfaces.

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ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.2 Surface of revolution with different mesh sizes.
ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Figure 7.3 Plane surface. Require three non- coincident points to define infinite plane. Surface Entities

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ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.4 Ruled (lofted) surface. Linearly interpolates between two boundary curves that define surface (rails). Represents surfaces without twists or kinks.
ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.5 Surface of revolution. Generated by revolving planar curve in space about the axis of symmetry through some angle of revolution.

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ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.6 Tabulated surface. Generated by translating a planar curve along a specified direction (directrix), generating extruded surfaces of identical cross sections.
ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.7 Bezier surface. Approximates or interpolates given input data. It extends Bezier curve to surfaces, and allows twists and kinks. Only allows global control of surface.

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ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.8 B-spline surface. Approximates or interpolates given input data. It is a general surface like the Bezier surface, but allows local control of the surface.
ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.9 Coons surface. Used to create surface using curves to form closed boundaries.

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ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.10 Fillet surface. B-spline surface that blends two surfaces together. Original surfaces may or may not be trimmed.
ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Entities Figure 7.11 Offset surface. Existing surface used to create a new one with same shape but different dimension – use of OFFSET function.

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ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Surface Representation Y X u Z Nonparametric equation of a sphere: Parametric equation of a sphere: ( 29 ( 29 2 2 , 2 0 sin cos sin cos cos , π - + + = v u v R v u R v u R v u k j i P 2 2 2 2 2 2 2 or 0 y x R z R z y x - - ± = = - + +
ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Explicit nonparametric representation of general 3D surface: Surface Representation [ ] ( 29 [ ] T T y x f y x z y x , = = P P is position vector of point P .

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Lecture 8 and 9 ENGR3030U Zeid Ch 7 - Surfaces Ch 7...

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