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1、,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Click to edit Master title style,Click to edit Master text styl

2、es,Second level,Third level,Fourth level,Fifth level,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Click to

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5、r title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Total Review of Computer-aided Design and Manufacturing,Total Review of Computer-aided,Score Assessment,Attendance(10%),Roll call 5 times(,2 marks each time,),course erercises,(15%),Course exercises 3

6、times(,5marks each time,),Term paper,(25%),Examination,(50%),2-hour open book paper,(CAD 90%plus CAM 10%),Calculation problems and nouns explain,Score AssessmentAttendance(10,Examination Material,Lecture notes,Tutorials and exercises,Teaching Material,(,MECHANICAL ENGINEERING CAD/CAM),References boo

7、ks,Surface modelling for CAD/CAM,Chapter 1-5,7,Geometric modelling,chapter 9-10,.,The CNC Workshop(ver 2),chapter 1,Examination Material Lecture n,Chapter 1:Instruction,What is CAD/CAM/CAE/CAPP?,How is the relationship among them?,),What is the HISTORY of CAD/CAM?,Hardware and software of CAD/CAM sy

8、stem?,What is Geometric Modelling and its typical applications?,Chapter 1:InstructionWhat is,Chapter 2:Curves,Four curve models,Standard polynomial,curve,Ferguson,curve,Bezier,curve,B,-spline,curve,Curve fitting,Chapter 2:CurvesFour curve mo,Polynomial Curve Models,Curve Segment Definition,:,A cubic

9、 polynomial curve model:,r,(,u,)=,a,+,b,u,+,c,u,2,+,d,u,3,used in representing a curve segment is specified by its,end conditions,e.g.,(a),4 points,(,P,0,P,1,P,2,and,P,3,),or,(b)two end points,P,0,and,P,1,;,two end tangents,t,0,and,t,1,.,P,0,P,1,P,2,P,3,In general,a degree-,n,polynomial curve can be

10、 used to fit(,n,+1)data points.,Polynomial Curve ModelsCurve S,Ferguson Curve Model,Constructing a curve segment:,Joining two,end points,P,0,and,P,1,;,Having specified,end tangents,t,0,and,t,1,i.e.,P,0,=,r,(0);,P,1,=,r,(1);,t,0,=,r,(0);,t,1,=,r,(1),P,1,P,0,t,1,t,0,r,(,u,),r,(,u,)=,U A,=,U MV,with,0,

11、u,1,Ferguson Curve Model Construct,Bezier Curve Model,with,0,u,1,On evaluating the Bezier equation and its derivative at,u,=0,1,r,(0)=,V,0,r,(1)=,V,n,r,(0)=,n,(,V,1,V,0,),r,(1)=,n,(,V,n,V,n,-1,),Be,z,ier,found a family of functions called,Bernstein Polynomials,that satisfy these conditions,:,Bezier

12、Curve Model with 0,Bezier Curve Model,Cubic(,n=,3)Bezier curve model,V,0,V,1,V,2,V,3,V,3,V,2,V,1,V,0,V,2,V,1,V,0,V,3,r,(,u,)=(1,u,),3,V,0,+3,u,(1,u,),2,V,1,+3,u,2,(1,u,),V,2,+,u,3,V,3,r,(,u,)=,=,U M R,r,(0)=,V,0,r,(0)=3,(,V,1,V,0,),r,(1)=,V,3,r,(1)=3,(,V,3,V,2,),The shape of the curve,resembles,that

13、 of the control polygon.,Bezier Curve ModelCubic(n=3,B,-spline Model,with,0,u,1,N,i,n,(,u,),=,The primary function,B,-spline Model defined by,n,+1 points,V,i,is given by the,Where,B-spline Model with 0 u,B,-spline Model,Quadratic,uniform,B,-spline,model with control points,V,0,V,1,and,V,2,r,(,t,)=,t

14、,2,t,1,=,U,3,M,3,P,3,0,t,1,Cubic,uniform,B,-spline,model with control points,V,0,V,1,V,2,and,V,3,r,(,t,)=,1/6,u,3,u,2,u,1,=,U,4,M,4,P,4,0,t,1,B-spline ModelQuadratic unifor,Parametric Continuity Condition,Two curve segments,r,a,(,u,)and,r,b,(,u,),r,a,(1)=,P,1,=,r,b,(0),(,C,0,-continuous),r,a,(1)=,t,

15、1,=,r,b,(0),(,C,1,-continuous),r,a,(1)=,r,b,(0),(,C,2,-continuous),Collectively called a,parametric,C,2,-condition.,The composite curve to pass through,P,0,P,1,P,2,and the tangents,t,0,and,t,2,are assumed to be,given.Thus,the,problem,here is to determine the,unknown,t,1,so that the two curve segment

16、s are,C,2,-continuous at the common join,P,1,.,P,0,P,1,P,2,t,2,t,0,t,1,=?,r,a,(,u,),r,b,(,u,),Parametric Continuity Conditio,Cubic Spline Fitting,(Ferguson Model),Employing Ferguson curve model,r,a,(,u,)=,U,C,S,a,r,b,(,u,)=,U,C,S,b,with,0,u,1,U,=,u,3,u,2,u,1,C,=,S,a,=,P,0,P,1,t,0,t,1,T,S,b,=,P,1,P,2,t,1,t,2,T,Applying C,2,continuity,:,r,a,(1),=,6,P,0,6,P,1,+2,t,0,+,4,t,1,r,b,(0),=,-,6,P,1,+6,P,2,-,4,t,1,-2,t,2,C,0,-continuity and C,1,-continuity,already applied,Cubic Spline Fitting(Ferguson,Cubi