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Introduction to virtual engineering

Óbuda University John von Neumann Faculty of Informatics Institute of Intelligent Engineering Systems. Introduction to virtual engineering. Lecture 2. Description of shapes in model space. László Horváth university professor. http://nik. uni-obuda .hu/lhorvath/. C ontents.

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Introduction to virtual engineering

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  1. Óbuda University John von Neumann Faculty of Informatics Institute of Intelligent Engineering Systems Introduction to virtual engineering Lecture 2. Description of shapes in model space László Horváth university professor http://nik.uni-obuda.hu/lhorvath/

  2. Contents Definition of shape by its boundary Basic groups of shapes to be described Problem of boundary representation of shape Topological and geometrical entities Shape independence of topology Topological consistency Geometry: creating a curve Geometry: creating a surface LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  3. Definition of shape by its boundary LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  4. Basic groups of shapes to be described Generated according to predefined rule Free form Analitical Linear Curved Complex surface F2 G1 F1 LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  5. Problem of boundary representation of shape G1 G12 G2 L2 L1 F2 F2 F1 F1 F1 Connections of surfaces at intersection curves are to be described. Method: Topology (Euler) LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  6. Topological and geometrical entities (1) P = point G12 C = curve Shell Consistent (complete) L = loop, ring S = Surface Shell + material = body V V = vertex F E E = edge, coedge F = face LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  7. Topological and geometrical entities (2) Topology Body = four lumps Combination of solids Prism – box = four prismatic segment LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  8. Shape independence of topology Same topology for three different shapes Same structure LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  9. Topological consistency (1) Topological consistency Complete topology. Check by using of topological rules. Three or more edges must run into a vertex. Face must be enclosed by a closed chain of edges. Edge is included always in two loops for adjacent faces. Euler rule Leonhard Euler (1707-1783) swiss mathematican. Euler number for boundary of body: V - E + F Euler number is a constant V - E + F = C. For simple bodies ( no through holes or separated bodies (lumps) V - E + F = 2 LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  10. Topological consistency (2) V-E+F=8-12+6=2 V-E+F=10-15+7=2 V-E+F=2-3+3=2 LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  11. Geometry: creating a curve Analitical P According to specified rule 2 P 1 Through specified points Interpolation P 0 P 3 Controlled by specified points Approximation Task Method LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  12. Geometry: creating a surface (1) Generator Contour Tabulated surface Rotational surface Axis Meridian curve Direction of rotation o Extension angle= 360 LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

  13. Geometry: creating a surface (2) Control of shape at the creation of a swept surface Joint Profil curves Path curve Generator curve Boundary curves Spine LászlóHorváth ÓU-JNFI-IIES http://nik.uni-obuda.hu/lhorvath/

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