Introduction to virtual engineering Óbuda University John von Neumann Faculty of Informatics Institute of Intelligent Engineering Systems Lecture 2. Description.

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Presentation transcript:

Introduction to virtual engineering Óbuda University John von Neumann Faculty of Informatics Institute of Intelligent Engineering Systems Lecture 2. Description of shapes in model space László Horváth university professor

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 Contents László Horváth ÓU-JNFI-IIES uni-obuda.hu/lhorvath/

Definition of shape by its boundary László Horváth ÓU-JNFI-IIES uni-obuda.hu/lhorvath/

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

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

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

Prism – box = four prismatic segment Combination of solidsTopology Body = four lumps Topological and geometrical entities (2) László Horváth ÓU-JNFI-IIES uni-obuda.hu/lhorvath/

Same topology for three different shapes Same structure Shape independence of topology László Horváth ÓU-JNFI-IIES uni-obuda.hu/lhorvath/

Euler rule Leonhard Euler ( ) 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 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. Topological consistency (1) László Horváth ÓU-JNFI-IIES uni-obuda.hu/lhorvath/

V-E+F=8-12+6=2 V-E+F= =2 V-E+F=2-3+3=2 Topological consistency (2) László Horváth ÓU-JNFI-IIES uni-obuda.hu/lhorvath/

TaskMethod Through specified pointsInterpolation Controlled by specified pointsApproximation P 0 P 1 P 2 P 3 According to specified rule Analitical Geometry: creating a curve László Horváth ÓU-JNFI-IIES uni-obuda.hu/lhorvath/

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

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