buda University John von Neumann Faculty of Informatics
Óbuda University John von Neumann Faculty of Informatics Institute of Applied Mathematics Master in Engineering Informatics and Applied Mathematics Course System Level Modeling for Cyber-Physical Engineering Structures in the Cloud Lecture and laboratory No. 10 Surface Definition Dr. László Horváth http: //users. nik. uni-obuda. hu/lhorvath/
Contents Lecture Curves as contexts of surfaces Surface generation by interpolation of curves Theory and practice of swept surface Blend surface with continuity definition Tabulating curve along a vector Joining surfaces Cloud of digitized points Activating and filtering a cloud Generating mesh on cloud Generating curve using scan Function-driven organic shapes Laboratory SLM laboratory task 10. 1 Definition of complex surface László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Curves as contexts of surfaces Reference planes are defined in the context of main coordinate planes. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Surface generation by interpolation of courves Sweeping one or more section curves along an automatically computed or user-defined spine. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Theory and practice of swept surface Basic parameters Spine Generator joint Path Spine Profiles Boundary curves Rotation and scale along path Sweeping a generator curve through planes normal to a spine curve. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Theory and practice of swept surface László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Blend surface with continuity definition Surface between two curves. Constraints: continuity, etc. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Tabulating curve along a vector Moving a contour along a vector. Swept area is the surface. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Tabulated surface László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Joining surfaces Individual surfaces are joined for joint usage László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Cloud of digitalized points in the model space László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Activating and filtering a cloud László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Activating and filtering a cloud Process: The sphere passes over the cloud, starting on the first point. All the points that are inside the sphere are then hidden. These points are deleted when physical removal is active. . In the course of its way, the sphere goes to the next remaining point and removes the points that it contains. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Activating and filtering a cloud Important! Protecting characteristic lines from filtering and removal. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Generating mesh on cloud A mesh consists of a set of triangles (polygonal faces) providing the neighborhood relation of all points of a cloud. Value of neighborhood is specified. However, when suitable points are not found the continuity of mesh can not be provided. Local irregularities of mesh Triangle that has the same vertex twice. Triangles that share the same (three) vertices. Non-manifold edge: edge is shared by more than two triangles. Non-manifold vertex: vertex is shared by two or more connected shells. Structural irregularities of mesh All the triangles are not oriented in the same direction. Isolated triangles belonging to small connected areas of the mesh. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Generating mesh on cloud László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Generating curve using scan Scan is a chain of selected points connected by edges on a cloud. Methods of scan creation Project curve on cloud Cut a cloud by plane Select points on cloud Create the free edges of a mesh Discretizing curves Scan is applied at generation of curve. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Generating curve using scan Projecting curve onto a cloud to achieve scan for the generation of curve. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Generating curve using scan ”Cutting” cloud by a plane or a set of planes to gain scan(s) for the generation of curve(s). László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Generating curve using scan Scans for free edges on a cloud. Mesh is required for this operation László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Function-driven organic shapes Physical system that includes both rigid elements and flexible structures. Flexible shape is generated by geometric law driving. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Function-driven organic shapes Organic shapes. Organic shape changes during its normal use. NURBS deformation methods are used to enable organic shape modeling. Not a well-proven solution. Organic shape behaves as a cloth. Facets were not proven. Mesh for a smooth mathematical surface: subdivision (Sub. D) surface. T-Spline behaves as Sub. D surface, but it is compatible with NURBS. Modeled in Rhino, using T-Splines. It would have been nearly impossible to model using NURBS surfaces. Photo: Peter Donders László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
Function-driven organic shapes Model of function driven organic shapes Optimized conceptual parts from a functional specification Function-driven conceptual and detailed organic shapes. Capture all functional specifications. Sets of loading and boundary conditions. Alternatives to explore different approaches. Varying inputs to generate multiple variations. Alternatives are compared analyzed. Model based organized collaboration between design, simulation and manufacturing engineers. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
SLM laboratory task 10. 1 Definition of complex surface Definition swept surface using two curves. Definition surface interpolating three curves. Definition surface connecting the above two surfaces. Definition join between the above three surfaces. Definition solid between the join and its offset surface. László Horváth ÓU-IAM http: //users. nik. uni-obuda. hu/lhorvath/
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