Introduction to virtual engineering László Horv á th Budapest Tech John von Neumann Faculty of Informatics Institute of Intelligent Engineering Systems Lecture 4. Construction of shape in the model space

Contextual modeling of structures of shapes Constructive solid geometry Modification of an initial shape by form features About building of topology Main groups of form features CONTENTS

Contextual modeling of structures of shapes Solids Combination Modification Form feature Volumetric Conditioning Surface Relationships of solids Placing Movements Contour Volume Analysis of solids Simulations Local characteristics Geometry Collisions Movements Associative characteristics Visualization Visualization of bodies Animation Position, scale Shape Hair, particle Scene Projection Rendering Surface characte- ristics Texture Bended sheet

Constructive solid geometry IntersectionDifference Primitives Union A, B ABABA - BB - A A - B

Modification of initial shape by form features Base feature Form feature Creation of body by tabulation Volume subtracting shape modification Modified shape

Extended topology of boundary

Building topology using Euler operators MEV – make edge and vertex!MEF– make edge and face!KEMR – kill edge and make ring (closed chain of edges)!

Start building of topology Edge removal and vertex merging operations result a model that consists of single edge and single polygon.

Main groups of form features 1. Defined by type, volume adding and volume subtracting Cuboids, cylinder, sphere, cone, and torus. 2. Contour based, volume adding and volume subtractingContour based Tabulated (extruded), revolved, pyramid, tube, swept, and lofted. 3. Transformed, added and volume subtracted volume.Transformed Constructive solid geometry in shape modification 4. Modification of shape by surfaceModification of shape by surface Building separately created surface. 5. Form features for conditioning existing form features (dress- up features)Form features for conditioning existing form features Fillet, chamfer, shell, and draft.

Contour based form features Reference planes

Connecting surface and solid

Intersection of solid by surface (sewing)

Conditioning (dress-up) form features Fillet Chamfer Draft Shell

Fillet form features spine curve (law) Constant radius Radius changing according to a law Linearly changing radius Filleting with automatic removal of topological entitiesCorner fillet Defined by boundary curve

Draft form features p E n F d p F d E n p F d pl E n2 E n1 p F d pl E n P n P P P n P P, Extrapolated fillet surface Outside neutral edge E n - neutral edge

Opening solid at surfaces to create shell

Irregular model construction: bended and cut sheets Fitted edgesBend It is not a bend! Form feature Bend panel