SOME 024: Computer Aided Design. E. Rozos
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1 SOME 024: Computer Aided Design E. Rozos
2 Introduction to CAD theory part 2
3 Lesson structure Why Solid modelling Solid modelling methods Representation based Manufacturing based Solid modelling storage database
4 Solid modelling Wire frame modelling + Quick and accurate calculation of the objects position (applications including movements of very complicated objects) Lack of surface, volume, validity and ambiguity Surface modelling + Good description of object surface properties and overall appearance (applications related with fluid dynamics) The objects are not solids Solid modelling + Representation of both surface and interior properties of a solid (kinematics, stress analysis) Skilful and imaginative object drawing procedure
5 Representation based techniques Parameterised primitive instancing An object is specified by reference to a library of parameterized primitives. Unit sphere Uniform scaling Differential scaling Unit cylinder (R 1, R 2 ) (R, H)
6 Representation based techniques Parameterised primitive instancing a b D Parameter vector P=(l, w, h 1, h 2 ) Parameter vector P=(Ht, Tp, D, L) a) (1,1.8, 3, 20) b) (2, 0.9, 9, 50) D
7 Representation based techniques Spatial occupancy enumeration-voxel The whole space is subdivided into regular cells (3D raster), and the object is specified by the set of cells it occupies. Models described this way are used in Finite Difference Analysis. This is usually done after a model is made, as part of automated pre-processing for analysis software.
8 Representation based techniques Spatial occupancy enumeration-octree The whole space is represented by layers of nodes, each layer is twice denser (2 2 2=8) than the parent layer. Each node is the centre of a cube containing 8 sub-cubes. This tree data structure facilitates the local refinement of a 3D grid. Quatree representation in 2D Full Empty Partial full
9 Representation based techniques Spatial occupancy enumeration-octree Universe Object
10 Representation based techniques Spatial occupancy enumeration-octree
11 Representation based techniques Cell decomposition The object is subdivided into small volumes. Models described this way are used in Finite Elements Analysis. This is usually done after a model is made, as part of automated pre-processing for analysis software.
12 Representation based techniques Cell decomposition Tiny subparts
13 Manufacturing based techniques Sweeping An area feature is "swept out" by moving a primitive along a path to form a solid feature. These volumes either add to the object ("extrusion") or remove material ("cutter path"). Analogous to various manufacturing techniques such as extrusion, milling, lathe and others. Generator surface Swept solid Google SketchUp almost completely relies on extrusion to create solids. Axis of revolution Manufacturing: Lathe Manufacturing: Extrusion
14 Manufacturing based techniques-csg Constructive solid geometry (CSG) Complex surfaces or objects are create by using Boolean operators to combine primitive objects. Boolean operators Intersection ( ) Union (U) Difference (-) Primitive objects Intersection ( ) Union (U) Difference (-)
15 Manufacturing based techniques-csg Primitive objects Intersection ( ) Manufacturing: Cut Union (U) Manufacturing: Drill and weld Difference (-) Manufacturing: Drill
16 Manufacturing based techniques-csg The CSG method under normal conditions creates valid solids. To determine the faces, edges or vertices the CGS tree must be evaluated (boundary evaluation).
17 Manufacturing based techniques-brep Boundary representation (BREP) A solid is represented as a collection of connected surface elements. Analogous to various manufacturing techniques: Injection moulding, casting, forging, thermoforming, etc. Topology is described by face-edge-vertex graphs. Geometric information is stored separately. The geometric elements are linked to the appropriate topologic elements. Topological element Face Edge Vertex Geometric element Surface Curve Point
18 Manufacturing based techniques-brep Boundary representation (BREP)
19 Manufacturing based techniques Euler-Poincare formula The geometric data includes: 1. Coordinates for the vertices 2. Curve geometry for the edges 3. Surface geometry for the faces Euler-Poincare formula necessary but not sufficient condition for solid validity: V E + F H = 2(S P) where F the number of faces, E the number of edges, V the number of vertices, H the number of hole loops in the object, S multiplicity of the object (number of disjoint pieces), P passageways.
20 Manufacturing based techniques Euler-Poincare formula Euler-Poincare formula ensures that an object is a valid polyhedron. F E + V H = 2 (S P) F E V H S P Cube Triangular passage Rectangular depression Triangular subface Total
21 Manufacturing based techniques Euler operations Euler-Poincare formula defines the permissible steps in constructing a solid Remains to be defined Defined in each step V E F H 2S 2P Make a body, a face and a vertex Make an edge and a vertex Make an edge and a vertex Make an edge and a vertex Make a face and an edge Make a face and an edge Make a face and an edge
22 Manufacturing based techniques Adjustments to an existing shape. Swinging Chamfering Tweaking Blending
23 Solid modeller storage database Major forms of storage: 1. CSG stores the part as a tree, where the leaves are primitives and the Interior nodes are Boolean operators i.e. CSG stores the instructions to make a part. 2. BREP stores the part as an explicit description of the solid bounds i.e. BREP stores the actual part. CSG BREP
24 Solid modeller storage database CSG The tree of CSG: + smaller than BREP the tree evaluation is more computational demanding can store only models created with CSG method Final object and objects used in Boolean operations
25 Solid modeller storage database BREP The tree of BREP is: + larger than the CGS. no need for any extra computation to query the object.
26 Solid modeller storage database BREP The Winged-Edge Data Structure Object is described with 3 tables. 1. the edges table holds the topology 2. the vertex table holds the geometric information of points 3. the face table holds the geometric information of surfaces The edges table defines for each edge: its vertices (start-end) its left and right faces the predecessor and successor of this edge when traversing its left face the predecessor and successor of this edge when traversing its right face The vertex table defines: 1. vertices geometry 2. one edge connected to that vertex The face table defines: 1. surfaces geometry 2. one edge connected to that vertex
27 Solid modeller storage database BREP The Winged-Edge Data Structure Edges table Vertex table Face table Edge Name a b c d Vertices Start End A D A B B D B C Faces Left Right Left Traverse Pred Succ e f c a a b e c Right Traverse Pred Succ b c f d d e b f Vertex Name A B C D Incident Edge a b d e Face Name Incident Edge a c a b e f
28 Feature recognition The figures 2.33 and 2.34 of the Computer-Integrated Design and Manufacturing should go here
29 Feature recognition
30 Feature recognition Not practical in CSG because of Non unique feature construction Need of complete tree examination to ensure no overlap BREP is the structure of choice. Example pseudo code that searches the stored data to find a hole. hole(facelist) IF entrance_face(face1) AND valid_hole_face(face2) AND adjacent(face1, Face2) AND valid_hole_face(face2) AND more_hole(face2, Facelist)
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