GL8: Computer-Aided Design (CAD)

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Aldous Randolph Snow
5 years ago
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1 GL8:1 GL8: Computer-Aided Design (CAD) History of CAD developments Representation of graphical information in a computer Modelling systems

2 History of CAD developments GL8:2 From early 1960s: Computer-aided 2D drafting Numerical control (NC) machine tools stimulated development of 2½D CAD systems 3D wireframe modellers: a natural extension of 2D drafting systems 3Dsurfacemodellers: define complex skin shapes in aero- and auto-industries 3D solid modellers: complete representation of solid properties

3 Computer-aided drafting 2D drawings, as on a drawing board geometry recorded as points and lines not faster to draw, but easier to modify and re-use GL8:3 Standard multiviews Object to be represented

4 2½D CAD systems Numerical control (NC) machine tools stimulated the development of 2½D CAD systems GL8:4 Machined object 2D model with depth info; dubbed 2½D

5 3D wireframe modellers a natural extension of 2D drafting systems geometry recorded as vertices, edges and limiting elements GL8:5 Wireframe model Object to be represented

6 Wireframe model GL8:6 Interpretation of wireframe model assisted by hidden line removal or suppression HL removed HL in grey

7 Hidden line suppression helps remove abiguity GL8:7 The isometric projection could represent: this or this

8 A wireframe model cannot represent a solid uniquely GL8:8 This wireframe model could equally represent this solid or this one

9 The software must check for validity of solid Each vertex has a unique location Each vertex associated with 3 edges Each edge has only 2 vertices Each face must have 3 edges which form a closed loop only two! Yes! -not yet a solid only two edges! A valid face, - still not a solid but not part 3 edges at vertex of a solid No! GL8:9

10 GL8:10 Computer representation and manipulation of geometry Things that are very easy to do with pencil, paper and an eraser can be quite difficult to organise in a computer! Simple example. We wish to be able to: add to a list of points on a plane display these points click on a point to delete it

11 Points on a plane Display GL8:11 List in memory x y x y Adding to the list is straightforward - until space allocated to list is full!

12 Picking points for deletion GL8: s 1 + x y Find distance from pick point (x p, y p ) to each data point (x i, y i ): s i 2 2 = ( xi x p ) + ( yi y p ) for i = 1 to end_of_list Find minimum distance

13 Some problems GL8:13 Find min { s = ( x x ) 2 + ( y y ) 2 } i i Square-root function is slow to compute for a long list compute just squared distance instead Economise further. For each list entry calculate both x i - x p and y i - y p then, square the larger of these if this is larger than the smallest s 2 so far, move on For a long list, this is still expensive p i p

14 Use a map reference x y A1 A2 A3 A4 B1 B2 B3 B C1 C2 2 C3 C4 GL8: A B C D Store pointers to x-y data for grid cells Identify grid cell of click Compute shortest distance for points in that cell only D1 D2 D3 D4 4 5

15 A tree structure uses memory more efficiently x y Upr 5 L R Lwr L R GL8: To store data, divide area: if sub-area contains one point, record pointer to x-y data else divide again Search thru tree for point in same cell as click

16 GL8:16 Data structures The previous simple example of management of data for a collection of points illustrates the importance of data structures Speed, accuracy and data capacity are only obtained with some effort Sophisticated data structures and search strategies are required

17 GL8:17 Representation of straight lines Familiar explicit equation to straight line: y = mx + c y c tan -1 m Problems: for vertical lines, m using alternative x = k is inconvenient x

18 GL8:18 Representation of straight lines Implicit equation for straight line: a 1 x + b 1 y + c 1 = 0 handles all slopes Normalise by dividing by (a 12 + b 12 ): ax + by + c = 0 Thena 2 + b 2 = 1 and c = perpendicular distance from line to origin

19 Normalised implicit equation of straight line Divides plane into two regions GL8:19 y ax + by + c > 0 Useful to find on which side of line is a given point (x p, y p ) c ax + by + c = 0 ax + by + c < 0 p x Calculate p = ax p + by p + c This is perp. distance from point to line

20 Parametric equation for a line GL8:20 z P 0 (x 0, y 0, z 0 ) y u P (x, y, z) x = x 0 + l u y = y 0 + m u z = z 0 + n u u is a parameter (the distance along the line from P 0 ) O x Global coordinate system

21 GL8:21 Follow up Read Bertoline: Chapter 7 Do problems from Bertoline: Prob 7.1

COMPUTER AIDED ENGINEERING DESIGN (BFF2612)

COMPUTER AIDED ENGINEERING DESIGN (BFF2612) BASIC MATHEMATICAL CONCEPTS IN CAED by Dr. Mohd Nizar Mhd Razali Faculty of Manufacturing Engineering mnizar@ump.edu.my COORDINATE SYSTEM y+ y+ z+ z+ x+ RIGHT