Geometry and Curve Definition

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1 Geometry and Curve Definition 1 NAPA 2014 What should I learn? How the Geometric hierarchy works How the coordinate system is defined Make curve definitions How to define the location surface How to define points and angle conditions Check the result by drawing objects 2 NAPA 2014

2 NAPA Geometric Hierarchy Points, angles o a Curves Surfaces Rooms Arrangements 3 NAPA 2014 Coordinate system Default: righthanded Can be changed in REF 4 NAPA 2014

3 Why curves? Curves can be seen as the starting point for geometric definitions in NAPA The curves form the curve grid that is the basis for the hull surface The hull surface consists of patches that are formed by the curve grid 5 NAPA 2014 Curve Definition Curves are defined in DEF task which can be entered directly from TASK level TASK GM SM DEF DR 6 NAPA 2014

4 Curve Definition The curve shape is defined in a main coordinate plane (xy, yz, xz) and projected onto a given location surface 7 NAPA 2014 Curve Example CUR EAMPLE Example curve (0 0) (4 1) (8 4) OK Name and description Location Shape 8 NAPA 2014

5 Location Surface A location surface can be: A principal plane 15 A general plane THR (0 0 6) (0 8 12) ( ) A curved surface (8 0) (9 4.8) (11 8) 9 NAPA 2014 Location Surface Example CUR C1 Plane location surface -2 (2 4) (5 5) (6.6 4) (8 5) PRO C1,C2 - PRO C1 C2 CUR C2 Curved location surface (3 2) (5 5) (9 8) (2 4) (5 5) (6.6 4) (8 5) PRO C1 C2 10 NAPA 2014

6 Definition Points The curve definition points can be given 1. Directly with coordinates (,),(,)or(,) 2. By referring to other curves 3. By using point objects CUR1 CUR2 Point object P1 CUR3 CUR EAMPLE Comment text 0 (1 2) CUR1 (4 6) CUR2 CUR3 P1 11 NAPA 2014 Sorting of Definition Points Default: The points are sorted according to The ascending values of the first symbol in the shape definition e.g. or Secondly by the given order Exception: Option * cancels the default sorting - points are set in the given order NOTE! Coordinates are always input in the order (x y) (y z) (x z) or (x y z) 12 NAPA 2014

7 Example CUR EAMPLE1 (2 2) (3 4) (4.5 3) (3.5 1) (2 2) (3 4) (3.5 1) (4.5 3) sorted by NAPA CUR EAMPLE2 * (2 2) (3 4) (4.5 3) (3.5 1) CUR EAMPLE3 (2 2) (3 4) (4.5 3) (3.5 1) (3.5 1) (2 2) (4.5 3) (3 4) sorted by NAPA 13 NAPA 2014 Curve Angles Angle conditions can be used to give the curve the correct shape An angle condition is marked by a slash / between the definition point and the angle Mathematical direction: + counter-clockwise - clockwise 0 along x-axis or y-axis NAPA 2014

8 Curve Angles Syntax A /60 0/ B /60 C From point A with angle 60 degrees To point B with angle of 0 degrees From point B with angle 60 degrees C B Without the 60 degree out angle A 15 NAPA 2014 Free Angle A free angle at a point means that the curve behaves as at endpoint The symbol of the free angle is the minus sign - C C A B C D A B -/ C D A B C 16 NAPA 2014

9 Free Angle The most simple way to create a knuckle is to add a free angle on both sides of a point: -/ A /- The most simple way to create a straight line between two points is to add free angles between them: A /- -/ B The syntax <> or >< before the curve coordinates specifies that ALL angles are free angles 17 NAPA 2014 Free Angle: Example C C C C A B C D A B -/ C D A B C /- D A B -/ C /- D 18 NAPA 2014

10 Curve Examples Pay attention to: Definition syntax Sorting of points Effect of angles 19 NAPA 2014 Example 1 CUR EA1 (15 55) (55 15) 20 NAPA 2014

11 Example 2 CUR EA2 (15 55) (30 25) (55 15) 21 NAPA 2014 Example 3 CUR EA3 (15 55) 0/ (30 25) (55 15) 22 NAPA 2014

12 Example 4 CUR EA5 (15 55) (30 25) /- (55 15) 23 NAPA 2014 Example 5 CUR EA6 (15 55) -/ (30 25) /- (55 15) 24 NAPA 2014

13 Example 6 CUR EA7 (15 55) -/ (20 30) (30 20) /- (55 15) 25 NAPA 2014 Example 7 CUR EA8 <> (15 55) (20 30) (30 20) (55 15) 26 NAPA 2014

14 Example 8 CUR EA10 * (10 35) /90 (35 60) /0 (60 35) /-90, (35 10) /180 90/ (10 35) 27 NAPA 2014 This is NOT a circle! Example 9 CUR EA11 (15 55) (30 20) /- (55 15) 28 NAPA 2014

15 Example 10 CUR EA12 (15 55) (30 20) /- (55 15) 29 NAPA 2014 Drawing Commands PLOT object Draws the specified object! W oom (fit) to window!e Clear the drawing area COL colour COL RND Change the colour Use random colour 30 NAPA 2014

16 Drawing Shortcut keys Useful shortcut keys (first click in the graphics area and then keyboard number key) 1 Fit to Window 2 Interactive zoom 3 Interactive projection Show x-projection (,,A and F work in the same way) PRO PRO PRO PRO A PRO F 31 NAPA 2014 Curve Definition Exercises Limiting curves of the fore body HULLF Limits of the surface Border curves of the flat areas Knuckle line 32 NAPA 2014

17 Exercise 1: Main frame ( ) Curve FRF 62 ( ) (0 0) (4.7 0) 33 NAPA 2014 Exercise 2: Stem Curve STEM 0 ( ) ( ) (81.9 5) (82.2 4) (84 2.2) FRF (80 0) 34 NAPA 2014

18 Exercise 3: Deck line (84 2.5) (75 6.3) (72 6.5) Curve DECKF 11.5 STEM FRF With rounded nose 35 NAPA 2014 Exercise 1: Answer ( ) CUR FRF 62 (0 0) -/ (4.7 0) ( ) /- (6.5, 11.5) ( ) (0 0) (4.7 0) 36 NAPA 2014

19 Exercise 2: Answer CUR STEM 0 FRF -/ (80 0) 90/ (84,2.2), (82.2 4) 90/ ( ), (81.9,5) /- ( ) ( ) ( ) (81.9 5) (82.2 4) (84 2.2) FRF (80 0) 37 NAPA 2014 Exercise 3: Answer (84 2.5) (75 6.3) CUR DECKF 11.5 FRF -/ (72 6.5) (75 6.3), (84 2.5) -90/ STEM (72 6.5) STEM FRF 38 NAPA 2014

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