48-175 Descriptive Geometry Planes in Descriptive Geometry A - PowerPoint PPT Presentation

48-175 
 Descriptive Geometry Planes in Descriptive Geometry

A spatial figure is a plane whenever for any two points on the figure, the line specified by the points also lies on the figure. A plane is the set of all points that lie on any line specified by two points one from each two intersecting lines. what is a plane? 2

Line moving parallel to itself will generate a plane Line rotated about a point form a sector of a plane circle generating a plane 3

By two intersecting lines specifying a plane 1 4

By three non-collinear points specifying a plane 2 5

By a line and a point off the line specifying a plane 3 6

By two parallel lines specifying a plane 4 7

Planes are always depicted to have B limited size A plane is completely and uniquely C defined by three non-collinear points A on the plane; That is, we can delineate a bounded C portion of the plane by points that form the corners of a triangle which belong to the plane A B depicting planes 8

B X P A Y C B Y Y P B X P C C A X LIne XY lies on plane ABC and passes through point P, which A is also in the plane ABC where is the point? 9

B 1 3 P C 4 A 2 C 4 2 P A 1 3 B where is the point? 10

Line CZ appears as a point plane ABC as an edge B Z A Y X Line BY appears as a point plane ABC as an edge Line AX appears as a point C plane ABC as an edge edge view of a plane 11

B RS seen in TL in view #3 S 3 4 R TL C 3 1 B A ABC seen in edge view (EV) in view #4 B RS seen in point view (PV in view #4 R,S S R A C A 1 2 C C A R S B edge view of a plane 12

B Horizontal line seen in TL X C A B A,X C C Edge view of plane ABC Line AX in point view A A Horizontal line in plane ABC X B edge view of a plane 13

l l m m t t f f practical - l l view of a house showing b a edge view of sloping ground 14 m m

l l m m t t f f l l b a how do we draw a and b ? 15 m m

l l l m m m C C A A t t t f f f C B B C C l l l A,B b b b a a a ground in edge view 16 m m m A A B B

C 1 Must be seen together in the same elevation in order for true slope to appear 1 3 #3 is an elevation view TLHL A 1 B 1 C 3 True slope angle 1 A,X 3 2 B 3 B 2 X 2 X 2 HL Plane ABC seen in edge view #2 is an elevation view Horizontal projection plane seen in edge view C 2 true slope of a plane – aka dip of the plane 17

3 4 C 3 C 3 3 3 1 1 C 4 C 1 C 1 C 1 A,X 3 A,X 3 X 4 TLHL TLHL B 3 B 3 A 1 A 1 A 1 B 1 B 1 B 1 B 4 A 4 True shape of plane ABC 1 1 1 2 2 2 B 2 B 2 B 2 A 2 A 2 A 2 HL HL true shape of a plane 18 C 2 C 2 C 2

C 1 C 1 X 1 X 1 Frontal Line Frontal Line B 1 B 1 A 1 A 1 1 1 2 2 B 2 B 2 A 2 A 2 TL TL True shape of plane ABC A 4 A 3 B 4 C 2 C 2 B,X 3 2 2 3 3 C 4 19

true size of a roof shape 20

B B B C C C slope = 41° C B A A A t t f f A A true shape of ABC C C A B B inscribing a circle in a triangle 21

1 1 t t B B B B C C B B C C A A A A 1 2 1 2 incircle seen incircle seen t t in true shape in true shape f f A A C C A A constructing ellipse by using transfer distances from views 2 & 1 B B incircle - last step (variation 1) 22

1 t B B C B C A A in-circle 1 seen in 2 t true shape f A C A using construction for an ellipse within an oblique rectangle B incircle - last step (variation 2) 23

Suppose a plane is given by diagonal lines, say AB and CD . Suppose three of the points, say A, B and C are given by their quad paper coordinates, for example, A (1, 2 ½ , 5 ½ ), B (3, 2, 5), and C (2, 1 ¼ , 3 ¾ ). In order to determine D we will need further constraints. Suppose the diagonals are of equal length, that is, AB = CD ; suppose further that they intersect at right angles. to determine the slope and true shape of the plane ABCD; to find the true length and bearing of CD; and to complete the top and front views of the plane A problem 24

8 7 6 • to determine the slope and true shape of the A plane ABCD; B 5 • to find the true length and bearing of CD; 4 C • to complete the top and front views of the plane. 3 A B 2 C 1 the problem and the steps 25 2 4 6

8 North A bearing of 7 true shape of plane CD = N22° E constraints CD = AB D CD ⊥ AB 6 1 TL A B D 2 1 C 5 B true length of CD = 8'-6" slope = 33° 54' 4 edge view of plane C 3 2 A D 2 B C 1 2 4 6 8 completing the views of a plane 26

4 5 3 10 9 11 12 8 6 2 7 11 10 4 1 12 5 9 6 7 3 12,11 8 7,10 1 2 8.9 6,5 1,4 2,3 true shape of a truncated face 27

B A D C C D A distance between parallel lines 28 B

1 1 1 3 3 3 parallel lines seen in edge parallel lines seen in edge parallel lines seen in edge B B B view, ie., as collinear lines view, ie., as collinear lines view, ie., as collinear lines B B B A A A d A d A d A 3 3 X X X D 4 D D 4 A A A D D D B B C C C D D C C d C C d C d D d D 1 1 1 2 2 2 d A d A d C d C C C C C C A A A X X X A HL HL A HL distance between lines 4 5 distance between parallel lines 29 A,B C,D

Edge view of the plane 1 t t t t f f f Two intersecting lines Two intersecting lines define a plane define a plane HL what is the angle of intersection ? 30

True angle of intersection TL TL 2 1 Edge view of the plane 1 t t f Two intersecting lines define a plane HL what is the angle of intersection ? 31

t t f f how do we handle these cases? 32