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48-175 Descriptive Geometry Planes in Descriptive Geometry A - - PowerPoint PPT Presentation
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
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generating a plane
3 Line rotated about a point form a sector of a plane circle Line moving parallel to itself will generate a plane
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specifying a plane 1
4
By two intersecting lines
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specifying a plane 2
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By three non-collinear points
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specifying a plane 3
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By a line and a point off the line
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specifying a plane 4
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By two parallel lines
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depicting planes
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Planes are always depicted to have limited size A plane is completely and uniquely defined by three non-collinear points
- n the plane;
That is, we can delineate a bounded portion of the plane by points that form the corners of a triangle which belong to the plane
A C B C B A
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where is the point?
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P P B C A C A B A B C P LIne XY lies on plane ABC and passes through point P, which is also in the plane ABC Y X Y Y X X
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A C B P C B A
where is the point?
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P 2 1 2 1 4 3 4 3
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edge view of a plane
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Line BY appears as a point plane ABC as an edge Line CZ appears as a point plane ABC as an edge Line AX appears as a point plane ABC as an edge
A C B Z Y X
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2 1
A C B C B A
edge view of a plane
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R S S R
TL RS seen in TL in view #3
1 3
S R B C A
ABC seen in edge view (EV) in view #4 RS seen in point view (PV in view #4
3 4
R,S A C B
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edge view of a plane
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A C B C B A
Horizontal line seen in TL Horizontal line in plane ABC
X X A
Line AX in point view Edge view of plane ABC
A,X B C
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practical - view of a house showing edge view of sloping ground
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f t l m m l b a f t l m m l
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how do we draw a and b ?
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f t l m m l b a f t l m m l
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b a f t l m m l B C A A C B b a f t l m m l A,B C B C A A C B
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b a f t l m m l
ground in edge view
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#2 is an elevation view
2 1
B2 C2 C1 B1 A1
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true slope of a plane – aka dip of the plane
HL TLHL X2 True slope angle Horizontal projection plane seen in edge view
1 3
#3 is an elevation view Plane ABC seen in edge view A,X3 C3 B3 X2 Must be seen together in the same elevation in order for true slope to appear
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HL TLHL 3 1 2 1
A,X3 C3 B3 B2 A2 C2 C1 B1 A1
HL TLHL
True shape of plane ABC
3 4 3 1 2 1
X4 A4 B4 C4 A,X3 C3 B3 B2 A2 C2 C1 B1 A1
true shape of a plane
18 2 1
B2 A2 C2 C1 B1 A1
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TL Frontal Line 3 2
True shape of plane ABC
2 1
C4 A4 B4 X1 B2 A2 C2 C1 B1 A1
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2 1
X1 B2 A2 C2 C1 B1 A1
TL Frontal Line 3 2
B,X3 A3
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true size of a roof shape
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true shape of ABC slope = 41° f t C A B C B A A C B B C A f t A C B B C A
inscribing a circle in a triangle
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constructing ellipse by using transfer distances from views 2 & 1 incircle seen in true shape
1 2 t 1 f t
B C A B A A C B B C A
incircle - last step (variation 1)
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incircle seen in true shape
1 2 t 1 f t
B C A B A A C B B C A
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incircle - last step (variation 2)
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using construction for an ellipse within an oblique rectangle in-circle seen in true shape 1 2 t 1 f t
B C A B A A C B B C A
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A problem
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Suppose a plane is given by diagonal lines, say AB and CD. Suppose three
- f the points, say A, B and C are given by their quad paper coordinates, for
example, A (1, 2½, 5½), B (3, 2, 5), and C (2, 1¼, 3¾). 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
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the problem and the steps
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- to determine the slope and true shape of the
plane ABCD;
- to find the true length and bearing of CD;
- to complete the top and front views of the plane.
8 7 6 5 4 3 2 1 2 4 6
C C A A B B
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completing the views of a plane
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8 7 6 5 4 3 2 1 2 4 6 8
TL 1 1 2 2
North slope = 33° 54' bearing of CD = N22° E true length of CD = 8'-6" constraints CD = AB CD ⊥ AB true shape of plane
edge view
- f plane
D D D C B A C C A A B B
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true shape of a truncated face
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5 6 7 2 10 3 9 8 4 11 12 1 1,4 7,10 11 12 12,11 6,5 9 8 8.9 2,3 7 10 6 3 5 2 4 1
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distance between parallel lines
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D A B C C B A D
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distance between parallel lines
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HL dA
parallel lines seen in edge view, ie., as collinear lines
3 1 2 1
D B A C X B A C D X C A
HL dD dA dC dC dA
parallel lines seen in edge view, ie., as collinear lines
4 3 3 1 2 1
A C D B D B A C X B A C D X C A
HL dD
distance between lines
dA dC dC dA
parallel lines seen in edge view, ie., as collinear lines
5 4 4 3 3 1 2 1
C,D A,B A C D B D B A C X B A C D X C A
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f t f t
Two intersecting lines define a plane
HL
1 t
Edge view of the plane
f t
Two intersecting lines define a plane
what is the angle of intersection ?
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what is the angle of intersection ?
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TL TL HL
2 1 1 t
True angle of intersection Edge view of the plane
f t
Two intersecting lines define a plane
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