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TA 101: Technical Arts 2015-16 II Dr. Prishati Raychowdhury
Department of Civil Engineering IIT Kanpur Office: FB 330; Phone: 6692
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Lecture 16 Space Geometry
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Recall: Glass box method for orthographic
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A Point in Space d h P h d PT Horizontal Plane H.P. V.P.
Vertical Plane PF
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A Line in Space Consider Line AB aH HP bH C A FVP aF aP B TL bP bF PVP
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A Line in Space Consider Line AC aH TL cH HP C A cP FVP aF aP B cF PVP
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A Line in Space Consider Line BC cH bH HP C A cP FVP TL cF B bP bF PVP
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Normal View or True Shape
The term ‘Normal’ means ‘perpendicular’ or at ‘right angles’ A Normal View is one in which the ‘direction of sight’ is perpendicular to a line/plane The Normal View of a line shows the True Length of the line The Normal View of a plane shows the True Shape of the plane A Normal View may or may not be in one of the principal orthographic views/projections
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Point View A Line lying on two principal planes of projection will appear in NORMAL VIEW (i.e., in TRUE LENGTH) in two views, and as a POINT VIEW (PV) in the third view N PV N PV N N N N PV Horizontal-Frontal Horizontal - Profile Frontal- Profile
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Point View A ‘Point View’ of a line is that view, which shows the line as a ‘single point’ The ‘direction of sight’ is parallel to the line in the Point View (PV)
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Edge View An ‘Edge View’ of a plane is that view, which shows the plane as a ‘line’. The ‘direction of sight’ should be parallel to the plane in an Edge View (EV) EV H.P. P.P. F.P. True Shape EV
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Space Geometry Terminology
In order to describe an object completely, one needs to be able to perform one or more of the following tasks Find the ‘Point View’ (PV) of a line Find the ‘Normal View’ of a line Find the ‘True Length (TL)’ of a line Find the ‘Edge View (EV)’ of a plane Find the ‘Normal View’ of a plane Find the True Size and Shape of a surface Find angle between lines and planes Find spacing between ‘elements’ of an object
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Important Observations: Lines
TL? TL? TL TL PV H.P. F.P. P.P. TL? TL? TL? TL TL PV TL TL PV
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Finding True Length of a Line
Direct Formula = 0 X Y (x2, y2, z2) X Z (x1, y1, z1) TL
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Finding True Length of a Line
Direct Formula = 0 X Y TL X Z
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Finding True Length of a Line
Method of Rotation Y X Z TL X
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Finding True Length of a Line
Method of Rotation Y TL X Z X
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Finding True Length of a Line
Method of Auxiliary Plane Y X TL Z X
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Auxiliary Plane: Concept
d2 H d1 AH BH TL AA A BA H d1 F AF d2 AA B TRUE LENGTH(TL) F AA BA BF P A BA LINE OF SIGHT Notice the distances from the hinge lines
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Auxiliary Plane: Concept
PV bH H A1 bA2, aA2 d aH Line of Sight bA1 A2 A1 TL H aA1 F d aF Notice the direction of Projectors bF Notice the distance Measurements along Projectors
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Auxiliary Plane: Concept
d1 d1 PV bH H A1 bA2, aA2 d aH Line of Sight bA1 A2 A1 TL H d aA1 F aF Notice the direction of Projectors bF Notice the distance Measurements along Projectors
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Thank You
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