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projection of points-engineering graphics

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Sangani Ankur

This document discusses the projection of points and lines in space. It begins by introducing the topic and presenters. It then covers the following: 1. The orientation and projection of points in different quadrants and planes. Various examples are shown with diagrams. 2. The definition and notation used for projecting straight lines, including their true length, front and top views, and inclinations. 3. The different positions of lines in relation to the horizontal and vertical planes, including perpendicular, parallel, and oblique lines. Several examples are shown diagrammatically.

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PROJECTION OF POINTS AND LINES PREPARED BY : - B.E.(IT) EN NO NAME 16BEITV120 DHRUNAIVI 16BEITV121 PRITEN 16BEITV122 ANKUR 16BEITV123 DHRUMIL 16BEIV124 16BEIV125 DARSHAN NIKUNJ Guided By : - PROF. ROMA PATEL INFORMATION TECHNOLOGY
PROJECTION OF POINTS
(d) Projections of Right & Regular Solids like; (Prisms, Pyramids, Cylinder and Cone) SOLID GEOMETRYSOLID GEOMETRY Following topics will be covered in Solid Geometry ; (a) Projections of Points in space (b) Projections of Lines (Without H.T. & V.T.) (c) Projections of Planes
(1)In quadrant I (Above H.P & In Front of V.P.) (2) In quadrant II (Above H.P & Behind V.P.) (3) In quadrant III (Below H.P & Behind V.P.) (4) In quadrant IV (Below H.P & In Front of V.P.) Orientation of Point in SpaceOrientation of Point in Space
(5) In Plane (Above H.P. & In V.P.) (6) In Plane (Below H.P. & In V.P.) (7) In Plane ( In H.P. & In front of V.P.) (8) In Plane ( In H.P. & Behind V.P.) (9) In Plane ( In H.P. & V.P.) Orientation of Point in SpaceOrientation of Point in Space
.. .. .. .. .. XX YY aa11’’ AA11 aa11 aa11’’ aa11 YYXX XX YY POSITION: 1 (I Qua.)POSITION: 1 (I Qua.) POINTPOINT Above H.P.Above H.P. In Front Of V.P.In Front Of V.P. AA11- Point- Point aa11’- F.V.’- F.V. aa11 - T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D In 2DIn 2D Point, AbovePoint, Above H.P.H.P. Point, In- FrontPoint, In- Front Of V.P.Of V.P. T.V.T.V. Below XYBelow XY F.V.F.V. Above XYAbove XY (3D)(3D) (2D)(2D)
.. .. .. .. .. POINTPOINT Above H.P.Above H.P. Behind V.P.Behind V.P. (3D)(3D) (2D)(2D) XX YY XX YY AA22 aa22 aa22’’ aa22 aa22’’ AA22- Point- Point XX aa22’- F.V.’- F.V. YY aa22 - T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, AbovePoint, Above H.P.H.P. Point, BehindPoint, Behind V.P.V.P. T.V.T.V. Above XYAbove XY F.V.F.V. Above XYAbove XY In 2DIn 2D POSITION:2 (II Qua.)POSITION:2 (II Qua.)
aa33 AA33 POINTPOINT Below H.P.Below H.P. Behind V.P.Behind V.P. aa33’’ XX YY .. ..aa33 aa33’’ XX YY XX YY (2D)(2D) (3D)(3D) AA33- Point- Point aa33’- F.V.’- F.V. aa33- T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, BelowPoint, Below H.P.H.P. Point BehindPoint Behind V.P.V.P. T.V.T.V. Above XYAbove XY F.V.F.V. Below XYBelow XY In 2DIn 2D .. .. .. POSITION: 3 (III Qua.)POSITION: 3 (III Qua.)
AA44 aa44 .. aa44’’ .. aa44’’ XX YY XX YY XX YY .. (2D)(2D) (3D)(3D) POINTPOINT Below H.P.Below H.P. In Front of V.P.In Front of V.P. AA44- Point- Point aa44’- F.V.’- F.V. aa44- T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, BelowPoint, Below H.P.H.P. Point, InPoint, In Front Of V.P.Front Of V.P. T.V.T.V. Below XYBelow XY F.V.F.V. Below XYBelow XY In 2DIn 2D .. ..aa44 POSITION: 4 (IV Qua.)POSITION: 4 (IV Qua.)
H.P. H.P. H.P. H.P. V.P. V.P. .. .. .. .. POINTPOINT Above H.P.Above H.P. In V.P.In V.P. In 3DIn 3D In 2DIn 2D Point, AbovePoint, Above H.P.H.P. Point,Point, In V.P.In V.P. T.V.T.V. On XYOn XY F.V.F.V. Above XYAbove XY YY XX aa55’’AA55 aa55 aa55’’ aa55 XX YY AA55 XX YY (3D)(3D) (2D)(2D) AA55- Point- Point aa55’- F.V.’- F.V. aa55 - T.V.- T.V. CONCLUSIONS:CONCLUSIONS: POSITION: 5POSITION: 5
..POINTPOINT Below H.P.Below H.P. In V.P.In V.P. XX YY XX YY AA66 aa66 aa66’’ aa66’’.. XX YY (2D)(2D) aa66 .. AA66 (3D)(3D) .. AA66- Point- Point aa66’- F.V.’- F.V. aa66- T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, BelowPoint, Below H.P.H.P. Point In V.P.Point In V.P. T.V.T.V. On XYOn XY F.V.F.V. Below XYBelow XY In 2DIn 2D POSITION: 6POSITION: 6
AA77 .. .. POINTPOINT In Front of V.P.In Front of V.P. In H.P.In H.P. AA77 aa77 aa77’’ XX YY YY XX (3D)(3D) (2D)(2D) YYXX AA77 PointPoint .. .. aa77’- F.V.’- F.V. aa77’’ aa77 T.V.T.V. Below XYBelow XY Point, In-Point, In- Front Of V.P.Front Of V.P. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D In 2DIn 2D Point In H.P.Point In H.P. F.V.F.V. On XYOn XY aa77 - T.V.- T.V. POSITION: 7POSITION: 7
AA88 .. .. POINTPOINT In H.P.In H.P. Behind V.P.Behind V.P. YY XX YY XX AA88 aa88 aa88’’ XX YY (3D)(3D) (2D)(2D) aa88 .. ..aa88’’ AA88- Point- Point aa88’- F.V.’- F.V. aa88 - T.V.- T.V. F.V.F.V. On XYOn XY Point, InPoint, In H.P.H.P. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, BehindPoint, Behind V.P.V.P. T.V.T.V. Above XYAbove XY In 2DIn 2D POSITION: 8POSITION: 8
POINTPOINT In VIn V.P..P. In H.PIn H.P H.P. H.P. (3D)(3D) (2D)(2D) XX YY YYXX ..AA99 AA99- Point- Point XX aa99’’ aa99’- F.V.’- F.V. ..aa99’’ aa99 aa99 AA99 CONCLUSIONS:CONCLUSIONS: In 3DIn 3D In 2DIn 2D Point, InPoint, In H.P.H.P. F.V.F.V. On XYOn XY T.V.T.V. On XYOn XY Point,Point, In V.P.In V.P. aa99 - T.V.- T.V. POSITION: 9POSITION: 9
PROJECTION OF STRAIT LINE
Definition of Straight lineDefinition of Straight line A straight line is the shortest distance between two points. - Top views of two end points of a straight line, when joined, give the top view of the straight line. - Front views of the two end points of a straight line, when joined, give the front view of the straight line. - Both the above projections are straight lines.
Orientation of Straight Line in SpaceOrientation of Straight Line in Space - A line in space may be parallel, perpendicular or inclined to either the H.P. or V.P. or both. - It may be in one or both the reference Planes. - Line ends may be in different Quadrants. - Position of Straight Line in space can be fixed by various combinations of data like distance of its end points from reference planes, inclinations of the line with the reference planes, distance between end projectors of the line etc.
Notations used for Straight LineNotations used for Straight Line True length of the lineTrue length of the line: Denoted by Capital letters. e.g. AB=100 mm, means that true length of the line is 100 mm. Front View LengthFront View Length: Denoted by small letters. e.g. a’b’=70 mm, means that Front View Length is 70 mm. Top View LengthTop View Length: Denoted by small letters. e.g. ab=80 mm, means that Top View Length is 80 mm. Inclination of True Length of Line with H.P.Inclination of True Length of Line with H.P.: It is denoted by θ. e.g. Inclination of the line with H.P. (or Ground) is given as 30º means that θ = 30º.
Inclination of Front View Length with XYInclination of Front View Length with XY : It is denoted by α. e.g. Inclination of the Front View of the line with XY is given as 50º means that α = 50º. Inclination of Top View Length with XYInclination of Top View Length with XY : It is denoted by β. e.g. Inclination of the Top View of the line with XY is given as 30º means that β = 30º. End Projector DistanceEnd Projector Distance: It is the distance between two projectors passing through end points of F.V. & T.V. measured parallel to XY line. Inclination of True Length of Line with V.P.Inclination of True Length of Line with V.P.: It is denoted by Φ. e.g. Inclination of the line with V.P. is given as 40º means that Φ = 40º.
Line in Different Positions with respectLine in Different Positions with respect to H.P. & V.P.to H.P. & V.P. CLASS A: Line perpendicular to (or in) oneCLASS A: Line perpendicular to (or in) one reference plane & hence parallel toreference plane & hence parallel to both the other planesboth the other planes (1)(1) Line perpendicular to P.P. & (hence) parallelLine perpendicular to P.P. & (hence) parallel to both H.P. & V.P.to both H.P. & V.P. (2) Line perpendicular to V.P. & (hence) parallel(2) Line perpendicular to V.P. & (hence) parallel to both H.P. & P.P.to both H.P. & P.P. (3) Line perpendicular to H.P. & (hence) parallel(3) Line perpendicular to H.P. & (hence) parallel to both V.P. & P.P.to both V.P. & P.P.
Line in Different Positions with respectLine in Different Positions with respect to H.P. & V.P.to H.P. & V.P. CLASS B: Line parallel to (or in) oneCLASS B: Line parallel to (or in) one reference plane & inclined to otherreference plane & inclined to other twotwo planesplanes (1)(1) Line parallel to ( or in) V.P. & inclined to H.P.Line parallel to ( or in) V.P. & inclined to H.P. byby .. (2) Line parallel to ( or in) H.P. & inclined to V.P.(2) Line parallel to ( or in) H.P. & inclined to V.P. byby .. (3) Line parallel to ( or in) P.P. & inclined to H.P.(3) Line parallel to ( or in) P.P. & inclined to H.P. byby  & V.P. by& V.P. by ..
Line in Different Positions with respectLine in Different Positions with respect to H.P. & V.P.to H.P. & V.P. CLASS C: Line inclined to all three referenceCLASS C: Line inclined to all three reference planes ( Oblique lines )planes ( Oblique lines ) Line inclined to H.P. byLine inclined to H.P. by , to V.P. by, to V.P. by  and also inclinedand also inclined to profile plane.to profile plane.
P.P. . H.P. V.P. Y X B A a’ b ’ b a b” a” z x Y Class A(1) : Line perpendicular to P.P. & henceClass A(1) : Line perpendicular to P.P. & hence parallel to both the other planesparallel to both the other planes
XX YY a’a’ b’b’ H.P. H.P. V.P. V.P. aa bb Line perpendicular to P.P. & hence parallel to bothLine perpendicular to P.P. & hence parallel to both the other planesthe other planes
P.P. P.P. a”, b”a”, b” YY11 .. H.P. H.P. V.P. V.P. a’a’ b’b’ aa bb XX YY Line perpendicular to P.P. & hence parallel to bothLine perpendicular to P.P. & hence parallel to both the other planesthe other planes
V.P. V.P. H.P. H.P. YY XX AA BB bb aa a’, b’a’, b’.. XX Class A(2):Line perpendicular to V.P. & (hence)Class A(2):Line perpendicular to V.P. & (hence) parallel to both the other Planesparallel to both the other Planes (i.e. H.P. & P.P.)(i.e. H.P. & P.P.)
a’, b’a’, b’ XX YY V.P. V.P. H.P. H.P. aa bb .. Line perpendicular to V.P. & (hence) parallel to bothLine perpendicular to V.P. & (hence) parallel to both the other Planesthe other Planes
H.P. H.P. V.P. V.P. P.P. P.P. Class B(3): Line parallel to (or contained by) P.P., inclined toClass B(3): Line parallel to (or contained by) P.P., inclined to H.P. byH.P. by  & to V.P. by& to V.P. by  YY XX AA BB a”a” b”b”  YY XX ZZ bb aa bb ’’ aa ’’  
H.P. H.P. V.PV.P .. XX YY aa bb a’a’ b’b’   YY XX BB AA Class C : Line inclined to H.P. byClass C : Line inclined to H.P. by  & V.P. by& V.P. by  (( i.e. Line inclined to both the planes)i.e. Line inclined to both the planes)
V.P.V.P. H.PH.P .. P.P.P.P.  Class B(3): Line parallel to (or contained by) P.P.,Class B(3): Line parallel to (or contained by) P.P., inclined to H.P. byinclined to H.P. by  & to V.P. by& to V.P. by   XX YY a’a’ b’b’ aa bb bb ”” a”a”

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projection of points-engineering graphics

  • 1. PROJECTION OF POINTS AND LINES PREPARED BY : - B.E.(IT) EN NO NAME 16BEITV120 DHRUNAIVI 16BEITV121 PRITEN 16BEITV122 ANKUR 16BEITV123 DHRUMIL 16BEIV124 16BEIV125 DARSHAN NIKUNJ Guided By : - PROF. ROMA PATEL INFORMATION TECHNOLOGY
  • 3. (d) Projections of Right & Regular Solids like; (Prisms, Pyramids, Cylinder and Cone) SOLID GEOMETRYSOLID GEOMETRY Following topics will be covered in Solid Geometry ; (a) Projections of Points in space (b) Projections of Lines (Without H.T. & V.T.) (c) Projections of Planes
  • 4. (1)In quadrant I (Above H.P & In Front of V.P.) (2) In quadrant II (Above H.P & Behind V.P.) (3) In quadrant III (Below H.P & Behind V.P.) (4) In quadrant IV (Below H.P & In Front of V.P.) Orientation of Point in SpaceOrientation of Point in Space
  • 5. (5) In Plane (Above H.P. & In V.P.) (6) In Plane (Below H.P. & In V.P.) (7) In Plane ( In H.P. & In front of V.P.) (8) In Plane ( In H.P. & Behind V.P.) (9) In Plane ( In H.P. & V.P.) Orientation of Point in SpaceOrientation of Point in Space
  • 6. .. .. .. .. .. XX YY aa11’’ AA11 aa11 aa11’’ aa11 YYXX XX YY POSITION: 1 (I Qua.)POSITION: 1 (I Qua.) POINTPOINT Above H.P.Above H.P. In Front Of V.P.In Front Of V.P. AA11- Point- Point aa11’- F.V.’- F.V. aa11 - T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D In 2DIn 2D Point, AbovePoint, Above H.P.H.P. Point, In- FrontPoint, In- Front Of V.P.Of V.P. T.V.T.V. Below XYBelow XY F.V.F.V. Above XYAbove XY (3D)(3D) (2D)(2D)
  • 7. .. .. .. .. .. POINTPOINT Above H.P.Above H.P. Behind V.P.Behind V.P. (3D)(3D) (2D)(2D) XX YY XX YY AA22 aa22 aa22’’ aa22 aa22’’ AA22- Point- Point XX aa22’- F.V.’- F.V. YY aa22 - T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, AbovePoint, Above H.P.H.P. Point, BehindPoint, Behind V.P.V.P. T.V.T.V. Above XYAbove XY F.V.F.V. Above XYAbove XY In 2DIn 2D POSITION:2 (II Qua.)POSITION:2 (II Qua.)
  • 8. aa33 AA33 POINTPOINT Below H.P.Below H.P. Behind V.P.Behind V.P. aa33’’ XX YY .. ..aa33 aa33’’ XX YY XX YY (2D)(2D) (3D)(3D) AA33- Point- Point aa33’- F.V.’- F.V. aa33- T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, BelowPoint, Below H.P.H.P. Point BehindPoint Behind V.P.V.P. T.V.T.V. Above XYAbove XY F.V.F.V. Below XYBelow XY In 2DIn 2D .. .. .. POSITION: 3 (III Qua.)POSITION: 3 (III Qua.)
  • 9. AA44 aa44 .. aa44’’ .. aa44’’ XX YY XX YY XX YY .. (2D)(2D) (3D)(3D) POINTPOINT Below H.P.Below H.P. In Front of V.P.In Front of V.P. AA44- Point- Point aa44’- F.V.’- F.V. aa44- T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, BelowPoint, Below H.P.H.P. Point, InPoint, In Front Of V.P.Front Of V.P. T.V.T.V. Below XYBelow XY F.V.F.V. Below XYBelow XY In 2DIn 2D .. ..aa44 POSITION: 4 (IV Qua.)POSITION: 4 (IV Qua.)
  • 10. H.P. H.P. H.P. H.P. V.P. V.P. .. .. .. .. POINTPOINT Above H.P.Above H.P. In V.P.In V.P. In 3DIn 3D In 2DIn 2D Point, AbovePoint, Above H.P.H.P. Point,Point, In V.P.In V.P. T.V.T.V. On XYOn XY F.V.F.V. Above XYAbove XY YY XX aa55’’AA55 aa55 aa55’’ aa55 XX YY AA55 XX YY (3D)(3D) (2D)(2D) AA55- Point- Point aa55’- F.V.’- F.V. aa55 - T.V.- T.V. CONCLUSIONS:CONCLUSIONS: POSITION: 5POSITION: 5
  • 11. ..POINTPOINT Below H.P.Below H.P. In V.P.In V.P. XX YY XX YY AA66 aa66 aa66’’ aa66’’.. XX YY (2D)(2D) aa66 .. AA66 (3D)(3D) .. AA66- Point- Point aa66’- F.V.’- F.V. aa66- T.V.- T.V. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, BelowPoint, Below H.P.H.P. Point In V.P.Point In V.P. T.V.T.V. On XYOn XY F.V.F.V. Below XYBelow XY In 2DIn 2D POSITION: 6POSITION: 6
  • 12. AA77 .. .. POINTPOINT In Front of V.P.In Front of V.P. In H.P.In H.P. AA77 aa77 aa77’’ XX YY YY XX (3D)(3D) (2D)(2D) YYXX AA77 PointPoint .. .. aa77’- F.V.’- F.V. aa77’’ aa77 T.V.T.V. Below XYBelow XY Point, In-Point, In- Front Of V.P.Front Of V.P. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D In 2DIn 2D Point In H.P.Point In H.P. F.V.F.V. On XYOn XY aa77 - T.V.- T.V. POSITION: 7POSITION: 7
  • 13. AA88 .. .. POINTPOINT In H.P.In H.P. Behind V.P.Behind V.P. YY XX YY XX AA88 aa88 aa88’’ XX YY (3D)(3D) (2D)(2D) aa88 .. ..aa88’’ AA88- Point- Point aa88’- F.V.’- F.V. aa88 - T.V.- T.V. F.V.F.V. On XYOn XY Point, InPoint, In H.P.H.P. CONCLUSIONS:CONCLUSIONS: In 3DIn 3D Point, BehindPoint, Behind V.P.V.P. T.V.T.V. Above XYAbove XY In 2DIn 2D POSITION: 8POSITION: 8
  • 14. POINTPOINT In VIn V.P..P. In H.PIn H.P H.P. H.P. (3D)(3D) (2D)(2D) XX YY YYXX ..AA99 AA99- Point- Point XX aa99’’ aa99’- F.V.’- F.V. ..aa99’’ aa99 aa99 AA99 CONCLUSIONS:CONCLUSIONS: In 3DIn 3D In 2DIn 2D Point, InPoint, In H.P.H.P. F.V.F.V. On XYOn XY T.V.T.V. On XYOn XY Point,Point, In V.P.In V.P. aa99 - T.V.- T.V. POSITION: 9POSITION: 9
  • 16. Definition of Straight lineDefinition of Straight line A straight line is the shortest distance between two points. - Top views of two end points of a straight line, when joined, give the top view of the straight line. - Front views of the two end points of a straight line, when joined, give the front view of the straight line. - Both the above projections are straight lines.
  • 17. Orientation of Straight Line in SpaceOrientation of Straight Line in Space - A line in space may be parallel, perpendicular or inclined to either the H.P. or V.P. or both. - It may be in one or both the reference Planes. - Line ends may be in different Quadrants. - Position of Straight Line in space can be fixed by various combinations of data like distance of its end points from reference planes, inclinations of the line with the reference planes, distance between end projectors of the line etc.
  • 18. Notations used for Straight LineNotations used for Straight Line True length of the lineTrue length of the line: Denoted by Capital letters. e.g. AB=100 mm, means that true length of the line is 100 mm. Front View LengthFront View Length: Denoted by small letters. e.g. a’b’=70 mm, means that Front View Length is 70 mm. Top View LengthTop View Length: Denoted by small letters. e.g. ab=80 mm, means that Top View Length is 80 mm. Inclination of True Length of Line with H.P.Inclination of True Length of Line with H.P.: It is denoted by θ. e.g. Inclination of the line with H.P. (or Ground) is given as 30º means that θ = 30º.
  • 19. Inclination of Front View Length with XYInclination of Front View Length with XY : It is denoted by α. e.g. Inclination of the Front View of the line with XY is given as 50º means that α = 50º. Inclination of Top View Length with XYInclination of Top View Length with XY : It is denoted by β. e.g. Inclination of the Top View of the line with XY is given as 30º means that β = 30º. End Projector DistanceEnd Projector Distance: It is the distance between two projectors passing through end points of F.V. & T.V. measured parallel to XY line. Inclination of True Length of Line with V.P.Inclination of True Length of Line with V.P.: It is denoted by Φ. e.g. Inclination of the line with V.P. is given as 40º means that Φ = 40º.
  • 20. Line in Different Positions with respectLine in Different Positions with respect to H.P. & V.P.to H.P. & V.P. CLASS A: Line perpendicular to (or in) oneCLASS A: Line perpendicular to (or in) one reference plane & hence parallel toreference plane & hence parallel to both the other planesboth the other planes (1)(1) Line perpendicular to P.P. & (hence) parallelLine perpendicular to P.P. & (hence) parallel to both H.P. & V.P.to both H.P. & V.P. (2) Line perpendicular to V.P. & (hence) parallel(2) Line perpendicular to V.P. & (hence) parallel to both H.P. & P.P.to both H.P. & P.P. (3) Line perpendicular to H.P. & (hence) parallel(3) Line perpendicular to H.P. & (hence) parallel to both V.P. & P.P.to both V.P. & P.P.
  • 21. Line in Different Positions with respectLine in Different Positions with respect to H.P. & V.P.to H.P. & V.P. CLASS B: Line parallel to (or in) oneCLASS B: Line parallel to (or in) one reference plane & inclined to otherreference plane & inclined to other twotwo planesplanes (1)(1) Line parallel to ( or in) V.P. & inclined to H.P.Line parallel to ( or in) V.P. & inclined to H.P. byby .. (2) Line parallel to ( or in) H.P. & inclined to V.P.(2) Line parallel to ( or in) H.P. & inclined to V.P. byby .. (3) Line parallel to ( or in) P.P. & inclined to H.P.(3) Line parallel to ( or in) P.P. & inclined to H.P. byby  & V.P. by& V.P. by ..
  • 22. Line in Different Positions with respectLine in Different Positions with respect to H.P. & V.P.to H.P. & V.P. CLASS C: Line inclined to all three referenceCLASS C: Line inclined to all three reference planes ( Oblique lines )planes ( Oblique lines ) Line inclined to H.P. byLine inclined to H.P. by , to V.P. by, to V.P. by  and also inclinedand also inclined to profile plane.to profile plane.
  • 23. P.P. . H.P. V.P. Y X B A a’ b ’ b a b” a” z x Y Class A(1) : Line perpendicular to P.P. & henceClass A(1) : Line perpendicular to P.P. & hence parallel to both the other planesparallel to both the other planes
  • 24. XX YY a’a’ b’b’ H.P. H.P. V.P. V.P. aa bb Line perpendicular to P.P. & hence parallel to bothLine perpendicular to P.P. & hence parallel to both the other planesthe other planes
  • 25. P.P. P.P. a”, b”a”, b” YY11 .. H.P. H.P. V.P. V.P. a’a’ b’b’ aa bb XX YY Line perpendicular to P.P. & hence parallel to bothLine perpendicular to P.P. & hence parallel to both the other planesthe other planes
  • 26. V.P. V.P. H.P. H.P. YY XX AA BB bb aa a’, b’a’, b’.. XX Class A(2):Line perpendicular to V.P. & (hence)Class A(2):Line perpendicular to V.P. & (hence) parallel to both the other Planesparallel to both the other Planes (i.e. H.P. & P.P.)(i.e. H.P. & P.P.)
  • 27. a’, b’a’, b’ XX YY V.P. V.P. H.P. H.P. aa bb .. Line perpendicular to V.P. & (hence) parallel to bothLine perpendicular to V.P. & (hence) parallel to both the other Planesthe other Planes
  • 28. H.P. H.P. V.P. V.P. P.P. P.P. Class B(3): Line parallel to (or contained by) P.P., inclined toClass B(3): Line parallel to (or contained by) P.P., inclined to H.P. byH.P. by  & to V.P. by& to V.P. by  YY XX AA BB a”a” b”b”  YY XX ZZ bb aa bb ’’ aa ’’  
  • 29. H.P. H.P. V.PV.P .. XX YY aa bb a’a’ b’b’   YY XX BB AA Class C : Line inclined to H.P. byClass C : Line inclined to H.P. by  & V.P. by& V.P. by  (( i.e. Line inclined to both the planes)i.e. Line inclined to both the planes)
  • 30. V.P.V.P. H.PH.P .. P.P.P.P.  Class B(3): Line parallel to (or contained by) P.P.,Class B(3): Line parallel to (or contained by) P.P., inclined to H.P. byinclined to H.P. by  & to V.P. by& to V.P. by   XX YY a’a’ b’b’ aa bb bb ”” a”a”