Content of the Lecture

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Content of the Lecture

• Recapitulation
• Definition of Oblique projection. Projection of a
  Point. Projection of a Straight Line.
• Object in the Horizontal Plane Revolving of the
  Horizontal Plane.
• Oblique Projection of a Circle in the Horizontal
  Plane.
• Object in the Frontal Plane Revolving of the
  Frontal Plane.
• Oblique Projection of a Circle in the Frontal
  Plane.
• Oblique Projection of a Circle in the Side Plane.

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1. Axonometric Projection
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Construction of an Object

• Unique representation of the point M
• M,M1, MM1z or
• M,M2, MM2y or
• M,M3, MM3x.

Real size of coordinates xM, yM, zM Axonometric
units (distortion of units) jx, jy, jz
Ex In the axonometry (jx2, jy1, jz1/2,
lt(x,z)150, lt(y,z) 120) draw regular
pyramid ABCDV with ABCD in ?(x,y), A3,0,0,
DO, yBgt0, height h8.
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Oblique projection
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2. Definition of Oblique Projection
Oblique projection is an axonometric projection
such that ? ?(y,z), s is not ??(y,z).
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2. Oblique Projection of a Point A
Uniqueness A1K, AK or A2K, AK or A3, AK ??
A1K, A3 or A1K, A2K or A2K, A3 ??
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2. Oblique projection - Point
Features A1AA1K AK why? A1KAKz similarity
(rectangle ? parallelogram)
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2. Definition of Oblique Projection

• Uniquely determined by a chamfer angle ? and a
  distortion coefficient q.
• ?lt(xK, y)
• qjxKjx

Interpretation (realization) of q
Graphically qdKd ... real length d on the
x-axis is projected to dK on xK
Numerically qjxKjx...coefficient of
multiplication
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2. Point

• Draw oblique projection of a point A and add all
  its projections.
• Oblique projection (140,3/4).
• A 4 8 6.

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2. Point
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2. Straight Line

• Draw oblique projection of a straight line pAB
  and add all its projections.
• Oblique projection (140,3/4).
• A 5 9 2.
• B 2 3 6

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2. Straight Line
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3. Object in Horizontal Plane revolving of the
horizontal plane

• Draw oblique projection of a square in the
  horizontal plane, that is determined by its
  centre and one its vertex.
• Oblique projection (140,3/4).
• Centre S 6 5 0.
• Vertex A 4 8 0.

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3. Object in Horizontal Plane revolving of the
horizontal plane

• There is an affinity between the oblique
  projections of the points in the horizontal plane
  and the revolution those points.
• Axis axis y.
• Direction X0XK.

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4. Oblique Projection of Circle in Horizontal
Plane

• Procedure
• Centre
• Real radius parallel to axis y
• Distorted radius parallel to xK
• Circumscribed parallelogram
• Parallelogram construction for ellipse

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5. Object in Frontal Plane Revolving of the
Frontal Plane

• Draw oblique projection of a regular hexangular
  in the frontal plane, that is determined by its
  centre and one its vertex.
• Oblique projection (120, 3/4).
• Centre S O.
• Vertex E 0 0 6.

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5. Object in Frontal Plane Revolving of Frontal
Plane

• There is an affinity between the oblique
  projections of the points in the frontal plane
  and the revolving of them.
• Axis axis z.
• Direction X0XK.

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6. Oblique Projection of Circle in Frontal Plane

• Procedure
• Centre
• Real radius parallel to axis z
• Distorted radius parallel to xK
• Circumscribed parallelogram
• Parallelogram construction for ellipse

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7. Oblique Projection of Circle in Side Plane
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Attention!

• Oblique projection is parallel projection
• for projection of an object in a plane parallel
  to the horizontal plane apply the same procedure
  as for an object in the horizontal plane
• for projection of an object in a plane parallel
  to the frontal plane apply the same procedure as
  for an object in the frontal plane
• for projection of an object in a plane parallel
  to the side plane apply the same procedure as for
  an object in the side plane

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and next time?

• Oblique projection of solids. Lighting.