This Web site is best viewed using Microsoft Internet Explorer V3 or Netscape Navigator V3. This site is currently being developed and should be completed by the start of May 1998. If you have suggestions or comments about this site please e-mail me at firstname.lastname@example.org.
Pupils: On this site I would like to introduce you to axonometric projection and help you develop your understanding of the topic to honours Leaving Certificate level. You will be introduced to new concepts and will be given an opportunity to test your understanding of these through problem solving. The concepts in axonometric projection are explained using illustrations and animations. The animations will take you through the process of solving axonometric problems step by step. You can test your own understanding of these concepts by attempting questions given throughout the site or by attempting the questions in the Q&A (Questions & Answers) page.
Teachers: As teachers you will be acutely aware of the difficulties many of your pupils experience in trying to visualise, conceptualise and solve problems in Axonometric projection. This site through the use of clear illustrations and animations helps the pupils to visualise and understand the concepts in axonometric projection. Until now this topic has only been on the Junior Certificate Technical Graphics syllabus. However, it is envisaged that it will also be in the new Leaving Certificate Technical Drawing syllabus. This site should act as a resource for you teachers and should prove a useful yardstick in establishing the level of understanding of the topic required at Leaving Certificate level.
The above diagram identifies where Axonometric Projection lies in relation to the other projection systems. Axonometric projection originates from Orthographic Projection. Lets examine this relationship more closely. In both orthographic projection and axonometric projection the problem is to represent a 3D object on a 2D surface e.g. to represent a cube(3D) on a drawing sheet(2D).
Take a sheet of clear perspex as your 2D surface. Imagine standing in front of an object so that your line of vision is perpendicular to the principal faces of the object. Hold the sheet of perspex in front of you. If you now take a pen and trace the outline of the principal faces on the perspex you will obtain a satisfactory representation of them. The sheet of perspex is called the "Picture Plane" in technical drawing.
This is approximately the approach taken in orthographic projection, but with some subtle differences to improve accuracy;
The viewer is assumed to be at infinity so projection lines are parallel. The line of sight (LOS) is always perpendicular to the three principal faces of the object.
The planes onto which the principal faces are projected (Vertical, Side-Vertical and Horizontal) are, in first angle projection, placed behind the object.
For practical purposes the object will be drawn to a suitable scale.
The object on the left is seen in the first
quadrant. The outline of the object is projected onto three
projection planes i.e. the Vertical (in red), Side-Vertical (in
yellow) and the Horizontal plane (in blue). As you can see the
object is always in front of the projection plane onto which it
is projected. Putting the object in the third quadrant puts the
projection planes between the viewer and the object. The line of
intersection between the Vertical plane and the horizontal plane
is known as the X-Y line. The line of intersection between the
Vertical plane (VP) and the Side-Vertical (SVP) plane is known as
the Vertical Trace (VT). The line of intersection between the
Side-Vertical and Horizontal plane (HP) is known as the
Horizontal Trace (HT).
This is the true plan view of the above object. The viewer changes his/her position until he/she is looking at the object from above.
This is the true elevation view of the object. The viewers line of sight is perpendicular to the front face of the object.
This is the true end view of the object. As with the previous two views the viewers line of sight is perpendicular to one of the principal faces i.e. the end view
The three views of the object i.e. plan, elevation and
end-view are still 3-dimensional. The final step to represent a
3D object on a 2D surface is to rotate the views until they all
lie in the same plane. The HP is rotated about the 'XY' line and
the 'SVP' is rotated about its 'VT' until all three planes of
projection lie in the same plane.
In orthographic projection three views are often required to give an accurate representation of an object. If a view is taken where the LOS is not perpendicular to the principal faces and two of the principal faces of the object are visible then an auxiliary view of the object is obtained e.g. Iso.2(b) below. If a view is taken where again the LOS is not perpendicular to the principal faces and three of the principal faces of the object are visible, then an axonometric projection results e.g. Iso.2(c).
In Iso. 2 (a) one of the principal faces of the object are perpendicular to the picture plane resulting in an elevation. In (b) the object has been rotated about the vertically axis allowing two of the principal faces to be viewed. An auxiliary elevation results. In (c) the object in (b) has been tilted forward allowing all three principal faces to be viewed. An axonometric projection results.
Because the object can be inclined in any position relative to the plane of projection, an infinite number of views are possible. The infinite number of views can, however, be classified into three general categories;
(1) Isometric, (2) Dimetric and (3) Trimetric.
These are the three forms of axonometric projection.
Lets take the lower corner of a typical box room. The two vertical walls and the floor give us three planes. Lets paint the walls red and yellow to distinguish one from the other and paint the floor blue. The dividing lines between the two vertical walls and the floor are known as the x, y and z-axis. If the viewer sees an equal angle between all three axes then this view is called an Isometric view i.e ß=Ø=µ. If a view is taken so that two of the angles between any two of the axes are the same and one is different then this is a Dimetric view. Finally, if a view is taken where all three angles between the three axes are not equal then, this view is a Trimetric view. Let's now deal with these three views in detail.