True Ellipses in Isometric

True ellipses can be drawn in isometric by the following methods,

• Offset Measurements

• Conjugate diameters

• Ellipse guides

Ellipses by Offset Measurements

If a circle lies on a plane that is not perpendicular to the line of vision then it will project as an ellipse. Lets take a square based prism and drill a hole down through the centre of its top face. In isometric the hole in the top of the prism will project as an ellipse. If we take the plan of the object and locate points on the circle by means of offset location measurements and then transfer these measurements to the isometric drawing, the ellipse is easily drawn. Two lines are required to find a single point on the circle. Start by drawing horizontal lines through the circle. Where these lines and the circle intersect draw vertical lines. Measure the distance from each of the horizontal and vertical lines to a corner of the prism. This will give the measurements required to draw the ellipse in the isometric view. Instead of measuring from a corner of the prism it is often convenient to use the centre lines of the circle as a datum line. A datum line is a line from which all measurements are taken from or with respect to. Follow the procedure shown in the animation to find measurements 'a' and 'b'.

Transfer the horizontal 'a' measurements onto the isometric drawing. Next transfer the 'b' measurements. Where these lines intersect give points on the ellipse. The ellipse on the top of the object is the same as that on the bottom. Transfer points on the top ellipse parallel to the vertical axes a distance equal to the heigth of the object i.e. 'c'. Follow the same procedure for each set of lines. Take as many sets of lines as necessary to draw a smooth ellipse.
It is not the purpose of this site to explain, illustrate and demonstrate the numerous methods of constructing true and approximate ellipses. Some methods are briefly discussed below. The offset location measurements method is the onle method shown for generating true ellipses. This method can also be used to draw ellipses in dimetric and trimetric.

Angles, Curves, Ellipses and Arcs in Isometric

Angles: Angles only project as true size when the plane of the angle is parallel to the plane of projection. As we saw earlier the angle between the adjacent edges of a cube in isometric project as 120º and not 90º. Thus, angles can project larger or smaller than true size.

Take this object whos outline projects as an equilateral triangle in plan. None of these angles will project as 60º in the isometric drawing. Establish this fact for yourself by drawing the object in isometric and then measure each of the angles. The isometric drawing of this object is shown below.

How about questions where we are not given all the dimensions and have to work them out from angles?

In the elevation view of the object we do not know dimension 'X' so how do we find it? Draw the plan and elevation and then draw the enclosing box for the isometric drawing. If we draw a rectangle around the outline of the elevation we can step off dimension 'X'. Simply step this distance off parallel to an isometric line in the isometric drawing. Complete the drawing in the usual way. Thus, the key to solving angular measurements in isometric is to convert them to linear measurements along isometric lines.

Curves: Curves in isometric are drawn by means of offset location measurements method (also known as offset measurements). Pick points on the plan and elevation and locate these points by offset measurements. These measurements are then transfered to the isometric view in the usual way. Use an irregular curve to connect all the points.

Ellipses: Circles will always appear as ellipses in isometric and can be drawn using offset measurements. Ellipses can be drawn in isometric using any off the conventional ellipse constructions. The Four Centre Ellipse is quite satisfactory in most cases. This involves circumscribing a square about the circle in the orthographic view. This square is then transferred to the isometric view where it will appear as an isometric square or a rhombus. Mark in the mid-points on the lines of the square where the ellipse is a tangent to the rhombus in this view also. Draw in the perpendicular bisectors of the sides of the rhombus. Where these intersect gives the centres for the four arcs forming the ellipse. For more accurate ellipses the Orth Four-Centre Ellipse can be used or ellipse guides.

Arcs: Arcs in isometric are simply sections of ellipses so any of the constructions used to draw ellipses can be used to draw arcs.

The Sphere In Isometric

Shown above is a sphere which has been enclosed in a cube. A vertical cut is taken through the centre of the sphere and on a plane parallel to one face of the cube so that a great circle results. This great circle appears as an ellipse on the isometric drawing. The only points of this ellipse which appear on the isometric drawing of the sphere, are the points on the extremities of the major axis. Using one of these points and the centre of the ellipse as radius the isometric drawing of the sphere is completed.

The isometric drawing of the sphere is a circle whose diameter is Ö(3/2) times that of the actual diameter of the sphere. The isometric projection of the sphere is simply a circle whose diameter is equal to the true diameter of the sphere. It is important when drawing in an isometric drawing that the circle drawn is an isometric drawing and not an isometric projection of the sphere. If a isometric projection of a sphere is drawn in an isometric drawing then the drawing will be distorted as the sphere will appear smaller than it should.

In axonometric the sphere will always project as a circle. The radius of this circle will be the radius of the sphere.

Hidden lines, Centre lines

and Dimensioning in Isometric

Hidden lines are always omitted unless they provide information not readily available from the axonometric drawing or projection.

Centre lines are drawn if they are needed to indicate symmetry or if they are needed for dimensioning. Where possible they are omitted.

Two systems of dimensioning are approved by ANSI namely, the pictorial plane system (aligned) and the unidirectional system. The former being the preferred system. Inclined lettering is usually not recommended for pictorials (it has been used on this web site for demonstration purposes). Typically, simple vertical lettering is used for either system. In Ireland we use the British Standard 308 (BS 308) when dimensioning. Here is an example of good dimensioning in isometric.