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Ellipse Construction Methods Guide

The document outlines four methods for constructing an ellipse given its major and minor axes: 1. The concentric circle method constructs concentric circles with diameters equal to the major and minor axes, and finds intersection points of lines drawn between the circles to form points on the ellipse. 2. The parallelogram method divides the major and minor axes into equal parts and finds intersection points of lines drawn between those points to form points on the ellipse. 3. The circle method for conjugate diameters constructs a circle using one diameter and draws perpendiculars and parallel lines to find intersection points on the ellipse. 4. The four-centered approximate method joins the major and minor axes at a point, draws perpendicular and

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344 views4 pages

Ellipse Construction Methods Guide

The document outlines four methods for constructing an ellipse given its major and minor axes: 1. The concentric circle method constructs concentric circles with diameters equal to the major and minor axes, and finds intersection points of lines drawn between the circles to form points on the ellipse. 2. The parallelogram method divides the major and minor axes into equal parts and finds intersection points of lines drawn between those points to form points on the ellipse. 3. The circle method for conjugate diameters constructs a circle using one diameter and draws perpendiculars and parallel lines to find intersection points on the ellipse. 4. The four-centered approximate method joins the major and minor axes at a point, draws perpendicular and

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Ria Sharma
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July 31, 2015

TA101A 2015-16, 1st semester


Instructor: Prof. Sudhir Misra
Handout-1: Construction of ellipse
Method 1: Concentric circle method

1. To construct an ellipse with AB as


major axis and CD as minor axis, use
their point of intersection, point O, to
draw concentric circles with diameters
equal to major and minor axis. From
various points on the outer circle, such
as P and Q, draw radii OP and OQ,
which intersect the inner circle at P and
Q respectively. From points on the
outer circle, draw lines parallel to minor
axis. Similarly, from points on the inner
circle, draw lines parallel to major axis.
The intersection of the lines gives a
point on the ellipse (such as points 1, 2,
3 ,4).

2. Repeat the procedure for more points


and connect the points to sketch the curve
in a light freehand.

Method 2: Parallelogram method

1. To construct an ellipse with AB and


CD as a pair of conjugate diameters,
construct a parallelogram on the given
diameters. Divide AO into any number
of equal parts, and divide AG into same
number of equal parts, numbering
points from A. Draw lines from point C
to points on AG, and draw lines from
point D to points on AO. Their
intersections will be the points on the
ellipse. The intersection of the lines
gives a point on the ellipse (such as
points 1, 2, 3)

2. Repeat the procedure for other


quadrants and connect the points to
sketch the curve in a light freehand.

Method 3: Circle method for conjugate diameters

1. To construct an ellipse with AB and CD


as a pair of conjugate diameters,
construct a circle with AB as the diameter.
From points such as P, Q, S on the circle,
draw perpendiculars PP, QO, SS on the
diameter AB. From points P and S, draw
lines parallel to QC, and from points P
and S, draw lines parallel to OC. The
intersection of the lines give the points on
the ellipse (such as 1, 2, 3, 4).

2. Repeat the procedure for more points


and connect the points to sketch the curve
in a light freehand

Method 4: Four-Centered method (Approximate method)

1. To construct an ellipse with AB and CD


as major and minor axis, join A and D.
Mark point E on line AD, such that DE =
AO DO. Draw the perpendicular bisector
of AE, which cuts the major axis at point K
and the minor axis at point H.

2. Mark the point M which is the mirror of


point K about O on major axis. Similarly,
mark the point L, which is the mirror of
point H on minor axis.

3. Using point H as center and HD as the


radius, construct the arc RDS. Similarly, using
point L as center, and with the same radius,
draw the arc PCQ. Using point K as the center
and AK as the radius, construct the arc PAR.
Similarly, using point M as center, and with
the same radius, draw the arc QBS.

For more details, refer to Pages 70-72, Engineering Drawing and Graphic Technology, 14th Edition, by Thomas E. French

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