HOW TO DRAW ELLIPSE
Two Circle Methode
Construct two concentric circles with the same diameter as the needed ellipse's major and minor axes. In Fig. 1, these diameters will be AB and CD.
Fig. 1 Two-Circle Construction For an Ellipse |
Draw short lines parallel to the minor axis CD where the radial lines cross the outer circle. Draw lines parallel to AB to intersect with those drawn from the outer circle when the radial lines cross the inner circle. On the ellipse, the points of intersection are located. Make a smooth curve connecting the two points.
Trammel Method
Draw major and minor axes at right angles, as shown in Fig. 2.
Fig. 2 Trammel Method For Ellipse Construction |
Place the trammel on the drawing in such a way that point F is always on the major axis AB and point G is always on the minor axis CD. Each place of the trammel should be marked with a point E, and these points should be connected to form the needed ellipse.
It's important to note that this method relies on the difference in half the lengths of the major and minor axes, and when these axes are roughly the same length, it's difficult to accurately position the trammel. The following procedure can be used as an alternative.
As before, draw the major and minor axes, but expand them in each direction as shown in Fig. 3. Mark half of the major and minor axes in line on a strip of paper, then label these places on the trammel E, F, and G.
Fig. 3 Alternative Trammel Method |
Position the trammel on the drawing so that point G always moves along the CD line, and point E always moves along the AB line. Mark point F for each trammel location and connect these points with a smooth curve to form the needed ellipse.
To Draw an Ellipse Using The Two Foci
As seen in Fig. 4, the major and minor axes intersect at point O. Let's call these axes AB and CD. Draw an arc from center C to intersect AB at places F1 and F2 with a radius equal to half the major axis AB. The foci are these two places. The sum of the distances PF1 and PF2 is a constant for every ellipse, where P is any point on the ellipse. The length of the major axis is equal to the sum of the distances.
Fig. 4 Ellipse By Foci Methode |
OF1 is divided into equal parts. Three of them are illustrated here, with the points G and H.
Define an arc above and below line AB using the center F1 and radius AG.
Define an arc with a center F2 and a radius BG that intersects the arcs above.
Take radius AG from point F2 and radius BG from point F1 and repeat these two procedures.
The technique described above should now be repeated with the radii AH and BH. To make the ellipse, draw a smooth arc through these points.
A tangent to a point on an ellipse is frequently required. P represents any point on the ellipse, and F1 and F2 are the two foci in Fig. 5. Angle F1PF2 bisects line QPR. Create a tangent to the ellipse at point P by erecting a perpendicular to line QPR at point P.
Fig.5 |
Approximate method 1
As illustrated in Fig. 6, draw a rectangle with sides equal to the main and minor axes of the desired ellipse.
Fig. 6 |
Approximate method 1
As illustrated in Fig. 7, draw a rectangle with sides equal to the lengths of the major and minor axes.
Fig. 7 |
Divide EC in half to get point F. Join AF and BE at point G to form a triangle. Join the CG. At points H and J, draw the perpendicular bisectors of lines CG and GA, which will intersect the center lines.
The ellipse can be built using four arcs of circles and the radii CH and JA.
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