How To Draw Ellipse With Compass Without String


Ovals and diverse "egg shaped" designs are often used in marquetry, particularly for such purposes as framing marquetry portraits in a similar manner to the ovals cutting in mount board every bit done by photographers. But, you may ask, how do I actually draw out such a design in the first place? Well, never fear, because I am about to guide you through the process of drawing all manner of such designs. And then, are you lot ready? right and then, off nosotros go: I am at present going to draw to you a few of the alternative methods used for the construction of an ellipse and various ovals. No function of an ellipse is an arc, which is part of a circle, and so a true ellipse cannot exist drawn with a compass. I accept always used the trammel method described by Eddie Stevens in Journal No. 219. I thought the string method too big and clumsy for marquetry purposes, and more suitable for setting out flower beds. Withal, on trying it I found that it was not difficult to get a skilful outcome. Here is the method: -
Describe the long and brusk centrelines, crossing at 0 and mark the extremities A,B,C, and D, Open the compass to AO and with point on D, depict arcs to cutting line AB at points F¹ and F², chosen the focal points. Make a "string loop" - I used button thread; with length from F¹ to B. I found the easiest way to do this was to cut a slice of veneer, say well-nigh ane inch wide, length F¹ to B and tie the loop around information technology. Put a modest nail or suitable pin (I used a cartoon pin which could be pushed through from behind) at each focal betoken, and at present use the loop as shown in the sketch - using a sharp pencil to depict the circumference of the ellipse. By ellipse we mean a true ellipse as obtained by the trammel method. By oval, nosotros mean a almost or approximation drawn with a compass.
The method of construction of an oval (which in my experience has been the virtually common) is equally follows; Draw a line A B (Fig 2) equal in length to the long diameter of the oval, and through the middle point O of this diameter depict a line at right angles. Brand O C and O D each equal to half the small diameter of the oval. From A mark off A E equal in length to C D. Divide E B into iii equal parts. Now set the compasses at a radius equal to ii of the parts, and with O as centre, marking points F1, F2. Then with O again as centre, and the compasses set to length F1 (F2), mark points P1, (P2). It volition be seen that either O P is equal to four of the parts into which E B has been divided. The points F and P will be centres from which the arcs volition be described. Bring together P1 to F1 F2, and P2 to F1 F2 and produce the lines through every bit shown in figure 2. At present with centre F2 and radius F2 B describe the end arcs, and with eye P and radius P2 C draw the side arcs. If carefully and properly fatigued, the arcs should meet and run into each other on the lines drawn through P and F. The object, indeed, for which these lines are fatigued is to determine the coming together points of the curves. Information technology should be noticed that the points P may come either within or without the figure, according as the oval is broad or narrow.
This method is to calculate the required radii. The oval shown is 6 inches by iv½ inches. The radius for the sides equal viii times the long diameter minus v times the short bore and divide the remainder by 6. This equals (8AB – 5CD) ÷ 6 = (48 - 22½) ÷ half dozen = 4¼" The radius for the ends equals 4 times the short bore minus the large diameter and divide by 6. This equals (4CD – AB) ÷ 6 = (18 – half dozen) ÷ 6 = 2" Lines may be drawn every bit in sketch 2 to give the exact indicate of contact of the curves, simply with intendance in drawing whatsoever slight discrepancy tin can be put right using a French curve.
Draw the major and minor axes, intersecting at O. On ane half the major axis draw an equilateral triangle OEA on OE marker off OP equal to OC. From C draw through P to find point Q. And so from Q draw QR parallel to OP. With centre R draw CQ. F¹ is the centre of the arc QA. For the opposite arcs, brand OF² equal to OF and BP equal to AF². A word most triangles. An equilateral triangle, three sides of equal length and three angles of sixty degrees. An isosceles triangle has 2 sides of equal length. A scalene triangle has iii sides all of unlike lengths.
This is a simple method of drawing an egg shaped oval, but with the drawback that whatever the size of the oval, the ratio of the long axis to the brusque centrality will always exist the same (considering radius OB will always exist twice radius OA). First, draw the circle ABCD. With centre D and radius DB draw arc DF. Draw lines BF through C and DE also through C. Now with center C draw arc EF.
This is merely a combination of a semicircle and a half ellipse drawn by the trammel method.
This is a relatively simple method of constructing an egg-shaped oval to choose the length and besides the small end radius. Starting time, describe the major and minor axes AB and CD intersecting at O. At present draw the semicircle for the large end then B to be at the small end, length OB to accommodate your requirements. Now marking point East so that EB will exist the small stop radius that you crave. Marking point F on the pocket-sized axes so that FC = EB, so draw a perpendicular bisector FF to cut OD at H. (H could be exterior the oval depending on what dimensions you have chosen - only extend OH to accommodate). Now with centre H depict Arc CG, and E is the centre for arc GB.
When the major axis is considerably longer than the minor axis, say iv to 1, all the foregoing methods are not so satisfactory, only for full general purposes this method, though non as elementary, is workable for all proportions long or broad. Draw the major and minor axis AB and CD, intersecting at O. Join CB. With eye O and radius OC, describe arc CE, cut line CB at F. With middle F and radius Fe describe arc EG. Draw GH parallel to OB. With compass point on B, make BR4 equal to CH. Join HR4. Bisect HR4 and extend the perpendicular bisector downwards to meet CD extended at R2. Then R2 is the centre for the side arc and R4 is the centre for the end arc. Make OR3 equal to OR4 to give the centre for the opposite end arc.
A variation on figure 7 above. This variation is a petty more than extended than the ones shown in figure 7. The method of construction is the same all the same.
A variation on figure eight above. The variation you run across in this diagram is that the oval is considerably more flattened than the 1 seen in effigy 8. You tin vary the shape and outline to fit in with your own design by following the guidelines given in the text side by side to figure viii.
The design methods shown above will requite you accurately defined shapes as seen in the ten examples I've included hither. You lot can calibration the designs quite hands to fit in with your needs. Do accept a go yourself, you volition detect it's much easier than you recollect to depict accurate ovals.
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