OVAL
An oval is a flat and closed curve that is formed by four arcs of a circumference. It is symmetrical with respect to its two perpendicular axes: the major axis and the minor axis.
Construct an oval given only the major axis
Step 1. Divide the major axis AB into three equal parts to define the points C and D. Use centre point C and radius CA. Draw a circle.
Step 2. Use centre point D and radius CA. Draw a circle A that intersects the one made in step 1 at points E and F.
Step 3. Draw the rays EC, ED, FC and FD. These rays intersect the circumferences at points H, J, G and M, respectively.
Step 4. Use centre point F and radius FG. Draw the arc GM. Then use centre point E and the same radius. Draw the arc HJ to complete the construction of the oval.
Construct an oval given only the minor axis
Step 1. Find the perpendicular bisector of CD. Label its midpoint M.
Step 2. Use centre point M and radius MC. Draw a circumference that intersects the perpendicular bisector of CD at points A and B.
Step 3. Draw the rays CA, CB, DA and DB.
Step 4. Use centre point C and radius CD. Draw the arc PORQUE. Then use centre point D and the same radius. Draw the arc RS.
Step 5. Use centre point A and radius AP. Draw the arc PR. Then use centre point B and radius BS. Draw the arc SQ to complete the construction of the oval.
OVOID
An ovoid is a flat and closed curve formed by half a circle, two equal circle arcs and another unequal one. An ovoid also has two axes: the major axis and the minor axis. However, it is only symmetrical to one of the axes.
Construction of an ovoid, given only the minor axis
Step 1. Draw MN and construct its perpendicular bisector. Label the midpoint O.
Step 2. Use centre point O and radius OM. Draw a circumference that intersects the perpendicular bisector of MN at point H. This also creates half a circumference from M to N.
Step 3. Draw the rays MH and NH.
Step 4. Use centre point M and radius MN. Draw the arc NK. Then use centre point N and the same radius. Draw the arc MJ.
Step 5. Use centre point H and radius J. Draw the arc JK that completes the ovoid.
Construction of an ovoid, given only the major axis
Step 1. Divide the major axis AG into six equal parts. Label the points that divide it B, C, D, E and F. Then draw a perpendicular line to AG that passes through C.
Step 2. Use centre point C and radius CA. Draw half a circle that passes through A and intersects the perpendicular line from step 1 at points M and N.
Step 3. Use centre point C and radius CG. Draw half a circle that passes through G and intersects the line MN at points P and Q. Then draw the rays PF and QF.
Step 4. Use centre point P and radius PN. Draw an arc that intersects the ray PF at point R. Then use centre point Q and the same radius. Draw an arc that intersects the ray QF at point S.
Step 5. Use centre point F and radius FS. Draw the arc SR that completes the ovoid.
