Method for designing structure by drawing curve approximately with circular segment, and structure thereby

A method for producing a drawing of a part of a structure where the part of the structure has an arbitrary S-shaped curve which is to be approximately represented with at least first and second joined circular segments, comprising the steps of:

• a) establishing a representative S-shaped curve of the arbitrary S-shaped curve of the structure which is to be approximated on a viewing medium, the representative S-shaped curve having first and second ends;
• b) drawing, on the viewable medium using an instrument, first arbitrary point on the representative S-shaped curve, and thereby establishing a first curved part and a second curved part,
• c) for the first curved part,
• i) drawing, on the viewable medium using the instrument,
• a first straight line which connects the first end and the first arbitrary point, and
• a first perpendicular line perpendicular to the first straight line at a first middle point of the first straight line, and thereby establishing a first intersection point of the first perpendicular line with the first curved part of the representative curve;
• ii) determining, on the viewable medium using the instrument, a first distance between the first intersection point and the first middle point, and a first length of a first straight-line segment from the first end and from the first arbitrary point of the first curved part to the first middle point,
• iii) ascertaining, using the determined first distance and the determined first length, a first curvature radius and a first radius center point of a first circular segment which approximates the first curved part and
• iv) drawing, on the viewable medium using the instrument, a first circular segment from the first end to the first arbitrary point of the first curved part using the ascertained first curvature radius and the first radius center point;
• d) for the second curved part, continuously from the first curved part,
• i) drawing, on the viewable medium using the instrument,
• a second straight line which is a straight extension of the first straight line, from the first arbitrary point to thus determine a second arbitrary point on the second curved part of the representative S-shaped curve,
• a second perpendicular line) perpendicular to the second straight line at a second middle point of the second straight line, and thereby establishing a second intersection point of the second perpendicular line with the second curved part of the representative curve;
• ii) determining, on the viewable medium using the instrument, a second distance between the second intersection point and the second middle point, and a second length of a second straight-line segment from the first arbitrary point and from the second endpoint up to the second middle point,
• iii) ascertaining, using the determined second distance and the determined second length, a second curvature radius of a second circular segment which approximates the second curve, and
• iv) drawing, on the viewable medium using the instrument, a second circular segment from the first arbitrary point up to the second arbitrary point using the ascertained second curvature radius and the second radius center point;
• and
• e) drawing, on the viewable medium using the instrument, further continuous circular segments by repeating the step d) successively as required.

A method for producing a drawing of an elliptical structure which is symmetrical with respect to a major elliptical axis and a minor elliptical axis thereof, where the elliptical structure has an elliptic outline which is to be approximated as the whole circumference thereof, and where the elliptical structure is a cylindrical body, said method comprising the steps of:

• a) establishing a first representative quadrant of the elliptical structure defined by the major and minor axes which is to be approximated on a viewing medium,
• b) for a first elliptic segment of the first representative quadrant:
• i)drawing, on the viewable medium using an instrument,
• a first arbitrary point on the first representative quadrant which starts from a first end point of the minor axis,
• a first straight line which connects the first end point and the first arbitrary point,
• a first perpendicular line to the first straight line at a first middle point of the first straight line, and thereby establishing a first intersection point of the first perpendicular line with the first representative quadrant which defines the first elliptic segment,
• ii) determining, on the viewable medium using the instrument, a first distance between the first intersection point and the first middle point, and a first length of a first straight-line segment from the first end points and from the first arbitrary point to the first middle point,
• iii) ascertaining, using the first determined distance and the first determined length, a first curvature radius of a first circular segment which approximates the first elliptic segment, and
• iv) drawing, on the viewable medium using an instrument,
• a first fixed point on the minor axis using the first curvature radius, and
• a first circular segment from the first end point to the first arbitrary point by using the first fixed point as the center thereof;
• c) for a second elliptic segment of the first representative quadrant which is to be continuous from the first elliptic segment:
• i) drawing, on the viewable medium using an instrument,
• a second arbitrary point which starts from the first arbitrary point and which thereby defines the second elliptic segment,
• a second straight line which connects the first arbitrary point and the second arbitrary point,
• a second perpendicular line to the second straight line at a second middle point of the second straight line, and thereby establishing second intersection point of the second perpendicular line with the first representative quadrant which defines the second elliptic segment,
• ii) determining, on the viewable medium using the instrument, a second distance between the second intersection point and the second middle point, and a second length of a second straight-line segment from the second arbitrary points and from the first arbitrary point to the second middle point,
• iii) ascertaining, using the second determined distance and the second determined length, a second curvature radius of a second circular segment which approximates the second elliptic segment, and
• iv) drawing, on the viewable medium using an instrument,
• a second fixed point at an intersection point of a first radial line from the first fixed point to the first arbitrary point of the curvature radius and this curvature radius from the first arbitrary point, and
• setting a second circular segment from the first arbitrary point to the second arbitrary point by using the second fixed point as the center thereof;
• d) similarly, repeating the step c) successively, by i) drawing successive arbitrary points, successive straight lines and successive perpendicular lines, ii) determining successive distances and successive lengths, iii) ascertaining successive curvature radii, and iv) drawing successive fixed points and successive circular segments one after of the first representative quadrant, up to an nth circular segment is drawn from an n-1 arbitrary point to a first end point of the major axis, whereby the first representative quadrant has been approximated;
• and
• e) repeating steps b), c) and d), as necessary, to approximate second to fourth quadrants of, the whole elliptic outline of the elliptic structure.