Descriptive Geometry/Mathematical Constructions/Ellipse/Parabola/Hyperbola

From Wikibooks, open books for an open world
Jump to navigation Jump to search

Ellipse

1. Create a rectangle ABCD. Find the midpoints of each line and connect the points to divide the rectangle into quadrants. Divide AG and GO into equal number of parts using the division method.

EllipseA.png













2. Connect the points on GO with F and connect the points on AG with E. Mark the intersection points of the lines.
3. Connect those points to create part of the ellipse.
4. Repeat in the same construction in the other quadrants of the rectangle to create a full ellipse

EllipseB.png














Parabola

1. Start with rectangle ABCD. Find midpoints of AB and CD and connect. Divide CE and AC into equal parts. Draw a perpendicular line to CE on each of the points on CE.

Parabola A.png














2. Connect the points with point F.
3. Mark the intersection points of the lines.

Parabola B.png













4. Connect the points to create half of the parabola
5. Repeat on the other half of the rectangle

Parabola C.png












Hyperbola with transverse axis and a point

HyperbolaD.png












1. First create point K' with CK' being the same distance as CK (transverse axis).
2. Construct rectangle KLMN. Then divide the top side and right side into equal parts.

HyperbolaE.png












2. Connect the points on LM with point K and connect the points on MN with K'.
3. Find the intersection points of the lines and connect to create the hyperbola.

Hyperbola3.png











http://www.salsburg.com/cadfaq/geometricconstructions.html