- Coordinates for 3D CAD Modeling
- Geometric Entities
- 4.1 Manually Bisecting a Line or Circular Arc
- 4.2 Drawing Tangents to Two Circles
- 4.3 Drawing an Arc Tangent to a Line or Arc and Through a Point
- 4.4 Bisecting an Angle
- 4.5 Drawing a Line through a Point and Parallel to a Line
- 4.6 Drawing a Triangle with Sides Given
- 4.7 Drawing a Right Triangle with Hypotenuse and One Side Given
- 4.8 Laying Out an Angle
- 4.9 Drawing an Equilateral Triangle
- 4.10 Polygons
- 4.11 Drawing a Regular Pentagon
- 4.12 Drawing a Hexagon
- 4.13 Ellipses
- 4.14 Spline Curves
- 4.15 Geometric Relationships
- 4.16 Solid Primitives
- 4.17 Recognizing Symmetry
- 4.18 Extruded Forms
- 4.19 Revolved Forms
- 4.20 Irregular Surfaces
- 4.21 User Coordinate Systems
- 4.22 Transformations
- Key Words
- Chapter Summary
- Skills Summary
- Review Questions
- Chapter Exercises

## 4.13 Ellipses

An ellipse can be defined by its major and minor axis distances. The major axis is the longer axis of the ellipse; the minor axis is the shorter axis. Some ellipses are shown and labeled in Figure 4.38.

**4.38** Major and Minor Axes of Some Ellipses

An ellipse is created by a point moving along a path where the sum of its distances from two points, each called a focus of an ellipse (foci is the plural form), is equal to the major diameter. As an aid in understanding the shape of an ellipse, imagine pinning the ends of a string in the locations of the foci, then sliding a pencil along inside the string, keeping it tightly stretched, as in Figure 4.39. You would not use this technique when sketching, but it serves as a good illustration of the definition of an ellipse.

**4.39** Pencil and String Method. *When an ellipse is created with the pencil-and-string method, the length of the string between the foci is equal to the length of the major axis of the ellipse. Any point that can be reached by a pencil inside the string when it is pulled taut meets the condition that its distances from the two foci sum to the length of the major diameter.*

Most CAD systems provide an Ellipse command that lets you enter the major and minor axis lengths, center, or the angle of rotation for a circle that is to appear elliptical.