Copyright Goodheart-Willcox Co., Inc. Chapter 4 Understanding Three-Dimensional Coordinates and User Coordinate Systems 81 To draw the fi rst sphere, select the SPHERE command. Specify the center point as 7,5 and the radius as 1.5 units. Display a southeast isometric pictorial view of the sphere. Alternately, you can use the view cube to create a different pictorial view. Also, set the Wireframe visual style current and switch to a parallel projection. Your drawing should look similar to Figure 4-2A. Since you know the radius of the sphere, but the center of the sphere is not at the origin of the current UCS (the WCS), a relative spherical coordinate will be used to draw the second sphere. The sphere you drew is a solid and, as such, you can snap to its center using object snap. Set the center running object snap and then enter the SPHERE command again to draw the second sphere: Specify center point or [3P/2P/Ttr]: FROM↵ Base point: (use the Center object snap to select the center of the existing sphere) Offset: @1.53060↵ (1.5 is the radius of the first sphere) Specify radius or [Diameter]: .4↵ The objects should now appear as shown in Figure 4-2B. The center of the new sphere is located on the surface of the original sphere. This is clear after setting the Conceptual visual style current, Figure 4-2C. If you want the surfaces of the spheres to be tangent, add the radius value of each sphere (1.5 + .4) and enter this value when prompted for the offset from the center of the fi rst sphere: Offset: @1.93060↵ Notice in Figure 4-2B that the polar axes of the two spheres are parallel. This is because both objects were drawn using the same UCS, which can be misleading unless you under- stand how objects are constructed based on the current UCS. Test this by locating a cone on the surface of the large sphere, just below the small sphere. First, display a 3D wire- frame view of the objects. Then, select the CONE command and continue as follows: Specify center point of base or [3P/2P/Ttr/Elliptical]: FROM↵ Base point: CEN↵ of (pick the large sphere) Offset: @1.53030↵ Specify base radius or [Diameter]: .25↵ Specify height or [2Point/Axis endpoint/Top radius]: 1↵ (before entering this value, make sure to move the crosshairs above the base of the cone to apply the value in the positive Z direction) The result of this construction with the Conceptual visual style set current is shown in Figure 4-3. Notice how the axis of the cone is parallel to the polar axis of the sphere. A B C Figure 4-2. A—A three-unit diameter sphere shown from the southeast isometric viewpoint. B—A .8-unit diameter sphere is drawn with its center located on the surface of the original sphere. Also, lines have been drawn between the poles of the spheres. Notice how the polar axes are parallel. C—The objects after the Conceptual visual style is set current.