Descriptive geometry . Fig. 193. Vir,. mi. Example 4 (Fig. 194). Given a sphere and a circular cylin-der. In this example it may not be so easy to vizualize theintersection by considering the plan view. Nevertheless alittle Btudy will show thai there must be two closed figureshaving a common point a. Asa matter of fad flic int.! lectionwhen found in elevation will he shaped like an irregular figure 124 DESCRIPTIVE GEOMETRY [XIII, § 131 8, the curve crossing itself (not tangent), at a. It is calleda one-curve intersection. The solution is left to the student. 132. The Intersection of a Cylinder
Descriptive geometry . Fig. 193. Vir,. mi. Example 4 (Fig. 194). Given a sphere and a circular cylin-der. In this example it may not be so easy to vizualize theintersection by considering the plan view. Nevertheless alittle Btudy will show thai there must be two closed figureshaving a common point a. Asa matter of fad flic int.! lectionwhen found in elevation will he shaped like an irregular figure 124 DESCRIPTIVE GEOMETRY [XIII, § 131 8, the curve crossing itself (not tangent), at a. It is calleda one-curve intersection. The solution is left to the student. 132. The Intersection of a Cylinder and a Torus. Anotherexample is shown in Fig. 195. An auxiliary plane, as Q, par-allel to H, cuts the cylinder in the elements A and B, and thetorus in the circles C and D, giving six points, 1, 2, ... 6, ofthe intersection. The chosen secant planes, parallel to H, should. Fig. 195. include one through the contour element E of the cylinder;one through the highest element, G; one through the center ofthe torus; and one tangent at the bottom of the torus. Thepoints 7 and 8 of the intersection evidently lie in the plane X,which passes through the center of the torus parallel to V. CHAPTER XIV PROBLEMS INVOLVING THE REVOLUTION OF PLANES 133. A Line Lying in a Given Plane. One method of locatinga line so that it will lie in a given plane is to assume the tracesof the line in the corresponding traces of the plane. This hasalready been explained in § 97. (See Fig. 123.)
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