Descriptive geometry . can project a point in the ^-projection to the P-projection, andfrom this to the F-projection;or vice versa. Construction (Fig. 75). Letab (ahbh, avb) be the givenline. Find apb. Now if ch isgiven, project from c* to cp inabp; and from cp to C in c is given, c* may be foundby reversing the process. The line may be pro-duced indefinitely, and the as-sumed point may be beyondthe limits of a and b. Thus, if(I is taken. dh is found asshown, and the point d lies on the line produced into thethird quadrant. Or, dh may be given, and d 40 DESCRIPTIVE GEOMETRY [V
Descriptive geometry . can project a point in the ^-projection to the P-projection, andfrom this to the F-projection;or vice versa. Construction (Fig. 75). Letab (ahbh, avb) be the givenline. Find apb. Now if ch isgiven, project from c* to cp inabp; and from cp to C in c is given, c* may be foundby reversing the process. The line may be pro-duced indefinitely, and the as-sumed point may be beyondthe limits of a and b. Thus, if(I is taken. dh is found asshown, and the point d lies on the line produced into thethird quadrant. Or, dh may be given, and d 40 DESCRIPTIVE GEOMETRY [VI, § 59 59. Profile Trace of a Line. The general line, oblique to H,V, and P, will pierce all these planes. Hence, besides thehorizontal trace s, and the vertical trace t, it will have a profiletrace, u, which must lie in the profile projection of the line. Given the horizontal and vertical projections of a general line,to find its profile projection and profile trace. Analysis. The profile projection of any straight line can beobtained from its horizontal and vertical projections by findingthe profile projections of any two points in the line (§ 57).The profile trace can be found by noting the point in whichthe given line pierces the edge view of P. Construction (Fig. 76). Ah and Av are the given the points s and t, the H- and P-traces of the line A(Prob. 1, § 37). Project s to sp in GL, and t to tp in VP; s»and V determine the required profile projection Ap. Since
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