Construction of the true size of a plane figure Plane figures in the horizontal/vertical/profile projecting planes 1. Determine the true size of a triangle in the horizontal projecting plane P. r1r1 r2r2 x A’’ B’’ C’’ A’ C’ B’ r20r20. A0A0 C0C0 B0B0 2. Construct the projection of a circle lying in the vertical projection plane if the horizontal projection of a center and the radius r are given. r2r2 x r1r1 S’ r S’’ A’ B’ C’’ D’’ C’ D’ Instruction. The true size is determined by rotating the plane figure into the plane  1. r r =A’’=B’’

Revolution of a point about the 1st trace of the plane into the plane  1. r2r2 r1r1 x S’ S’’ S0S0 (S) Remark. The revolution about the 2nd trace into the plane  2 is analoguous. t’ t0t0 (S*) T1’T1’

1. Construct the projections of a square whose one side lies on the line p, and one vertice is the point A. Instruction. a) (p, q) =  (using two parallel lines) b) Rotate the point A into  1. c) p || q  (p) || (q) p’’ p’ x A’’ A’ q’’ q’ s1s1 s2s2 A0A0 (p) d) (A)(B)(C)(D) one of the two solutions (A) (B) (C) (D) C’ D’ B’ B’’ C’’ D’’ (q) Remark. Projection of a square is always a parallelogram. e) Using afinity  A’B’C’D’ f) Lines of recall  A”B”C”D” Exercises.

2. Plane  is determined with the traces s 1 and s 2. Construct the projection of the circle k   whose center id the point S, and the radius is r. x s2s2 s1s1 S’’ S’ S0S0 r Projection of a circle is an ellipse for which the axes have to be determined. REMARK! In every projection the major axis is on the apropriate principal line, and the minor axis is on apropriate the steepest line (the lenght of the minor axis is determined with the rotated steepest line). r r k’ r r S0S0 k’’ Horizontal projection of the major and minor axis is projected into the conjugated diameters of the elipse in the vertical projecting plane.

Exercises. 1. Construct the true size of the triangle ABC. A’ B’ C’ B’’ A’’ C’’ Instruction. a) Construct the traces of the triangle plane determined by two intersecting lines. r1r1 r2r2 b) Rotate the point A into  1. A0A0 (A) c) Construct the point (B) and (C) with the afinity (axis r 1 ). (B) (C)

2. Construct the projection of a regular hexagon lying in the plane , whose longer diagonal is the line segment AD. D’ A” D” s2s2 s1s1 z y s3s3 A’’’ D’’’ D0D0 A0A0 S0S0 E0E0 F0F0 C0C0 B0B0 S’’’ S” S’ E’’’ E” F’’’ F” C” B” E’ F’ A’ C’ B’’’ B’