# Note

## plane, lines, parallel and picture

NOTE. - This is true of all lines in an object which are parallel to the picture plane. Thus, the perspective of any line which is parallel to the picture plane, will actually be parallel to the line itself ; and the perspectives of the elements of a system of lines parallel to the picture plane, will be drawn parallel to, and not con verging towards, one another. That this must be so, is evident, since, if the perspectives of such a system of lines did converge towards one another, they would meet within finite limits. But it has just been found that the perspective of the vanishing point of such a system is at infinity. The perspectives of the elements of any system can meet only at the perspective of their vanish ing point, and must, therefore, in'a system parallel to the picture plane, be drawn parallel to one another.

The directions of the perspectives of all lines in the object have now been determined, and will be as follows : All lines parallel to ab will meet at v".

All lines parallel to ad will meet at v"..

All vertical lines will be drawn vertical.

Since the point e is in the of the Object, it lies on the plane of the ground, and also, since the line ae lies in the picture plane, the point e must lie on the intersection of the plane of the ground with the picture plane. Therefore, the point e must lie in and must be vertically under the point e in the diagram. Since the point e lies in the picture plane, it will be its own per spective; and eP will be found on VI-1„ vertically under e in the diagram, as shown in the figure. From eP the perspective of the

lower edges . of the cube will vanish at v" and respectively, as indicated.

fP is the perspective. of the point f, and will be found on the lower edge of the block, vertically under the intersection of HPP with the horizontal projection of the visual ray drawn through the Point f in the diagram.

Similarly, kP is found on the lower edge of the block, verti cally under the intersection of HPP and .the visual ray drawn through the point k in the diagram.

Vertical lines drawn through fr, eP, and kP, will represent the perspectives of the visible vertical edges of the block.

The edge ePaP being in the picture plane will be its own per spective, and show in its true size (§ 24 h). Therefore, aP may be established by making the distance eP ar equal to evav as taken from the given elevation. Froin aP two of the upper horizontal edges of the block will vanish at v" and v", respectively, estab lishing the points bP and dP, by their intersections with the vertical edges drawn through kr and fP, respectively. Lines drawn through dP and and vanishing respectively at eh and v"a, will intersect at e", and complete the perspective of the block.

Before going farther in the notes, the student should solve, the problems on Plate I.