The Theory and Practice of Perspective Part 20

CII

TO DRAW SEMICIRCLES STANDING UPON A CIRCLE AT ANY ANGLE

[Ill.u.s.tration: Fig. 190.]

Given the circle _ACBH_, on diagonal _AB_ draw semicircle _AKB_, and on the same line _AB_ draw rectangle _AEFB_, its height being determined by radius _OK_ of semicircle. From centre _O_ draw _OF_ to corner of rectangle. Through _f_, where that line intersects the semicircle, draw _mn_ parallel to _AB_. This will give intersection _O_ on the vertical _OK_, through which all such horizontals as _mn_, level with _mn_, must pa.s.s. Now take any other diameter, such as _GH_, and thereon raise rectangle _GghH_, the same height as the other. The manner of doing this is to produce diameter _GH_ to the horizon till it finds its vanishing point at _V_. From _V_ through _K_ draw _hg_, and through _O_ draw _nm_. From _O_ draw the two diagonals _og_ and _oh_, intersecting _mn_ at _O_, _O_, and thus we have the five points _GOKOH_ through which to draw the required semicircle.

CIII

A DOME STANDING ON A CYLINDER

[Ill.u.s.tration: Fig. 191.]

This figure is a combination of the two preceding it. A cylinder is first raised on the circle, and on the top of that we draw semicircles from the different divisions on the circ.u.mference of the upper circle.

This, however, only represents a small half-globular object. To draw the dome of a cathedral, or other building high above us, is another matter.

From outside, where we can get to a distance, it is not difficult, but from within it will tax all our knowledge of perspective to give it effect.

We shall go more into this subject when we come to archways and vaulted roofs, &c.

CIV

SECTION OF A DOME OR NICHE

[Ill.u.s.tration: Fig. 192.]

First draw outline of the niche _GFDBA_ (Fig. 193), then at its base draw square and circle _GOA_, _S_ being the point of sight, and divide the circ.u.mference of the circle into the required number of parts. Then draw semicircle _FOB_, and over that another semicircle _EOC_. The manner of drawing them is shown in Fig. 192. From the divisions on the circle _GOA_ raise verticals to semicircle _FOB_, which will divide it in the same way. Divide the smaller semicircle _EOC_ into the same number of parts as the others, which divisions will serve as guiding points in drawing the curves of the dome that are drawn towards _D_, but the shading must a.s.sist greatly in giving the effect of the recess.

[Ill.u.s.tration: Fig. 193.]

In Fig. 192 will be seen how to draw semicircles in perspective.

We first draw the half squares by drawing from centres _O_ of their diameters diagonals to distance-point, as _OD_, which cuts the vanishing line BS at _m_, and gives us the depth of the square, and in this we draw the semicircle in the usual way.

[Ill.u.s.tration: Fig. 194. A Dome.]

CV

A DOME

First draw a section of the dome ACEDB (Fig. 194) the shape required.

Draw _AB_ at its base and _CD_ at some distance above it. Keeping these as central lines, form squares thereon by drawing _SA_, _SB_, _SC_, _SD_, &c., from point of sight, and determining their lengths by diagonals _fh_, _fh_ from point of distance, pa.s.sing through _O_.

Having formed the two squares, draw perspective circles in each, and divide their circ.u.mferences into twelve or whatever number of parts are needed. To complete the figure draw from each division in the lower circle curves pa.s.sing through the corresponding divisions in the upper one, to the apex. But as these are freehand lines, it requires some taste and knowledge to draw them properly, and of course in a large drawing several more squares and circles might be added to aid the draughtsman. The interior of the dome can be drawn in the same way.

[Ill.u.s.tration]

[Ill.u.s.tration: Fig. 195.]

CVI

HOW TO DRAW COLUMNS STANDING IN A CIRCLE

In Fig. 195 are sixteen cylinders or columns standing in a circle. First draw the circle on the ground, then divide it into sixteen equal parts, and let each division be the centre of the circle on which to raise the column. The question is how to make each one the right width in accordance with its position, for it is evident that a near column must appear wider than the opposite one. On the right of the figure is the vertical scale _A_, which gives the heights of the columns, and at its foot is a horizontal scale, or a scale of widths _B_. Now, according to the line on which the column stands, we find its apparent width marked on the scale. Thus take the small square and circle at 15, without its column, or the broken column at 16; and note that on each side of its centre _O_ I have measured _oa_, _ob_, equal to s.p.a.ces marked 3 on the same horizontal in the scale _B_. Through these points _a_ and _b_ I have drawn lines towards point of sight _S_. Through their intersections with diagonal _e_, which is directed to point of distance, draw the farther and nearer sides of the square in which to describe the circle and the cylinder or column thereon. I have made all the squares thus obtained in parallel perspective, but they do not represent the bases of columns arranged in circles, which should converge towards the centre, and I believe in some cases are modified in form to suit that design.

CVII

COLUMNS AND CAPITALS

This figure shows the application of the square and diagonal in drawing and placing columns in angular perspective.

[Ill.u.s.tration: Fig. 196.]

CVIII

METHOD OF PERSPECTIVE EMPLOYED BY ARCHITECTS

The architects first draw a plan and elevation of the building to be put into perspective. Having placed the plan at the required angle to the picture plane, they fix upon the point of sight, and the distance from which the drawing is to be viewed. They then draw a line _SP_ at right angles to the picture plane _VV_, which represents that distance so that _P_ is the station-point. The eye is generally considered to be the station-point, but when lines are drawn to that point from the ground-plan, the station-point is placed on the ground, and is in fact the trace or projection exactly under the point at which the eye is placed. From this station-point _P_, draw lines _PV_ and _PV_ parallel to the two sides of the plan _ba_ and _ad_ (which will be at right angles to each other), and produce them to the horizon, which they will touch at points _V_ and _V_. These points thus obtained will be the two vanishing points.

[Ill.u.s.tration: Fig. 197.

A method of angular Perspective employed by architects.

[_To face p. 171_] ]

The next operation is to draw lines from the princ.i.p.al points of the plan to the station-point _P_, such as _bP_, _cP_, _dP_, &c., and where these lines intersect the picture plane (_VV_ here represents it as well as the horizon), drop perpendiculars _bB_, _aA_, _dD_, &c., to meet the vanishing lines _AV_, _AV_, which will determine the points _A_, _B_, _C_, _D_, 1, 2, 3, &c., and also the perspective lengths of the sides of the figure _AB_, _AD_, and the divisions _B_, 1, 2, &c.

Taking the height of the figure _AE_ from the elevation, we measure it on _Aa_; as in this instance _A_ touches the ground line, it may be used as a line of heights.