The Theory and Practice of Perspective Part 14

Let _A_ be the nearest angle touching the base. Draw AV1, AV2. From _A_, raise vertical _Ae_, the height of the cube. From _e_ draw eV1, eV2, from the other angles raise verticals _bf_, _dh_, _cg_, to meet eV1, eV2, fV2, &c., and the cube is complete.

LXV

AMPLIFICATION OF THE CUBE APPLIED TO DRAWING A COTTAGE

[Ill.u.s.tration: Fig. 127.]

Note that we have started this figure with the cube _Adhefb_. We have taken three times _AB_, its width, for the front of our house, and twice _AB_ for the side, and have made it two cubes high, not counting the roof. Note also the use of the measuring-points in connexion with the measurements on the base line, and the upper measuring line _TPK_.

LXVI

HOW TO DRAW AN INTERIOR AT AN ANGLE

Here we make use of the same points as in a previous figure, with the addition of the point _G_, which is the vanis.h.i.+ng point of the diagonals of the squares on the floor.

[Ill.u.s.tration: Fig. 128.]

From _A_ draw square _Abcd_, and produce its sides in all directions; again from _A_, through the opposite angle of the square _C_, draw a diagonal till it cuts the horizon at _G_. From _G_ draw diagonals through _b_ and _d_, cutting the base at _o_, _o_, make s.p.a.ces _o_, _o_, equal to _Ao_ all along the base, and from them draw diagonals to _G_; through the points where these diagonals intersect the vanis.h.i.+ng lines drawn in the direction of _Ab_, _dc_ and _Ad_, _bc_, draw lines to the other vanis.h.i.+ng point V1, thus completing the squares, and so cover the floor with them; they will then serve to measure width of door, windows, &c. Of course horizontal lines on wall 1 are drawn to V1, and those on wall 2 to V2.

In order to see this drawing properly, the eye should be placed about 3 inches from it, and opposite the point of sight; it will then stand out like a stereoscopic picture, and appear as actual s.p.a.ce, but otherwise the perspective seems deformed, and the angles exaggerated.

To make this drawing look right from a reasonable distance, the point of distance should be at least twice as far off as it is here, and this would mean altering all the other points and sending them a long way out of the picture; this is why artists use those long strings referred to above. I would however, advise them to make their perspective drawing on a small scale, and then square it up to the size of the canvas.

LXVII

HOW TO CORRECT DISTORTED PERSPECTIVE BY DOUBLING THE LINE OF DISTANCE

Here we have the same interior as the foregoing, but drawn with double the distance, so that the perspective is not so violent and the objects are truer in proportion to each other.

[Ill.u.s.tration: Fig. 129.]

To redraw the whole figure double the size, including the station-point, would require a very large diagram, that we could not get into this book without a folding plate, but it comes to the same thing if we double the distances between the various points. Thus, if from _S_ to _G_ in the small diagram is 1 inch, in the larger one make it 2 inches. If from _S_ to M2 is 2 inches, in the larger make it 4, and so on.

Or this form may be used: make _AB_ twice the length of _AC_ (Fig. 130), or in any other proportion required. On _AC_ mark the points as in the drawing you wish to enlarge. Make _AB_ the length that you wish to enlarge to, draw _CB_, and then from each division on _AC_ draw lines parallel to _CB_, and _AB_ will be divided in the same proportions, as I have already shown (Fig. 117).

There is no doubt that it is easier to work direct from the vanis.h.i.+ng points themselves, especially in complicated architectural work, but at the same time I will now show you how we can dispense with, at all events, one of them, and that the farthest away.

[Ill.u.s.tration: Fig. 130.]

LXVIII

HOW TO DRAW A CUBE ON A GIVEN SQUARE, USING ONLY ONE VANIs.h.i.+NG POINT

_ABCD_ is the given square (Fig. 131). At _A_ raise vertical _Aa_ equal to side of square _AB_, from _a_ draw _ab_ to the vanis.h.i.+ng point.

Raise _Bb_. Produce _VD_ to _E_ to touch the base line. From _E_ raise vertical _EF_, making it equal to _Aa_. From _F_ draw _FV_. Raise _Dd_ and _Cc_, their heights being determined by the line _FV_. Join _da_ and the cube is complete. It will be seen that the verticals raised at each corner of the square are equal perspectively, as they are drawn between parallels which start from equal heights, namely, from _EF_ and _Aa_ to the same point _V_, the vanis.h.i.+ng point. Any other line, such as _OO_, can be directed to the inaccessible vanis.h.i.+ng point in the same way as _ad_, &c.

_Note._ This is only one of many original figures and problems in this book which have been called up by the wish to facilitate the work of the artist, and as it were by necessity.

[Ill.u.s.tration: Fig. 131.]

LXIX

A COURTYARD OR CLOISTER DRAWN WITH ONE VANIs.h.i.+NG POINT

[Ill.u.s.tration: Fig. 132.]

In this figure I have first drawn the pavement by means of the diagonals _GA_, _Go_, _Go_, &c., and the vanis.h.i.+ng point _V_, the square at _A_ being given. From _A_ draw diagonal through opposite corner till it cuts the horizon at _G_. From this same point _G_ draw lines through the other corners of the square till they cut the ground line at _o_, _o_.

Take this measurement _Ao_ and mark it along the base right and left of _A_, and the lines drawn from these points _o_ to point _G_ will give the diagonals of all the squares on the pavement. Produce sides of square _A_, and where these lines are intersected by the diagonals _Go_ draw lines from the vanis.h.i.+ng point _V_ to base. These will give us the outlines of the squares lying between them and also guiding points that will enable us to draw as many more as we please. These again will give us our measurements for the widths of the arches, &c., or between the columns. Having fixed the height of wall or dado, we make use of _V_ point to draw the sides of the building, and by means of proportionate measurement complete the rest, as in Fig. 128.

LXX

HOW TO DRAW LINES WHICH SHALL MEET AT A DISTANT POINT, BY MEANS OF DIAGONALS

This is in a great measure a repet.i.tion of the foregoing figure, and therefore needs no further explanation.

[Ill.u.s.tration: Fig. 133.]

I must, however, point out the importance of the point _G_. In angular perspective it in a measure takes the place of the point of distance in parallel perspective, since it is the vanis.h.i.+ng point of diagonals at 45 drawn between parallels such as _AV_, _DV_, drawn to a vanis.h.i.+ng point _V_. The method of dividing line _AV_ into a number of parts equal to _AB_, the side of the square, is also shown in a previous figure (Fig. 120).

LXXI

HOW TO DIVIDE A SQUARE PLACED AT AN ANGLE INTO A GIVEN NUMBER OF SMALL SQUARES