Linear Perspective.
It should be mentioned that this subject is outside the limits of mechanical drawing, which only deals with objects that can be measured, projected or dimensioned to an accurate scale.
But, in rounding out the more formal subjects it is well to look a little outside the rigid lines of mechanics into the methods of nature, for no system of teaching drawing is complete that does not include some explanations for sketching from nature—the objects being always around the student, the eye always clear to see and the hand only needing the training to make permanent the impressions received.
The word perspective means tosee through; the word perspective being derived from the Latin wordperspicere, to look through, hence, perspective is a science which teaches us toseecorrectly and enables us to represent theappearanceof anything we may wish to draw; care should be taken in perspective drawing, to select objects interesting in themselves, and the best specimens of their class, so as to cultivate taste, while they at the same time afford useful and instructive drawing lessons.
The meaning of the term linear perspective is a line view; the previous examples have been composed of surfaces placed fronting the eye; perspective is the science which treats of the changes of form produced by viewing them in various oblique positions.
The slightest alteration ofpositionwill change theappearanceof an object; this can be easily shown—for illustration take a coin, the actual shape of which is a perfect round; or, strictly speaking, a circle. If we take the coin between the thumb and the first finger, holding it in an upright position, and exactly facing the eyes, as inFig. 296, it appears of its true form, viz., a circle. If we alter its position, balancing it upon the thumb, in a level position, with its edge directly opposite the eye, as inFig. 297, its appearance is changed, and what we know to be really a circle, appears to us as a straight line.
PerspectiveFig. 296.—Fig. 297.—Fig. 298.
Fig. 296.—Fig. 297.—Fig. 298.
Now, still balancing the coin upon the thumb, but changing its position with regard to the eye, by holding it a little lower than in the last position, that is slightly beneath the level of the eye, as infig. 298, we see both the edge and the surface, the coin now appearing neither a circle nor a straight line, but a curved figure of an elliptical form. Thus the same coin held in three different positions has assumed three different shapes.
Let us take two coins of the same size, holding (in the position shown atfig. 296) one in each hand. Now, closing one eye, (which will make the experiment more clear), hold one coin out at arm’s length, and the other at about the distance of a foot from the eye. On comparing them, we find that the coin which is further from the eye appears less than the nearer one. We know that the coins are really equal in size, yet one appears smaller than the other.
We thus see that when we change the position of an object, we have as a consequence a change of appearance; also that the change of appearance may affect both the shape and the size of the object.
These diversities of appearance may be remarked in everything around us. We can observe them in the street by looking at a building from different points of view, or by comparing the apparent sizes of the street lamps; in the railway station, by watching the arriving or departing train; and at sea, by noticing the vessels as they approach, or as they retire, ultimately vanishing from our sight in that line where the sea and sky appear to meet.
All these interesting variations of appearance are in strict accordance with the laws ofGEOMETRYandOPTICS. The former subject has been enlarged upon beginning withpage 81of this work, where a line, a point, an angle, etc., are defined; other terms are explained atpage 41and the following pages; to these we add a few definitions essential to the subject.
A PLANEis a surface which is perfectly even and flat; to use a familiar illustration, a plane is like the surface of a sheet of plate glass; recollect particularly, that a surface which is at all curved, is not a plane.
TheGROUND-PLANEis the plane on which we stand; thebase-lineis an imaginary line passing through the middle of the feet as we stand square and erect; and thevertical planeis supposed to stand on the base-line and perpendicular to it.
PerspectiveFig. 299.—Seepage 255.
Fig. 299.—Seepage 255.
Planes are parallel to each other when they are throughout their entire surfaces the same distance apart.
View planeFig. 300.
Fig. 300.
THE PERSPECTIVE PLANEis an upright square of glass, usually framed like a picture, with a base, so that it can stand up alone. This is placed between the eye of the spectator and the subject to be drawn, and as the drawing is sometimes made directly upon it, it is sometimes called thePictureor thePlane of the Picture.
HouseFig. 301.
Fig. 301.
HORIZONTALmeans perfectly level, like the surface of still water. We must be careful to understand perfectly the difference between the terms “level” and “even” or “flat.” A surface may be even or flat, without being level. Thus the wall is even and flat, but it is upright, not level; level means a fixed, constant position.
Infig. 301a house is shown in perspective in which the lineH Lis the line of the horizon andV Pisthe,—
VANISHING POINT.—The vanishing point is familiarly represented by the rails on a trolley track on a straight road, which seem to approach each other in the distance, as shown infig. 302atV P.
PerspectiveFig. 302.
Fig. 302.
All parallel lines seen in perspective appear to meet in the same vanishing point.
The value of the vanishing point may be seen in the view of a wooden house,fig. 303, where it (V P) gives direction to the retiring lines of the roof, side planks and door.
PerspectiveFig. 303.
Fig. 303.
POINT OF SIGHT.—This is that point in the eye where the lines or rays from the object cross each other, as shown atPinfig. 305, also infig. 299atS.
VERTICALmeans perfectly upright. If we attach a piece of thread to a weight, a small piece of lead forexample, and hold the thread with the lead hanging downwards, the thread will fall in an upright or vertical position.
PARALLELlines are said to be parallel to each other when they are throughout their whole lengths the same distance apart.
PERPENDICULAR.When one straight line, meeting another, makes the angles at the point of contact equal, each of the angles is called a right angle, and the lines are said to be perpendicular to each other. Remember especially that perpendicular and vertical have not the same meaning. Vertical means an unvarying upright position. Perpendicular means that one line or plane meets another line or plane at right angles.
Thefig. 295onpage 246is a study in perspective, showing a water reflection. As rays from every visible part of the object are reflected, all following the same law, the reflection will appear to the eyeinverted, and of thesame size as the object. The arch itself forms the upper half of a hollow cylinder, and the reflection forms the lower half. The reflection shows much more of the interior of the arch than can be seen directly. The leaning tree, the boy fishing, and the receding banks, all are seen in accordance with the laws of reflection and perspective.
THE HORIZONTAL LINE, THE POINT OF SIGHT AND THE VANISHING POINTSare the principal items. These should be studied in every room and during every walk, and the more pleasing accidents of form stored in the mind or committed to paper for future use.
EyeFig. 304.
Fig. 304.
OPTICS, the science of sight, gives us the following laws:
1. That we see by the agency of light.
2. That light passes from objects to our eyes.
3. That light travels in straight lines, which are called Visual Rays.
The human eye may be briefly described as a chamber of a spherical or globular form, with a circular opening in front. This circular opening is called the pupil, and through it the visual rays pass to the interior of the eye. The visual rays, passing from space in all directions through the small pupil, are received upon what may be called the interior wall of the globular chamber forming the eye (seefig. 305). This interior wall is called the retina, and upon it the impressions of external objects are received, just as they are received upon a screen in a dark chamber. These impressions are conveyed by the optic nerve from the retina to the brain.
In front of the pupil is a segment of a small sphere, composed of the cornea and the aqueous humor, both of which are transparent, and from their shape and density have a convergent effect upon the rays passing through them.
Behind the pupil is the transparent crystalline lens, which, from its shape and its elasticity, is a powerful agent in aiding the convergence of the rays, and in bringing objects at various distances to a clear focus upon the retina.
EyeFig. 305.
Fig. 305.
The pupil has the power of contraction and dilation, which is influenced by the quantity of light entering the eye, but when it is dilated to the utmost itssize is very small in comparison with the great chamber forming the body of the eye.
Infig. 305we have a rough sectional diagram of the eye and an object in front of it. This object, an arrow, is seen by means of the visual rays proceeding from it, the principal two of which are shown. The visual ray fromApasses through the pupil and is received upon the retina ata. In the same way the visual ray fromBpasses through the pupil and is received upon the retina atb. It will thus be seen that the impressions or images received upon the retina are inverted; but, by long reason and experience, the mind has acquired the habit of determining the real positions of objects, and does not, though the image is so received, imagine them to be upside down.
It will also be observed, in the same way, that that portion of an object which is upon the right will be pictured upon the retina upon the left, andvice versa, but the mind, for the reasons before stated, never imagines the object to be reversed. This fact is another proof that, as mentioned at the commencement of our study, to see accurately is a matter of education and practice.
And first of Optics; it was asserted,page 252, that we see by the agency of light which passes from objects to our eyes in straight lines which are called Visual Rays.
We see by the agency of light, as all objects, except such as may be styled self-luminous, when placed in a dark chamber are not perceivable by us, except by touch, smell or hearing; we cannotseethem; they are invisible. But when, by removing a shutter or igniting a flame, we introduce something to the chamber which was not present when the chamber was dark, we become at once conscious of the appearance of the object, we perceive it by the sense of sight.
This something which must always be present to enable us to see, is called Light; all objects are made visible to the sense of seeing by its agency.
Without light, natural or artificial, it would be impossible to distinguish one object from another.
ExperimentFig. 306.
Fig. 306.
That the Visual Rays pass from objects in straight lines to the eye may be proved by the following experiment (seefig. 306):—Pierce two screens with a large pin, and place them so that the holes are in a straight line with a flame, as the light of a candle or lamp. On fixing the eye to one of these holes we are able to see the flame; but if we slightly move the flame, one of the screens, or the eye, the flame is no longer visible. To be visible, the flame, the holes in the screens, and the eye must all be in the same straight line. Seefig. 306.
Infig. 299the picture plane is represented by the rectangleW X Y Z. Although the picture plane is here shown as a rectangle, it may be of any shape or of any size.
The observer is atS, looking through the picture plane at the crossR C O H. The observer is standing upon a horizontal surface, which is called the ground plane. If we are in a room, the window may be called a picture plane and the floor a ground plane.
The picture plane rests, as it were, upon the ground plane, in a line which passes fromYtoZ. Thetwo planes meet or intersect in this line, which is called the ground line. The ground line is sometimes called the picture line, or the measuring line.
The visual rays, by means of which the observer sees the cross, will, in their course from it to the eye, pass through the picture plane. These visual rays will intersect the picture plane in a number of points, and if we mark the true positions of these points the result will be a perspective image of the cross.
The rays are shown passing from the cross to the eye of the observer, and meeting the picture plane in pointsr,c,o,h;rbeing joined too, andctoh, we have the perspective image of the cross as it would appear to the observer atS. Of course an infinite number of rays proceed from the cross to the eye of the observer; but it is quite evident that we need only consider those proceeding from the extremities of the object.