# Learn to Draw > Advanced perspective

Looking with one eye is thus better for seeing surfaces in one plane. Besides helping you to select your subject matter to the best advantage, the vertical edges of the viewer divide up the horizon, and you can transfer this important check on proportion onto your drawing. You must then find the vanishing points. Take several related receding lines, as steep as possible, and carry them as far as the horizon. They must come together at one point. To find the vanishing point, you need only one receding line, but it is safer to check with several.

The second vanishing point is found in a similar way, but it often lies lies outside the area of the picture, as in the illustrated example with vanishing lines drawn in. Since it is not practical to extend the size of the drawing, the slope of the lines vanishing beyond the edge must be judged. Separate vanishing points have to be worked out for streets sloping up or down. If a sloping street runs parallel to one of the receding lines of a building, its vanishing point will lie on a perpendicular dropped from the appropriate vanishing point of the building. Then all that needs determining is its height above or below the eye-level horizon.

So far, perspective is fairly simple, but every perspective problem has difficulties which need special consideration and guiding lines for its solution. The perspective of round or protruding or receding objects, for example, has its particular problems, and there are others in the rendering of reflections in water.

In the treatment of the perspective of round bodies, the sphere always remains a circle. A circular surface, however, has to be altered according to the same laws of perspective as employed elsewhere. Its alteration is best determined by surrounding it with a square. First draw the alteration in the square. Then join the center of the circle, which is also the center of the square, to the two vanishing points of the plane in which the circle lies.

The two lines to these points will quarter both square and circle. They are thus diameters, which meet the tangents now to be made. These are each formed from two further vanishing lines which form the quartered square. From this it is not very difficult to draw in the foreshortened circle. It must always be an ellipse in the geometric sense and not the kind of egg shape which often appears! Mistakes are most easily spotted by tracing off the ellipse and examing it without its guide lines.

If you have to draw a pillar, imagine it to be transparent, and first draw the base and top surfaces before putting in the vertical joining lines. This is the best method for ridges too, such as the overhanging eaves on a house. It is best to imagine the main cube as transparent and draw the two diagonals onto the wall, since you have to intersect the protruding corners. When you have judged the distance of the edge of the eave from the corner of the house, you find the points of the remaining corner with vanishing lines. The intersection of the diagonals is also the base line of the perpendicualr to the center of the roof; for example, the apex of a tent roof or a steeple.

Reflections in water are always much admired by the layman and considered the mark of very great skill. Yet mirror perspective in a landscape is easily mastered with a little thought, since the reflecting water is always horizontal. Sloping mirrors, such as those hanging from a wall, make matter so much more complicated from the construction point of view, and require very close observation.

Water reflections can easily be finished at home once the real object is taken from nature. The house in our drawings stands slightly above the level of the water, which you can then imagine as lying below the house. You continue the lines of the corners of the house to the water level and from there draw downwards the corner lines of the reflected house. In reflections all mirrored points lie vertically under the thing reflected, and the vanishing lines of the objects run to vanishing points which correspond with those of the reflection. The only difficulty is in judging the height of the building, or whatever the subject is, above the water surface, as there are rarely any definite control points.

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