# Basic Three-Dimensional Forms

At the three-dimensional level there are five basic forms: the sphere, the cone, the cylinder, the torus, and the cube. All three-dimensional objects can be constructed from the parts of these five forms. Things with flat surfaces and abrupt changes in surface plane, like the corners of a house or the hexagonal head of a bolt, relate to cubes. Curved planes, like the rounded arms of a sofa or the ripples of a flag, relate to cones or cylinders. Bumps, dents, and hills relate to spheres. A barbecue is composed of spheres and cylinders; a mailbox is a half-cylinder and a cube. The rounded circular rim of a cup relates to the torus, which is also the basic form of a coiled snake or chain links.

In studying the basic forms, you must also consider how they appear in the negative. For example, a crater is a negative sphere; a rut or a groove is a negative cylinder; an empty rectangular swimming pool is part of a negative cube.

The Sphere
The sphere is the easiest of the forms to draw because no matter what your angle of view, it is always drawn as a circle. Nearly pure examples of spherical forms are oranges, the moon, soccer balls, and bubbles.

The sphere drawn in line is simply a circle.

The Cone
The cone is the next easiest to draw. It is simply a V with a circle between its ends. When seen at an angle, the circle is an ellipse. A line drawn from the center of the circular base to the point of the V is the cone's midline. If the cone's base is perpendicular to the midline, the cone's sides are drawn from the narrow ends of the ellipse. If not, the base of the cone will be seen as though cut at an angle. Nearly pure examples of cone forms are pencil points, Christmas trees, ships' masts, and witches' hats.

A cone is drawn as a triangle with an ellipse on one end. A line drawn from the middle of the ellipse to the point of the cone is called the midline. If a line drawn through the widest part of the ellipse is not perpendicular to the midline, the cone will not stand up straight.

Complex forms can be seen as combinations of the basic forms.

The Cylinder
The cylinder is drawn with parallel lines for the sides and circles between the parallel lines. (As with the cone, the circles become ellipses when seen at an angle.) If the top and bottom of the cylinder are perpendicular to its sides, the parallel lines are drawn from the narrow ends of the ellipses. A line from the center of one ellipse to the center of the other is the cylinder's midline. A line drawn through the widest part of the ellipse will be perpendicular to the midline of the cylinder. It is important to remember that although the top and bottom surfaces of a cylinder are parallel, they are not drawn as identical ellipses. The closer one of these surfaces IS to your eye level (also known as the horizon line), the narrower the ellipse will appear; the farther from eye level, the rounder the ellipse will appear. (For more on this, see the chapter on elliptical perspective.) A foreshortened cylinder-one that is drawn narrower at one end to give the illusion of projection or extension into space-will appear to have sides that are not parallel, because they are drawn in perspective. In perspective, parallel lines appear to converge as they recede into space. Nearly pure examples of cylindrical forms are cans, broom handles, and curtain rods.

A cylinder is drawn as a pair of parallel lines with an ellipse at each end between the parallel lines. The ellipse nearer to your eye level will appear narrower than the one farther away from your eye level.

In this illustration cylinder #1, at left, is drawn correctly, while the other three are wrong. In #2, the top and bottom ellipses are the same, but this cannot be the case because they are seen at different levels. Cylinder #3 is wrong because even though it sits on a flat surface, the bottom should not be drawn flat because the bottom of the form itself is curved. In cylinder #4, the top ellipse should be narrower because it is closer to our eye level than the bottom ellipse.

The Torus
The torus is a doughnut shape. Seen from above, it is just two circles, one within the other. From a three-quarter view, the middle of the external edge is the middle portion or an ellipse; the ends are portions of two small circles. The inside of the torus (the hole in the doughnut) is depicted by two arcs that form an ovoid (oval-like) shape with pointed ends. Nearly pure examples of a torus are a bagel, a coiled garden hose or snake, and a chain link.

A torus is drawn either as two ellipses, one within the other, or as an ellipse with two opposing arcs forming a pointed ellipse within. Seen (rom the side, a torus con be two parallel fines with a half- Circle on either end.

The Cube
A cube is a box with six square sides. Pure examples of cubes are dice, filing cabinets, sheds, and washing machines. The cube is the most difficult form to draw correctly because it involves linear perspective. A more thorough explanation of linear perspective will be presented later in this book, but on the following pages you will find some basic concepts.

A cube is a six-sided form; each side is a flat square. This is the most difficult of the five basic forms to draw because it requires an understanding of linear perspective.