Distinguishing Concave from Convex

Imagine two blocks of wood, each six inches square. On top of one is a wooden sphere five inches in diameter. The top of the other has a five- inch-wide, half-spherical hole carved into it. The sphere is a convex form; the half-spherical hole is a concave form. Imagine you are looking down at the top of these two blocks and are asked to draw them. In both drawings the contours would look the same, a square with a circle inside. What value clues would you use to distinguish these two objects? How do we distinguish what goes in (concave) from what goes out (convex)?

Convex objects receive reflected light; thus, the darkest part of a shadow on a convex object is not on the object's edge. Concave objects do not receive reflected light: thus, the darkest part of a shadow on a concave form is on its edge. In drawing the convex wooden sphere, include some reflected light on the side opposite the one In by the primary light source. This will place the darkest part of the shadow closer to the middle of the object. The brighter the reflected light, the nearer to the middle of the form the darkest dark will be. In drawing the concave half-sphere, place the darkest dark on the edge nearest the primary light source. The darkest shadows on concave forms are on the side nearest the light.

It is important to note that concave objects can appear, at first glance, as either convex or concave, but that convex objects only appear convex.

We distinguish between concave and convex forms through reflected light. Concave forms receive no reflected light; convex forms do. The darkest dark on a concave form is on the edge closest to the light. Because of reflected light, which appears on the side opposite the light, the darkest dark on a convex form will not be on the edge.



One of these pictures seems to describe a concave form, the other a convex form. Turn the page upside down and see what happens. Concave forms at first glance can appear either convex or concave. Both of these examples are concave.

When depicting convex objects in almost purely frontal light or back light (light sources that least define an object's three-dimensionality), it is useful to include some trace of reflected light in order to enhance the illusion of convexity.

Concave forms are also identified by value shapes. In cone-shaped holes, shadow and light will take the shape of triangles; inside cylinders, they will appear as stripes; in concave spheres, they will appear as portions of crescents or ovals; and inside cubes, they will appear as gradual blends.

Here we compare concave and convex forms. What are the important differences?

At the top of each column is a line drawing that can imply any of the forms shown below it. Value has been used to define the many three-dimensional possibilities. To the right of each form is its profile in silhouette.

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