7
Rendering Tonal Values

This chapter focuses on the principles that regulate how well a composition of lines and shapes conveys the illusion of a three-dimensional construction or spatial environment on a two-dimensional surface, be it a sheet of paper, an illustration board, or a computer monitor. While lines are essential to the task of delineating contour and shape, there are also visual qualities of light, texture, mass, and space that cannot be fully described by line alone. In order to model the surfaces of forms and convey a sense of light, we rely on the rendering of tonal values.

Tonal Values

Vision results from the stimulation of nerve cells in the retina of the eye, signaling patterns of light intensity and color. Our visual system processes these patterns of light and dark, and is able to extract specific features of our environment—edges, contours, size, movement, and color. If seeing patterns of light and dark is essential to our perception of objects, then establishing contrasts in value discernible to the eye is the key to the graphic definition of light, form, and space.

Through the interplay of tonal values we are able to:

Describe how light reveals the form of objects.
Clarify the arrangements of forms in space.

Depict the color and texture of surfaces.

Creating Tonal Values

Using the traditional media of pencil and pen-and-ink to make dark marks on a light surface, there are several basic techniques for creating tonal values.

Hatching
Crosshatching
Scribbling
Stippling

These shading techniques all require a gradual building up or layering of strokes or dots. The visual effect of each technique varies according to the nature of the stroke, the medium, and the texture of the drawing surface. Regardless of the shading technique we use, we must always be fully aware of the tonal value being depicted.

Because tonal value is expressed primarily through the relative proportion of light to dark areas on the drawing surface, the most important characteristic of these techniques is the spacing and density of the strokes or dots.

The law of simultaneous contrast states that the stimulation of one tonal value is projected instantaneously on a juxtaposed value. For example, a tonal value superimposed upon a darker tone will appear lighter than the same value set against a lighter tone.

Secondary characteristics include the visual texture, grain, and direction of the strokes.
When rendering the darkest values, we should be careful not to lose the white of the paper. Covering the paper surface entirely can cause a drawing to lose depth and vitality.

Hatching

Hatching consists of a series of more or less parallel lines. The strokes may be long or short, mechanically ruled or drawn freehand, and executed with either a pen or a pencil on smooth or rough paper. When spaced close enough together, the lines lose their individuality and merge to form a tonal value. We therefore rely primarily on the spacing and density of lines to control the lightness or darkness of a value. While thickening the linear strokes can serve to deepen the darkest values, using too thick of a line can result in an unintentional coarseness and heaviness of texture.

By applying additional layers of diagonal strokes at only slightly different angles to the preceding sets, we can build up the density, and therefore the tonal value, of an area. Maintaining the diagonal direction of the strokes in this manner avoids confusion with the underlying drawing and unifies the various tonal areas of a drawing composition.

Do not attempt to produce a range of values by varying the grade of lead. Be careful not to use too dense a grade of lead or press so hard that the pencil point embosses the drawing surface.
Unlike a pencil line, the tonal value of an ink line remains constant. You can only control the spacing and density of the hatching.

Crosshatching

Crosshatching uses two or more series of parallel lines to create tonal values. As with hatching, the strokes may be long or short, mechanically ruled or drawn freehand, and executed with either a pen or a pencil on smooth or rough paper.

Scribbling

Scribbling is a shading technique that involves drawing a network of random, multidirectional lines. The freehand nature of scribbling gives us great flexibility in describing tonal values and textures. We can vary the shape, density, and direction of the strokes to achieve a wide range of tonal values, textures, and visual expression.

By maintaining a dominant direction, we produce a grain that unifies the various areas and shades of value.
As with hatching, we have to pay attention to both the scale and density of the strokes, and be aware of the qualities of surface texture, pattern, and material they convey.

Stippling

Stippling is a technique for shading by means of very fine dots. Applying stippling is a slow and time-consuming procedure that requires the utmost patience and care in controlling the size and spacing of the dots. The best results occur when using a fine-tipped ink pen on a smooth drawing surface.

We use stippling to establish tonal values in pure-tone drawings—drawings that rely on value alone to define edges and contours. The procedure involves applying stippling over faintly drawn shapes of the areas to be toned.

Resist the temptation to deepen a value by enlarging the dots. If the scale of the dots is too large for the toned area, too coarse a texture will result.

Digital Tonal Values

2D drawing and 3D modeling programs usually permit colors and tonal values to be selected from a menu or palette and assigned to the surfaces of forms. Image-processing software further allows the creation and application of visual textures, some of which mimic the traditional techniques outlined on the previous pages.

Shown on this and the facing page are two digital examples using simple gray tones and gradients. The first illustrates a line-and-tone technique to model the forms.

This example of a pure tone drawing relies primarily on the selection and arrangement of tonal values to model the three-dimensional qualities of forms.

Because there are no lines in the drawing, we must rely on discernible contrasts in tonal value to define the planar corners and spatial edges of the forms.

Value Scale

White represents the lightest possible value and black the darkest. In between exists an intermediate range of grays. A familiar form of this range is represented by a gray or value scale having ten equal gradations from white to black. It is worthwhile to practice producing both a stepped series and a graduated scale of tonal values using a variety of media and techniques.

Note that a series of dots rather than a line defines the edge of the field.
It is also possible to execute a gray scale on a tinted or colored surface, using a black pencil to define values darker than the tone of the surface and a white pencil to establish the lighter values.

Tonal Values and Texture

We use the term “texture” most often to describe the relative smoothness or roughness of a surface. It can also describe the characteristic surface qualities of familiar materials, as the hewn appearance of stone, the grain of wood, and the weave of a fabric. This is tactile texture that can be felt by touch.

Our senses of sight and touch are closely intertwined. As our eyes read the visual texture of a surface, we often respond to its apparent tactile quality without actually touching it. We base these physical reactions on the textural qualities of similar materials we have experienced in the past.

Whenever we use hatching or stippling to create a tonal value, we simultaneously create visual texture.
Likewise, as soon as we begin to describe the nature of a material with lines, we simultaneously create a tonal value.
We should always be aware of this relationship between tonal value and texture, whether smooth or rough, hard or soft, polished or dull. In most cases, tonal value is more critical than texture to the representation of light, shade, and the way they model forms in space.

Modeling Form

“Modeling” refers to the technique of rendering the illusion of volume, solidity, and depth on a two-dimensional surface by means of shading. Shading with tonal values extends a simple drawing of contours into the three-dimensional realm of forms arranged in space.

Since the definition of edges gives rise to shape recognition, we look to edges to discover the configuration of the surfaces of a three-dimensional form. We must therefore be careful how we define the nature of the edge or boundary wherever two shapes of contrasting values meet. The skillful manipulation of tonal edges is critical to defining the nature and solidity of a surface or object.

Conveying Light

While tonal values can imply depth on a flat drawing surface, we turn to light to more vividly describe the three-dimensional qualities of forms and spaces in our environment. Light is the radiant energy that illuminates our world and enables us to see three-dimensional forms in space. We do not actually see light but rather the effects of light. The way light falls on and is reflected from a surface creates areas of light, shade, and shadow, which give us perceptual clues to the surface's three-dimensional qualities.

The light-and-dark patterns we see emanate from the interaction of light with the objects and surfaces around us. Within these patterns of light and dark shapes, we can recognize the following elements:

Modeling and Lighting

Digital Lighting

A range of digital techniques exist for modeling and simulating the lighting of three-dimensional forms and spaces. The simplest approach is ray casting.

Ray Casting

Ray casting is a technique that analyzes the three-dimensional geometry of forms and determines the illumination and shading of surfaces based on their orientation to an assumed light source. The primary advantage of ray casting is the speed with which an illuminated three-dimensional image or scene can be generated, often in real-time. This makes ray casting a useful tool in preliminary design to study the solar consequences of the massing and composition of building forms and the shadows they cast.

Ray casting, however, does not take into account the way light travels after intersecting a surface and therefore cannot accurately render reflections, refractions, or the natural fall off of shadows. For this, ray tracing is necessary.

Ray Tracing

As a ray of light travels from its source to a surface that interrupts its progress, it may be absorbed, reflected, or refracted in one or more directions, depending on the material, color, and texture of the surface. Ray tracing is a digital technique for tracing these paths to simulate the optical effects of illumination.

Local illumination is a basic level of ray tracing that is limited to direct illumination and the specular reflections of light rays. While local illumination does not take into account the diffuse inter-reflection of light among the surfaces in a three-dimensional space or scene, some ray tracing programs can approximate this ambient light in their lighting algorithms.

A better predictor of how a space would be illuminated by any number of light sources is global illumination. Global illumination techniques use sophisticated algorithms to more accurately simulate the illumination of a space or scene. These algorithms take into account not only the light rays that are emitted directly from one or more sources. They also track the light rays as they are reflected or refracted from one surface to another, especially the diffuse inter-reflections that occur among the surfaces in a space or scene. This enhanced level of simulation comes at a cost, however. The process requires time and is computationally intensive, and should therefore be used only when appropriate to the design task at hand.

Tonal Values in Architectural Drawings

The drawings on this and the following seven pages illustrate how we can use tonal values to enhance spatial depth and focus attention in various types of architectural drawing.

We use tonal values in site plan drawings to define the relationship between the form of a building and its spatial context. These two drawings of the Piazza San Marco in Venice illustrate how the tonal contrast can be achieved either by rendering the building as a dark figure against a light background or by reversing the figure-ground relationship and rendering the tonal values of the site.
See also the site plans illustrated on pages 67 and 68.

The principal use of tonal values in floor plans is to emphasize the shape and arrangement of cut elements.

Rendering the floor surface in a plan drawing with a material pattern will give that plane both a textural and a tonal value. These values can effectively isolate and provide a base for elements that are situated above the floor plane.

When a plan drawing has several floor levels within its field, varying the intensity of the tonal values can help convey the relative depth of the floor planes below the plan cut. The lower the floor plane, the darker its value.

If the space defined in a plan drawing is given a tonal value along with the surrounding field, the cut elements can be left white or be given a very light value. Be sure, however, that there is sufficient contrast to emphasize the dominance of the cut elements. If necessary, outline the cut elements with a heavy line weight.
For more examples of how tonal values can be used in floor plans.

We use tonal values in section drawings to establish contrast between the cut elements and what is seen in elevation beyond the plane of the cut.

The top drawing uses a heavy line weight to outline the cut elements.
The center drawing projects the cut elements forward with a dark value.
The bottom drawing reverses the value system and renders the cut elements as light figures against a dark field.
Note that in the latter two cases, the relationship of the building to the supporting ground mass is clearly indicated by the manner in which the ground is given a value similar to that of the cut elements of the building.

We use contrasting tonal values in elevation drawings to define layers of spatial depth. The most important distinctions to establish are between the cut through the ground plane in front of the building elevation and the building itself, and between the building elevation and its background.

First, contrasting values for the foreground and background are established.
Elements are projected forward by having their tonal contrasts defined more sharply and by having their materials, textures, and details drawn more distinctly.
Areas are pushed into the background by diminishing contrast and detail.

In paraline drawings, the three-dimensional nature of forms and the spaces they define are more readily apparent than in plan, section, and elevation drawings. Tonal values are therefore used primarily to articulate the orthogonal relationship between horizontal and vertical planes.

It is usually better to apply tonal values to the horizontal rather than the vertical planes of a paraline drawing. Toning the horizontal planes not only establishes a visual base for the drawing but also aids in defining the shape and orientation of the vertical planes.
Indicate cuts to reveal the interior spaces of a building with either a contrasting line weight or a change in tonal value.

In perspective drawings, we use tonal values to enhance spatial depth, define the drawing field, and develop focus.

Perspective drawings should use the principles of atmospheric perspective to enhance the sense of spatial depth.

Values are lightened and tonal contrasts are softened to push elements back.
Values are darkened and tonal contrasts are sharpened to bring elements forward.

These exterior perspectives employ a value system similar to that used in elevation drawings.

Above, the contour drawing of the building and foreground contrasts with the darker field of the background.
In the drawing below, the building and foreground are rendered in some detail to contrast with a lighter, more diffuse background.

Turn to page 128 to see how contrasting the cut elements of a section perspective helps to isolate and frame the space seen beyond in perspective.

The depth of the interior perspective above is enhanced by contrasting light foreground elements with a continuous darker wall in the background.

In the drawing to the right, dark foreground elements help frame what is seen beyond.

Digital Rendering

Although improvements continue to be made, the rendering of atmospheric and texture perspective remains problematic in many graphics programs. Image-processing software, however, allows us to modify digital drawings and simulate the pictorial effects of atmospheric and texture perspective.

Shade and Shadows

“Shade and shadows” refers to the technique of determining areas in shade and casting shadows on surfaces by means of projection drawing. The depiction of light, shade, and shadow can model the surfaces of a design, describe the disposition of its masses, and articulate the depth and character of its details.

The light source for architectural shade and shadows is assumed to be the sun. The sun is so large and distant a source that its light rays are considered to be parallel.
The sun angle is the direction of the sun's rays, measured in terms of either bearing or azimuth and altitude.
Bearing is a horizontal angular direction expressed in degrees east or west of a standard north or south direction.
Azimuth is a horizontal angular distance, measured clockwise, of a bearing from due north.
Altitude is the angular elevation of the sun above the horizon.

A shade line or casting edge separates an illuminated surface from one in shade.
A shadow line is the shadow cast by a shade line on a receiving surface.
A shadow plane is a plane of light rays that passes through adjacent points of a straight line.
Every part of an object in light must cast a shadow. The corollary to this is that any point that is not in light cannot cast a shadow because light does not strike it.
A shadow is visible only when there is an illuminated surface to receive the shadow. A shadow can never be cast on a surface in shade, nor can it exist within another shadow.

Multiview Drawings

The casting of shade and shadows is especially useful to overcome the flatness of multiview drawings and enhance the illusion of depth. It generally requires two related views—either a plan and elevation or two related elevations—and the transferring of information back and forth from one view to the other.

Digital Shade and Shadows

While the drafting of architectural shade and shadows in multiview drawings assumes the conventional direction of sunlight to be the diagonal of a cube, 3D modeling software typically includes the ability to specify the direction of sunlight according to the hour of the day and the time of the year, and to cast shade and shadows automatically. This feature can be especially useful in the schematic design phase to study the form of a building or the massing of a building complex on a site and to evaluate the impact of the shadows they cast on adjacent buildings and outdoor areas.

The digital technique for determining what surfaces are in shade and the shapes of the shadows cast in a three-dimensional image or scene is referred to as ray casting. While efficient and useful for preliminary design studies, ray casting does not take into account the way the light rays from an illuminating source are absorbed, reflected, or refracted by the surfaces of forms and spaces. For a visual comparison of digital lighting methods.

The shadow of a straight line is the intersection of its shadow plane with the surface receiving the shadow. The hypotenuse of the triangular shadow plane establishes the direction of the light rays, and its base describes their bearing.

The shadow of a curved line or irregular shape is the line that connects the shadows of critical points along the curve or shape.

The shadow of a plane figure on a parallel plane is identical in size and shape to the figure.

The shadow of any polygonal figure on a plane is circumscribed by the shadows of its shade lines.
The shadow of a circle is the intersection of the cylinder of light rays passing through adjacent points of the circle and the surface receiving the shadow. The shape of the shadow is elliptical since the section of a cylinder cut by any plane oblique to its axis is an ellipse. The most convenient method of determining the shadow of a circle is to determine the shadow of the square or octagon circumscribing the given circle, and then to inscribe within it the elliptical shadow of the circle.

The shadow cast by a solid is bound by the shadows of the shade lines of the object. It is usually best to begin by determining the shadows of significant points in the form, such as the end points of straight lines and the tangent points of curves.
Note that shadows of parallel lines are parallel when they fall on the same plane or on parallel planes.
The orthographic projection of a straight line perpendicular to the plane of projection is a point. The shadow of the line will appear to be straight regardless of the shape of the surface receiving the shadow.

In clarifying the relative depth of projections, overhangs, and recesses within the massing of a building, shade and shadows can also model the relief and texture of surfaces.

Most often simply use a flat or slightly textured field of gray to indicate shade and shadows.
An alternate method is to intensify the texture or pattern of a material so that we do not lose a sense of the material that is in shade or receiving the shadow.

We use shade and shadows in site plans to convey the relative heights of building masses as well as to reveal the topographical nature of the ground plane on which the shadows are cast.

The intent of cast shadows is not to render the actual condition of sunlight at a specific point in time. Rather, they merely indicate the relative heights of the parts of a building above the ground plane.
A change in shadow depth can indicate either an increase in building height or a rise in the ground slope.

Shade and shadows are not usually employed in floor plans and building sections. However, they may be used to emphasize the cut elements and the relative heights of objects within the space.
In a building section, shadows clarify the projection of cut elements beyond surfaces seen in elevation.

Paraline Views

Shade and shadows are not often used in paraline drawings. However, they can be used effectively to distinguish between horizontal and vertical elements, and the three-dimensional nature of their forms.

It is relatively easy to visualize the three-dimensional relationships between light rays, shade lines, and cast shadows in paraline views because they are pictorial in nature and display the three major spatial axes simultaneously.
Parallel light rays and their bearing directions remain parallel in a paraline drawing.

To construct shade and shadows in a paraline drawing, it is necessary to assume a source and direction of light. Deciding on a direction of light is a problem in composition as well as communication. It is important to remember that cast shadows should clarify rather than confuse the nature of forms and their spatial relationships.

There are occasions when it may be desirable to determine the actual conditions of light, shade, and shadow. For example, when studying the effects of solar radiation and shadow patterns on thermal comfort and energy conservation, it is necessary to construct shades and shadows using the actual sun angles for specific times and dates of the year.

For ease of construction, the bearing direction of the light rays is often parallel with the picture plane, and they emanate from either the left or the right.
Consequently, the altitude of the light rays appears true in the drawing, and their bearing direction remains horizontal.
While the desired depth of shadows should determine the altitude of the light rays, we often use 45°, 30°, or 60° angles when drafting with 45° and 30°-60° triangles.

A shadow's profile is continuous, except where interrupted by a surface in light.
A shadow's profile changes direction with every change in form that receives the shadow.

Cast shadows anchor an object to the surface on which it sits.
Cast shadows reveal the distance between a form and the surface upon which it is cast.
Cast shadows clarify the form of the surface upon which they are cast.

Shown below is an example of a paraline drawing that uses shade and shadows to reveal the forms and spaces within the interior of a building.
To determine the shadow cast by a complex subject, break down the form into its simplest geometric components.
Determine the shadows cast by these components.
The overall shadow pattern will be a composite of these shadows.

Perspective Views

The casting of shade and shadows in linear perspective is similar to their construction in paraline drawings, except that the sloping lines representing the conventional or actual light rays appear to converge when oblique to the picture plane.

To determine the vanishing point for inclined light rays, construct a triangular shadow plane for a vertical shade line in perspective, having a hypotenuse establishing the direction of the light rays and a base describing their bearing direction.
Because the bearing directions of light rays are described by horizontal lines, their vanishing point (VP) must occur somewhere along the horizon line (HL).
Establish a vanishing trace through VP.
Extend the hypotenuse until it intersects the vanishing trace. This intersection represents the source of the light rays, and is above HL when the light source is in front of the observer and below HL when behind the observer.
Light sources behind us illuminate the surfaces we see and cast shadows away from us.
Sources in front of us cast shadows toward us and emphasize backlit surfaces in shade.
Low light angles lengthen shadows, while high sources shorten them.

In two-point perspective, the simplest method for casting shadows is to assume that the bearing direction for the light rays originates from either the left or right and is parallel to the picture plane. You can then use 45° triangles to determine the direction of the light rays and the shadows cast by vertical elements in perspective.

Construct a 45° triangle with the vertical element as one of the sides of the triangle.
Slice the sloping surface along the plane of the triangle.
The shadow falls along this slice line and terminates at the hypotenuse of the 45° triangle.