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Overshadowing projections can be performed within a range of different software, from CAD programs to rendering packages. Many include built-in solar position calculators - requiring only location, date and time data from the user. Others require directional light sources to be explicitly created using raw solar azimuth and altitude angles.

From ECOTECT

Figure 1 - Example output of computerised 3D shadow projection.

Such projections can provide a great deal of information, and are often required for approval by the local council. However, their use as a design and analysis tool often involves a great deal of trial and error - requiring large numbers of images to be generated at different times and dates in order to get anything close to a clear understanding of what is going on. This can take enormous amounts of time, constantly adjusting the Sun position and re-rendering images.

Of course, all this used to be done using manual methods of generating shadow diagrams on the drawing board.

### Manual Calculation

Given the azimuth and altitude of the sun at any particular time, you can use two simple trigonometric relationships to determine the relative X and Y offset co-ordinates of shadow points on a flat plane.

The diagram below illustrates this process. Constructing the shadow of a complex 3D object is simply a process of translating each of its vertexes in turn to produce an outline on the ground. With some judgement as to where a shadow is likely to fall, it is possible to use this same method on undulating ground surfaces, in which case the height value of the point of interest above the likely ground point is used instead of the wall height.

Figure 2 - The calculation of shadow points on a flat
ground given the azimuth and altitude of the Sun.

As an example, assume the Sun at an azimuth of 33.7° and an altitude of 53.1° and a wall 2400 mm high (similar to the diagram above). Thus:

$\large dx = \frac{2400 \times \sin(33.7)}{\tan(53.1)} = 999.81 mm$

and:

$\large dy = \frac{2400 \times \cos(33.7)}{\tan(53.1)} = 1499.16 mm$

As discussed in detail within the Solar Position topic, the Sun continually changes position throughout the day and the year. The shadow diagrams described above produce only instantaneous snapshots of what is a highly dynamic process. To represent the real patterns of change, many diagrams are required at different times of the day and different days of the year. Usually only the solstices (21st June and 22nd December) are used as these represent the extreme conditions. Sometimes an equinox (21st March or 22nd September) is used to represent a mid-year condition. Alternatively, local building regulations may dictate their own set of specific dates and times.

### Butterfly Diagrams

It is possible to represent multiple shadows on the one diagram, producing a shadow profile. These are sometimes termed 'butterfly diagrams' after the shapes they produce when drawn for the whole year. In them, the outline of each shadow is drawn at each hourly or half-hourly interval over a day, producing a pattern of shadows running from west to east. This can then be repeated for a range of days throughout the year. Normally a different shade or colour is used to differentiate between different times/dates. The diagram below shows such a set of shadows generated for a simple massing massing model in Northern Italy (latitude 43.5°).

Figure 3 - Multi-shadow butterfly diagrams drawn on the 21st day of each month between 9:00am and 4:00pm in 30 minute steps.

Another way to visualise the dynamics of overshadowing is to generate a sun-path diagram and plot the outlines of obstructing buildings and vegetation as overshadowing blocks. This produces what is known as a solar aperture, the 3D solid angle through which a particular point can 'see' unobstructed sky.

Figure 4 - An example of overshadowing blocks mapped onto a stereographic sun-path diagram.

For a single point this results in a hard-edged diagram. For a large surface, however the potential for partial shading means that the diagram will look quite soft-edged, depending on the relative size of the surface. The surface shading method used in Square One software calculations break the hemispheric sky dome into 2°x2° sections (though the uses can select the segment size) and determines the percentage of each surface that is 'visible' from each sky section. The result is a surface shading mask as shown in Figure 5 below.

Figure 5 - An example surface shading mask mapped onto a stereographic sun-path diagram.