A step by step guide to constructing an architectural perspective drawing at the drawing board:
Locate an appropriate viewpoint and determine a 'cone of vision' to include the desired view.
The angle of view is usually approximately 60°, since wider angles can give rise to distortion whilst smaller/narrower angles tend to minimise the perspective effect, flattening the image in the same way as a telephoto lens on a camera.
The viewing position should be considered in the same way as one would frame a photograph. Simply placing the object in the middle may not result in the most interesting or appropriate view. Views from above or below (if for instance the building is on a hill) may be relevant. Looking through or out of a building may also help capture its spatial qualities.
Now plot the centre line, achieved by bisecting the cone of vision.
The 'picture plane' can now be drawn perpendicular to the centre line, bearing in mind two factors:
- i. It is useful for the picture plane to intersect some point of the object in the plan to provide a datum for the vertical scale.
- ii. The width of the final perspective drawing will be equivalent to the length of the picture plane that lies within the cone of vision.
2. Re-orientate the plan on the drawing board so that the picture plane is horizontal, and leaving sufficient space below the plan for the perpective to be drawn. A new sheet of paper may now be overlaid across the plan onto which the perspective drawing can be constructed.
Commence the perspective drawing by drawing the horizon line.
3. Determine the 'vanishing points' for the various planes of the object by projecting lines parallel to such planes from the viewpoint to the picture plane. Complex, non-orthogonal shapes will have numerous vanishing points.
Transfer the positions of the vanishing points onto the horizon by projecting them vertically downwards from the setting-up plan.
4. Project down a 'vertical datum' from the point where the object intersects the picture plane. All vertical dimensions at this point will be at the same scale as the plan, as measured above or below eye-level (usually about 1.5 - 1.75m) from the horizon. The vertical datum may be divided into appropriately scaled increments.
If you already have an elevation drawing of the building at the same scale as the plan, this may be used to mark of the vertical dimensions by positioning it correctly against the drawing.
5. Project lines from the major edges and corners of the object to the viewpoint. The position at which these 'visual rays' intersect the picture plane can then be projected down into the perspetive drawing to give the vertical outlines of the object. Horizontals are then established using the vertical datum.
6. Further detail is built up following the same technique with each point being first located in plan, then establishing its intersection with the picture plane and projecting down to give its location in the perspective drawing.
7. Other elements such as a projecting roof, or doors/windows at different floor levels can be drawn on the plan, prior to plotting the visual rays and finding the intersections with the picture plane.
Alternatively, plans of other levels of the building can be carefully superimposed over the plan, so that visual rays can be plotted.
8. Sloping lines (such as stairs or roofs) will have separate vanishing points which will be positioned above or below the horizon. Their vanishing point will be directly above or below the vanishing point of the equivalent horizontal lines.
The outlines of other complex forms (such as curved and irregular profiles) can be determined by establishing a rectangular 'crate' into which they can be inserted.
9. Again, additional details are added in plan, in order to help find the relevant points for the roof structure.
10. The cone of vision can finally be used to mark the borders of the picture.
The area on the left of the drawing is discarded as it is outside of the cone of vision and shows quite severe distortion. In this example, the square buttresses are stretched significantly (the issues of perspective distortion will be discussed in a separate section).
The reflections in the pool can also be accurately calculated and are constructed to the same vanishing points.
A SketchUp model of this perspective construction can be downloaded from Google 3D Warehouse.
Sectional perspectives
11. In a sectional perspective the picture plane coincides with the plane where the section is taken. This means that the section can be drawn to the same scale as the plan.
The position of points behind the section are determined by plotting the visual rays in plan and then projecting the intersections down into the perspective drawing.
The diagonal vanishing points (marked on the horizon line) can help determine further intersections along receding lines.
Complex shapes
12. A complex object such as a spiral staircase will have numerous vanishing points. These can be plotted in plan and projected down onto the horizon line using the method described above, although it is possible that some may not fit within the drawing or board that you are working on.
Initially, the key points are plotted on the ground plane and a vertical datum is established at the centre of the stair (which in this example is conveniently on the picture plane).
13. Firstly, all the risers of the stair are drawn, using the vertical datum and the relevant vanishing point. The length of each riser is determined by the equivalent point on the ground plane.
14. The treads of the stair can then be added along with the handrail.
This example was deliberately drawn using a wide angle of view, so that the vanishing points will fit in the diagram and to make the technique as explicit as possible. This results in considerable distortion at the top of the stair. A more conventional angle of view (approx. 60 degrees) would result in a more natural appearance.
Perspectives from photos
15. Photography is governed by the same laws of optics as perspective drawing. It is therefore possible to use the principles of perspective to work out the position of horizon lines and vanishing points in a photograph.
This is easiest to do in a photograph that has been taken horizontally, so that uprights are all vertical.
16. The superimposed lines show how vanishing points can be established. A horizon line can then be drawn through the vanishing points.
17. In this example, a view of a CAD model of the proposed alteration was set up from an identical viewpoint.
18. This was then superimposed over the photograph using Photoshop. The scale of the CAD image was adjusted until it was a perfect fit.
Shadows
Accurate shadows can also be constructed in perspective. The following images are from Richard Brown's 'Principles of Practical Perspective' of 1815. (images copyright © Russell Light)
In external perspectives, where the sun is the source, shadows can be constructed using the method shown above. In this case the sun is in front of the viewer. It is effectively at an infinite distance and can be considered as directly above a point on the horizon line. The outline of the shadows can be found from the intersections of the rays of sunlight with their equivalent projections on the ground plane (in the picture above, ignore the lines projecting from points B and Z, these are part of a different diagram).
When the sun is directly to the side viewer and is in the same plane as the picture plane, the projected lines of shadows will all be parallel to each other.
In cases where the sun is behind the viewer, there will be a notional vanishing point for the projection of the rays of sunlight, which is below the horizon line.
Artifical lights (in this instance a candle) will generate a different set of shadows. The outline of the shadows can again be found from the intersections of the rays of light with their equivalent projections on the ground plane and other surfaces of the room.
