Vanishing Points

As shown in Fig. 2.9 the construction of the object perspective view using the horizon line, is usually located at eye level.

Fig.2.9. Vanishing and Trace Points

The main vanishing points are points on the horizon, which converge in straight lines parallel to the main axes in the original space. In general, the various set parallel lines have different principal vanishing point, as shown in Fig. 2.9b. For the object plane, located obliquely relative to the source of the principal axes, the vanishing point lies above or below the horizon. As shown in Fig. 2.9, such points are often referred to as the trace points.

Of interest are two methods to determine the vanishing point. The first simply calculates the intersection point of the transformed pair of projected parallel lines. The second method is complicated, but gives more accurate results. In this method, the object, whose sides are parallel to the original main axes, is transformed to desired position and orientation. Then we apply one-point perspective projection. The resulting transformation matrix is applied to points located at infinity on the main axes. The resulting normal coordinates are the main vanishing point for this object. To find the traces of points that arise for inclined planes are placed first in the infinity point on the inclined plane and then transform them.

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