New geometric analyses are presented of three impressive examples of the effects of location of the vantage point on virtual 3-D spaces conveyed by linear-perspective images. In the 'egocentric-road' effect, the perceived direction of the depicted road is always pointed towards the observer, for any position of the vantage point. It is shown that perspective images of real-observer-aimed roads are characterised by a specific, simple pattern of projected side lines. Given that pattern, the position of the observer, and certain assumptions and perspective arguments, the perceived direction of the virtual road towards the observer can be predicted. In the 'skewed balcony' and the 'collapsing ceiling' effects, the position of the vantage point affects the impression of alignment of the virtual architecture conveyed by large-scale illusionistic paintings and the real architecture surrounding them. It is shown that the dislocation of the vantage point away from the viewing position prescribed by the perspective construction induces a mismatch between the painted vanishing point of elements in the picture and the real vanishing point of corresponding elements of the actual architecture. This mismatch of vanishing points provides visual information that the elements of the two architectures are not mutually parallel.