Abstract: The widely used rectilinear perspective projection cannot render realistic looking flat views with fields of view much wider than 70°. Yet 18th century artists known as 'view painters' depicted wider architectural scenes without visible perspective distortion.We have found no written records of how they did that, however, quantitative analysis of several works suggests that the key is a system for compressing horizontal angles while preserving certain straight lines important for the perspective illusion. We show that a simple double projection of the sphere to the plane, that we call the Pannini projection, can render images 150° or more wide with a natural appearance, reminiscent of vedutismo perspective. We give the mathematical formulas for realizing it numerically, in a general form that can be adjusted to suit a wide range of subject matter and field widths, and briefly compare it to other proposed alternatives to the rectilinear projection.