Vanishing point is below the horizon line, its vanishing lines angle up to the horizon line. If the object is above, they slope down. All vanishing lines end at the horizon line. 1. Projections of two sets of parallel lines lying in some plane appear to converge, i.e. the vanishing point associated with that pair, on a horizon line, or vanishing line formed by the intersection of the image plane with the plane parallel to and passing through the pinhole. Proof: Consider the ground plane , as which is, for the sake of simplicity, orthogonal to the image plane. Also, consider a
Ideal point qb. In the Poincaré half-plane model the ideal points are the points on the boundary axis. There is also another ideal point that is not represented in the half-plane model (but rays parallel to the positive y-axis approach it). In the hyperboloid model there are no ideal points. Ideal point In hyperbolic geometry, an ideal point, omega point or point at infinity is a well defined point outside the hyperbolic plane or space. Given a line "l" and a point "P" not on "l", right- and left-limiting parallels to "l" through "P" converge to "l" at "ideal points". Unlike the