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![plane geometry plane geometry](https://i.stack.imgur.com/l1CIg.jpg)
Specifically, let r 0 be the position vector of some point P 0 = ( x 0, y 0, z 0), and let n = ( a, b, c) be a nonzero vector. In a manner analogous to the way lines in a two-dimensional space are described using a point-slope form for their equations, planes in a three dimensional space have a natural description using a point in the plane and a vector orthogonal to it (the normal vector) to indicate its "inclination". Point–normal form and general form of the equation of a plane Two distinct planes perpendicular to the same line must be parallel to each other.Two distinct lines perpendicular to the same plane must be parallel to each other.A line is either parallel to a plane, intersects it at a single point, or is contained in the plane.Two distinct planes are either parallel or they intersect in a line.The following statements hold in three-dimensional Euclidean space but not in higher dimensions, though they have higher-dimensional analogues: Three non- collinear points (points not on a single line).In a Euclidean space of any number of dimensions, a plane is uniquely determined by any of the following: The underlying cause lies in the structure of vision, which privileges the horizontal ground and downward gravity.This section is solely concerned with planes embedded in three dimensions: specifically, in R 3.Äetermination by contained points and lines In Renaissance scene paintings feet are usually visible our experiments show that the feet provide the viewer with an accurate perception of relative depth, configuring the scene elements into clusters.
![plane geometry plane geometry](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/naming-of-planes-1620131289.png)
Furthermore, the horizontal construction lines, which abstract the horizontal guides present in Renaissance paintings the tiled floors, improve depth perception substantially. Among the directions of gravity participants best perceive depth when the ground plane is horizontal and gravity downward, as measured by response time at 97% accuracy. The presence or absence of ground constructions and its orientation are varied in SVG images to minimize pixellation artifacts. In psychophysical experiments we measured the response time and accuracy of forced-choice closer/farther judgments between two objects placed in simple scenes based on traditional artist's perspective. From them a third constancy emerges, objects in contact with the ground at the same distance lie along a horizontal line, which artists' floor constructions highlight. Human sensitivity to horizontal and vertical orientations exemplifies the important effect that gravity and the ground have on human perception. Our experiments, which measure the precision of depth perception in perspective images, hypothesize that spatial perception evolved in the presence of two constancies, vertical gravity and an almost horizontal ground. This practice created a scale for placing and sizing objects on a minimally patterned ground plane. Thus, the artist constructs the geometry of pictorial space, based on the station point and the view direction, then places objects in it. Subsequently, they developed methods for geometric calculation of perspective by drawing construction lines defining the ground plane. Renaissance artists noticed that placing objects on a visible ground plane anchors them stably, making it easy to perceive their depth.