Showing papers on "Perspective (geometry) published in 1984"
TL;DR: In this paper, the authors introduce and solve an interesting puzzle that serves to highlight the fascinating interplay between the geometric nature of point-and-line configurations and their representations as rectangular arrays of integers.
Abstract: Today, in contrast to Hilbert's assertion, most students have limited knowledge about configurations-except perhaps Pappus' 93, Desargues' 103 and Petersen's 103152 (the logo on the cover of the Journal of Graph Theory). These configurations are shown in FIGURE 1. The configuration labeled 93 illustrates Pappus' Theorem: If three points { 1, 3, 5 } on one line are joined in consecutive order to three points {4, 6, 2} on another line, the three intersection points {9, 7, 8} are collinear. The configuration 103 illustrates Desargues' Theorem: When extended, the corresponding sides of triangles (1, 2, 3) and (4, 5, 6) (which are said to be in perspective from the point 7), meet in a set of collinear points {8, 10, 9} (so that the triangles are said to be in perspective from a line also). In this note, we introduce and solve an interesting puzzle that serves to highlight the fascinating interplay between the geometric nature of point-and-line configurations and their representations as rectangular arrays of integers. We hope that our exposition will provide a rich source of challenges for students of varying levels of mathematical sophistication.
11 citations
Patent•
22 Nov 1984
TL;DR: In this paper, the authors propose to improve graphic technique by applying perspective processing to three dimensional picture information in a program and expressing it as status of picture elements on a picture processing plane.
Abstract: PURPOSE:To improve graphic technique by applying perspective processing to three dimensional picture information in a program and expressing it as status of picture elements on a picture processing plane. CONSTITUTION:For instance, numberless xk-yk planes are prepared by three dimensional picture information, and a function is set on a plane that passes Z=0 using straight line approximation etc. For searching by a straight line, any point P1 (x1, y1, z1) is set on a space, and a plane perpendicular to a segment OP1 that connects an original point 0 is determined. Length of a segment that becomes a unit is determined on the center of vertical axis by calculating the distance between the point P1 and another point (arbitrary), and displacement in the direction of three axes xm0, ym0, zm0 of this unit displacement is calculated. Basing on this displacement, a picture processing area is set on a picture processing plane, and picture elements are prepared. Then, a proper picture element is selected on the picture processing, and three dimensional picture information function is searched by a straight line that connects the picture element and corresponding picture element on an auxiliary picture processing plane.