Computer graphics is a defining application for computational geometry. The interaction between these fields is explored through two scenarios. Spatial subdivisions studied from the viewpoint of computational geometry are shown to have found application in computer graphics. Hidden surface removal problems of computer graphics have led to sweepline and area subdivision algorithms in computation...

ly, the motion planning problem is that of computing a path between two points in the topological space FP. In the rst two of ve seminal papers on the \Piano Movers' Problem" ([220{222, 229, 223], collected in the book [131]), Schwartz and Sharir show that the boundary of FP is a semialgebraic set (assuming the original constraints of the problem are semialgebraic). This then allows the motion ...

Article history: Available online 17 January 2012 Communicated by S. Durocher

Iranian Islamic gardens like almost every cultures, represent beauty and happiness and improve the public perception. It has also special geometry with philosophical concept related to Islam’s doctrine that is the focus of this research. Following Quran’s contents, paradise is a beautiful sophisticated garden that something flows under its trees. So the comparison between the somatic geometry o...