2.17 Image of polyhedral sets under perspective function. In this problem we study the image of hyperplanes, halfspaces, and polyhedra under the perspective function P(x,t) = x/t, with dom P = R" x R++: For each of the following sets C, give a simple description of P(C) = {v/t| (v,t) € C, t> 0}. (a) The polyhedron C = conv{(v1, t1),..., (vK,tK)} where vi E R" and ti > 0. (b) The hyperplane C = {(v, t) | fTv+ gt = h} (with f and g not both zero). (c) The halfspace C = {(v, t) | f"v+ gt < h} (with f and g not both zero). (d) The polyhedron C = {(v, t) | Fv + gt < h}.
2.17 Image of polyhedral sets under perspective function. In this problem we study the image of hyperplanes, halfspaces, and polyhedra under the perspective function P(x,t) = x/t, with dom P = R" x R++: For each of the following sets C, give a simple description of P(C) = {v/t| (v,t) € C, t> 0}. (a) The polyhedron C = conv{(v1, t1),..., (vK,tK)} where vi E R" and ti > 0. (b) The hyperplane C = {(v, t) | fTv+ gt = h} (with f and g not both zero). (c) The halfspace C = {(v, t) | f"v+ gt < h} (with f and g not both zero). (d) The polyhedron C = {(v, t) | Fv + gt < h}.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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