The Upper Envelope of Piecewise Linear Functions and the Boundary of a Region Enclosed by Convex Plates: Combinatorial Analysis (Classic Reprint) - Hardcover

Janos Pach

9780656030095: The Upper Envelope of Piecewise Linear Functions and the Boundary of a Region Enclosed by Convex Plates: Combinatorial Analysis (Classic Reprint)

Hardcover

ISBN 10: 0656030097 ISBN 13: 9780656030095

Publisher: Forgotten Books, 2018

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Explore how many pieces a surface can have when many simple shapes meet in 3D .

This book answers how complex the top surface can be when you combine many triangular or polyhedral parts.

Two accessible sections show how the upper envelope of piecewise linear functions behaves in two and three dimensions, with precise bounds that grow slower than naive expectations. It also connects these ideas to the shape of regions created by removing convex plates from space, a topic with practical implications in design and planning.

Learn what the upper envelope looks like for many triangles in three-space and how its complexity scales.
See how these ideas extend to higher dimensions and different types of polyhedral pieces.
Discover applications to motion planning, visibility, and other problems in computational geometry.
Understand how combinatorial results help estimate the boundary complexity of regions formed by removing convex sets.

Ideal for readers of discrete geometry and those interested in efficient algorithms for geometric problems, including motion planning and spatial reasoning.

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