Mathematical Reasoning and Visualization -- Visualization in Logic and Mathematics -- From Symmetry Perception to Basic Geometry -- Naturalism, Pictures, and Platonic Intuitions -- Mathematical Activity -- Mathematical Explanation and Proof Styles -- Tertium Non Datur: On Reasoning Styles in Early Mathematics -- The Interplay Between Proof and Algorithm in 3rd Century China: The Operation as Pr…
Mathematics, Art and Architecture -- Mathematics, Art and Architecture -- From Tiling the Plane to Paving Town Square -- Mathematics in Contemporary Arts — Finite and Infinity -- De Insana Geometria -- Ovals in Borromini’s Geometry -- Fractals: A Resonance between Art and Nature -- Mathland — From Topology to Virtual Architecture -- Visual Mathematics and Computer Graphics -- Introduction…
Syntax -- How To Make a Pie -- Data -- Variables -- Algebra -- Scales -- Statistics -- Geometry -- Coordinates -- Aesthetics -- Facets -- Guides -- Semantics -- Space -- Time -- Uncertainty -- Analysis -- Control -- Automation -- Reader -- Coda.This book was written for statisticians, computer scientists, geographers, researchers, and others interested in visualizing data. It presents a unique …
Basic Concepts and Simplest Properties of Convex Polyhedra -- Methods and Results -- Uniqueness of Polyhedra with Prescribed Development -- Existence of Polyhedra with Prescribed Development -- Gluing and Flexing Polyhedra with Boundary -- Congruence Conditions for Polyhedra with Parallel Faces -- Existence Theorems for Polyhedra with Prescribed Face Directions -- Relationship Between the Congr…
Approximate Parametrisation of Confidence Sets -- Challenges in Surface-Surface Intersections -- Computing the Topology of Three-Dimensional Algebraic Curves -- Distance Properties of ?-Points on Algebraic Curves -- Distance Separation Measures Between Parametric Curves and Surfaces Toward Intersection and Collision Detection Applications -- Elementary Theory of Del Pezzo Surfaces -- The Geomet…
Compression -- Recent Advances in Compression of 3D Meshes -- Shape Compression using Spherical Geometry Images -- Data Structures -- A Survey on Data Structures for Level-of-Detail Models -- An Algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components -- Encoding Level-of-Detail Tetrahedral Meshes -- Multi-Scale Geographic Maps -- Modelling -- Constrained…