The provided outline covers a comprehensive range of topics in discrete and computational geometry, including:
1. **Density Problems for Packings and Coverings**: This section explores various packing and covering problems, such as the least economical convex sets for packing and covering, lattice arrangements, packing semidisks, equal circles in squares, circles, and spheres, densest packings of specific convex bodies, and linking packing and covering densities.
2. **Structural Packing and Covering Problems**: It delves into the decomposition of multiple packings and coverings, solid and saturated packings, stable packings and coverings, kissing and neighborly convex bodies, thin packings with many neighbors, and permeability and blocking light rays.
3. **Packing and Covering with Homothetic Copies**: This part discusses problems like the potato bag problems, covering a convex body with its homothetic copies, the Levi-Hadwiger covering problem, covering a ball by slabs, and point trapping and impassable lattice arrangements.
4. **Tiling Problems**: It covers tiling the plane with congruent regions, aperiodic tilings, tilings with fivefold symmetry, and tiling space with polytopes.
5. **Distance Problems**: This section includes problems on the maximum number of unit distances, the number of distinct distances, repeated distances in point sets, chromatic number of unit-distance graphs, and integral or rational distances.
6. **Problems on Repeated Subconfigurations**: It explores repeated simplices, directions, angles, areas, and Euclidean Ramsey problems.
7. **Incidence and Arrangement Problems**: This part discusses the maximum number of incidences, Sylvester–Gallai-type problems, and line arrangements spanned by a point set.
8. **Problems on Points in General Position**: It covers the structure of the space of order types, convex polygons, halving lines, and extremal number of special subconfigurations.
9. **Graph Drawings and Geometric Graphs**: This section includes graph drawings, drawing planar graphs, crossing numbers, forbidden geometric subgraphs, Turán-type problems, Ramsey-type problems, and geometric hypergraphs.
10. **Lattice Point Problems**: It addresses packing and covering lattice points in subspaces, avoiding regularities, and visibility problems for lattice points.
11. **Geometric Inequalities**: This part covers isoperimetric inequalities, Heilbronn-type problems, circumscribed and inscribed convex sets, universal covers, and approximation problems.
12. **Index**: The book concludes with an author index and a subject index for easy reference.The provided outline covers a comprehensive range of topics in discrete and computational geometry, including:
1. **Density Problems for Packings and Coverings**: This section explores various packing and covering problems, such as the least economical convex sets for packing and covering, lattice arrangements, packing semidisks, equal circles in squares, circles, and spheres, densest packings of specific convex bodies, and linking packing and covering densities.
2. **Structural Packing and Covering Problems**: It delves into the decomposition of multiple packings and coverings, solid and saturated packings, stable packings and coverings, kissing and neighborly convex bodies, thin packings with many neighbors, and permeability and blocking light rays.
3. **Packing and Covering with Homothetic Copies**: This part discusses problems like the potato bag problems, covering a convex body with its homothetic copies, the Levi-Hadwiger covering problem, covering a ball by slabs, and point trapping and impassable lattice arrangements.
4. **Tiling Problems**: It covers tiling the plane with congruent regions, aperiodic tilings, tilings with fivefold symmetry, and tiling space with polytopes.
5. **Distance Problems**: This section includes problems on the maximum number of unit distances, the number of distinct distances, repeated distances in point sets, chromatic number of unit-distance graphs, and integral or rational distances.
6. **Problems on Repeated Subconfigurations**: It explores repeated simplices, directions, angles, areas, and Euclidean Ramsey problems.
7. **Incidence and Arrangement Problems**: This part discusses the maximum number of incidences, Sylvester–Gallai-type problems, and line arrangements spanned by a point set.
8. **Problems on Points in General Position**: It covers the structure of the space of order types, convex polygons, halving lines, and extremal number of special subconfigurations.
9. **Graph Drawings and Geometric Graphs**: This section includes graph drawings, drawing planar graphs, crossing numbers, forbidden geometric subgraphs, Turán-type problems, Ramsey-type problems, and geometric hypergraphs.
10. **Lattice Point Problems**: It addresses packing and covering lattice points in subspaces, avoiding regularities, and visibility problems for lattice points.
11. **Geometric Inequalities**: This part covers isoperimetric inequalities, Heilbronn-type problems, circumscribed and inscribed convex sets, universal covers, and approximation problems.
12. **Index**: The book concludes with an author index and a subject index for easy reference.