Algorithms in a Nutshell

(^252) | Chapter 9: Computational Geometry Two-dimensional structures (lines, rectangles, and circles) have three-dimensional co ...

Overview | 253 Computational Geometry These concepts naturally extend into multiple dimensions, as shown in Figure 9-2: IMultiPo ...

(^254) | Chapter 9: Computational Geometry Today’s computers are sufficiently advanced that this no longer is an obstacle to per ...

Overview | 255 Computational Geometry In the sections of this chapter, we present the various computational abstractions used to ...

(^256) | Chapter 9: Computational Geometry Given an input set of line segments, can there be horizontal or vertical segments? G ...

Overview | 257 Computational Geometry by the angle formed with a vertical line. One must be careful when processing collinear po ...

(^258) | Chapter 9: Computational Geometry This computation requires O(n^2 ) individual executions of its core step. Deter- mini ...

Overview | 259 Computational Geometry Answering nearest neighbor queries Given a set of pointsPin a two-dimensional plane, answe ...

(^260) | Chapter 9: Computational Geometry Convex Hull Scan To develop an efficient algorithm for computing the convex hull (who ...

Convex Hull Scan | 261 Computational Geometry Figure 9-7. Convex Hull Scan fact sheet Figure 9-8. Incremental construction of a ...

(^262) | Chapter 9: Computational Geometry Input/Output Input A set of two-dimensional pointsP in a plane. Output An ordered lis ...

Convex Hull Scan | 263 Computational Geometry initial points, and since these points are discarded before the sort operation, th ...

(^264) | Chapter 9: Computational Geometry Figure 9-11. PartialHull supporting class Example 9-2. Convex Hull Scan solution to c ...

Convex Hull Scan | 265 Computational Geometry Consequences Because the first step of this algorithm must sort the points, we rel ...

(^266) | Chapter 9: Computational Geometry The loop that computes the upper partial hull (lines 4–7 in Figure 9-7) processes n–2 ...

Convex Hull Scan | 267 Computational Geometry and the code repository. As a baseline for comparison, we include performance resu ...

(^268) | Chapter 9: Computational Geometry Also, the implementation using balanced binary trees shows the best perfor- mance of ...

LineSweep | 269 Computational Geometry The innovation of LINESWEEPis recognizing that line segments can be ordered from left to ...

(^270) | Chapter 9: Computational Geometry Looking closer at the nine selected locations of the horizontal sweep line in Figure ...

LineSweep | 271 Computational Geometry Figure 9-15. LineSweep fact sheet (part II) Algorithms in a Nutshell Algorithms in a Nuts ...