AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 2 Solution Notes
(1). (a). Consider performing the Bentley-Ottmann sweep, in report mode, with a vertical line, sweeping
from left to right. It is not always the case that t
AMS 545/CSE 555 (Spring, 2016)
COMPUTATIONAL GEOMETRY
Homework Problem # 1
(1). We defined a set Q to be convex if for any two points p and q in Q the line segment pq also
lies in Q.
Let us define the notion of rectangle-convex as follows: Q is rectangle-
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 2
Due in class on Thursday, February 28, 2013.
Reminder: Show your reasoning! Also, all hw should be submitted with the cover sheet (last
page of this assignment).
Recommend
CSE555/AMS545 Homework 3
Jie Gao
March 1, 2012
The following problems are due in 2 weeks (March 15th) before class.
1. The weight of a triangulation is the sum of the length of all edges of the triangulation. The minimum weight triangulation is the triang
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 1
Due in class on Thursday, February 14, 2013.
Reminder: Show your reasoning! Also, all hw should be submitted with the cover sheet (last
page of this assignment).
Quiz 1 wi
CSE555/AMS545 Homework 4
Jie Gao
April 11, 2012
The following problems are due in 2 weeks (April 24th) before class.
Textbook [Computatioal Geometry: Algorithms and Applications], 2nd or 3rd edition: Problem 3.12,
3.13, 3.14, 5.5, 5.8.
The problems are co
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 7
Due in class on Thursday, May 2, 2013. Reminder: Show your reasoning! Quiz 5 will be
2:30-2:50 on May 2, covering hw7 material.
Recommended Reading: BCKO/BKOS: Chapter 10.
CSE555/AMS545 Homework 1
Jie Gao
February 10, 2012
The following problems are due in 2 weeks (Feb 9th) before class.
1. Prove that the convex hull of a set of points S has the smallest perimeter among all convex polygons
that contain S .
The proof is by c
AMS 545/CSE 555 (Spring, 2009)
Joe Mitchell
COMPUTATIONAL GEOMETRY Homework Set # 7 Solution Notes
(1). [20 points] Problems 8.6 and 8.8 of BCKO. Problem 8.6: Let S be a set of n points cfw_p1 , ., pn and L be a set of m lines cfw_l1 , ., ln . Suppose we
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 4
Due in class on Thursday, March 28, 2013. Reminder: Show your reasoning!
Recommended Reading: BKOS: Chapter 4 (you may skip sections 4.6 and 4.7) and Chapter 5.
DO ANY 3 O
CSE555/AMS545 Homework 2
Jie Gao
February 21, 2012
The following problems are due in 2 weeks (Feb 23rd) before class.
1. Let S be a set of n triangles in the plane. The boundaries of the triangles are disjoint, but it is possible
that a triangle lies comp
CSE555/AMS545 Final Exam
Jie Gao
May 11, 2012
Submit by 6pm 12th to instructors mailbox at CS department. Assume no degeneracy for all the problems below unless specied.
1. Range queries for polygons (10pts) Let P consist of a set of n polygons in the pla
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 6 Solution Notes
(1). Here is a proposed solution to the following problem: Given a set S of n points in the
plane, no 3 of which are collinear, nd three points of S, cfw_pi
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 6
Due in class on Thursday, April 18, 2013. Reminder: Show your reasoning! Quiz 4 will be
2:30-2:50 on April 18, covering hw6 material.
Recommended Reading: BCKO/BKOS: Chapt
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 3 Solution Notes
(1). (a). Give an example of a rectilinear1 simple polygon P for which the maximum number,
imax (P ), of independent witness points in P is strictly less th
CSE555/AMS545 Homework 2
Jie Gao
February 9, 2012
The following problems are due in 2 weeks (Feb 23rd) before class.
1. Let S be a set of triangles in the plane. The boundaries of the triangles are disjoint, but it is possible
that a triangle lies complet
AMS 545/CSE 555
Joe Mitchell
Another Practice Final Solution Notes
(1). [15 points] For the set S of 8 points shown below, do the following:
(a). Draw the (Euclidean) Delaunay diagram. In order to assist you in making some decisions (in case you do not ha
AMS 545/CSE 555
Joe Mitchell
Another Practice Final
(1). [15 points] For the set S of 8 points shown below, do the following:
(a). Draw the (Euclidean) Delaunay diagram. In order to assist you in making some decisions (in case you do not have
a compass wi
AMS 545/CSE 555
Joe Mitchell
COMPUTATIONAL GEOMETRY
Practice Final
Statistics: n = 36, = 67.6, median 67, = 12.8; score range: 4293
(1). [12 points] For the set S of 7 points shown below, do the following:
(a). Draw the (Euclidean) Delaunay diagram. In or
AMS 545/CSE 555
Joe Mitchell
COMPUTATIONAL GEOMETRY
Practice Final Solution Notes
Statistics: n = 36, = 67.6, median 67, = 12.8; score range: 4293
(1). [12 points] For the set S of 7 points shown below, do the following:
(a). Draw the (Euclidean) Delaunay
AMS 545/CSE 555
Joe Mitchell
Notes on Voronoi and Delaunay Diagrams
Let S = cfw_p1 , . . . , pn be a set of n points (sites) in the plane.
Denition of Voronoi diagram. For any subset Q S of sites we dene the Voronoi region,
V (Q), for Q to be the set of
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
Quiz # 5 Solution Notes
Statistics: n = 45, = 18.93, median 20, quartile Q1=17, quartile Q3=22, = 4.05; score range: 4-25.
(1). In the gure below, we show where all 5 segments are stored in the segment tree. (an
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
Quiz # 4 Solution Notes
Statistics: n = 47, = 20.3, median 20, quartile Q1=18, quartile Q3=23, = 3.28; score range: 12-25.
(1). (a). The x-coordinates of the points are increasing in the order q, p, r. Thus, the
AMS 545/CSE 555 (Spring, 2013)
Joe Mitchell
Quiz # 3 Solution Notes
Statistics: n = 47, = 15.0, median 15, quartile Q1=12, quartile Q3=18, = 3.98; score range: 7-25.
(1). Let S be a set of n axis-parallel rectangles in the plane. We want to be able to rep
AMS 545/CSE 555 (Spring, 2016)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Problems # 34-40 Solution Notes
(34). (a). For each of the following cardinalities v, e, f of vertices, edges, and cells (2-faces),
indicate whether or not there exists an arrange
AMS 545/CSE 555 (Spring, 2016)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Problem # 8 Solution Notes
(8). (a). Assume that we execute Melkmans convex hull algorithm on the vertices of the chain
shown below in the order v0 , v1 , v2 , v3 , etc. (In the f
AMS 545/CSE 555 (Spring, 2016)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Problems # 23-27 Solution Notes
(23). [Problem 5.9, BCKO/BKOS]. One can use the data structures described in this chapter to
determine whether a particular point (a, b) is in a gi
AMS 545/CSE 555
Joe Mitchell
COMPUTATIONAL GEOMETRY
Practice Final Solution Notes
Statistics: n = 36, = 67.6, median 67, = 12.8; score range: 4293
(1). [12 points] For the set S of 7 points shown below, do the following:
(a). Draw the (Euclidean) Delaunay
AMS 545/CSE 555 (Spring, 2016)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Problem # 13 Solution Notes
(13). (a). Give an example of a simple n-gon P and a set A of points within P such that A is a
minimal guard set for P (i.e., it is not possible to rem