lecture 3: line segment intersection, circumcenters...line segment intersection triangle...
TRANSCRIPT
![Page 1: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/1.jpg)
Lecture 3: Line Segment Intersection, Circumcenters
![Page 2: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/2.jpg)
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Mini Assignment 1 Part 1 Due SundaySubmit README
Part 2 Changed to 2D!
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![Page 3: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/3.jpg)
Piazza
http://www.piazza.com/duke/spring2016/compsci29004/home
Ditching Daily BQOTD
![Page 4: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/4.jpg)
Line Segment Intersection
Triangle Circumcenter
JSON / Visual Debugging
![Page 5: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/5.jpg)
Let’s do lines first……
![Page 6: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/6.jpg)
![Page 7: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/7.jpg)
Want: a + s u = b + t v
![Page 8: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/8.jpg)
Want: a + s u = b + t v
This means
(1) ax + sux = bx + t vx
(2) ay + suy = by + t vy
![Page 9: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/9.jpg)
Want: a + s u = b + t v
This means
(1) ax + sux = bx + t vx
(2) ay + suy = by + t vy
Put variables on left side together
(1) sux - tvx = bx - ax
(2) suy - tvy = by - ay
![Page 10: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/10.jpg)
(1) sux - tvx = bx - ax
(2) suy - tvy = by - ay
What happens if lines parallel?
![Page 11: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/11.jpg)
a + s(b-a) = b + t(d-c)
Need
0 <= t <= 1
0 <= s <= 1
![Page 12: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/12.jpg)
![Page 13: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/13.jpg)
![Page 14: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/14.jpg)
What if vertical line?
What if very close to vertical line?
![Page 15: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/15.jpg)
Line Segment Intersection
Triangle Circumcenter
JSON / Visual Debugging
![Page 16: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/16.jpg)
p + R(1, 0)cos(theta) + R(0,1)sin(theta)
![Page 17: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/17.jpg)
How many degrees of freedom?
![Page 18: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/18.jpg)
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![Page 20: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/20.jpg)
Draw a triangle whose circumcenter is outside of the triangle
![Page 21: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/21.jpg)
Triangulation such that every circumcenter is empty
![Page 22: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/22.jpg)
Triangulation such that every circumcenter is empty
![Page 23: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/23.jpg)
Brute Force Algorithm??
![Page 24: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/24.jpg)
Brute Force Algorithm??
![Page 25: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/25.jpg)
Line Segment Intersection
Triangle Circumcenter
JSON / Visual Debugging
![Page 26: Lecture 3: Line Segment Intersection, Circumcenters...Line Segment Intersection Triangle Circumcenter JSON / Visual Debugging t(d-c) c(0.5, o, 0) Title COMPSCI/MATH 290-04 Author ctralie](https://reader034.vdocuments.us/reader034/viewer/2022042802/5f3b8f85b7cf9b02bb052c93/html5/thumbnails/26.jpg)