Lecture 3: Line Segment Intersection, Circumcenters

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Piazza

http://www.piazza.com/duke/spring2016/compsci29004/home

Ditching Daily BQOTD

Line Segment Intersection

Triangle Circumcenter

JSON / Visual Debugging

Let’s do lines first……

Want: a + s u = b + t v

Want: a + s u = b + t v

This means

(1) ax + sux = bx + t vx

(2) ay + suy = by + t vy

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

(1) sux - tvx = bx - ax

(2) suy - tvy = by - ay

What happens if lines parallel?

a + s(b-a) = b + t(d-c)

Need

0 <= t <= 1

0 <= s <= 1

What if vertical line?

What if very close to vertical line?

Line Segment Intersection

Triangle Circumcenter

JSON / Visual Debugging

p + R(1, 0)cos(theta) + R(0,1)sin(theta)

How many degrees of freedom?

Draw a triangle whose circumcenter is outside of the triangle

Triangulation such that every circumcenter is empty

Triangulation such that every circumcenter is empty

Brute Force Algorithm??

Brute Force Algorithm??

Line Segment Intersection

Triangle Circumcenter

JSON / Visual Debugging