Convex hull smallest convex set containing all the
![Convex hull smallest convex set containing all the points Convex hull smallest convex set containing all the points](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-1.jpg)
![Convex hull smallest convex set containing all the points Convex hull smallest convex set containing all the points](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-2.jpg)
![Convex hull 3 smallest convex set containing all the points 2 4 1 start Convex hull 3 smallest convex set containing all the points 2 4 1 start](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-3.jpg)
![Jarvis march (assume no 3 points colinear) s find the left-most point Jarvis march (assume no 3 points colinear) s find the left-most point](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-4.jpg)
![Jarvis march (assume no 3 points colinear) s find the point that appears most Jarvis march (assume no 3 points colinear) s find the point that appears most](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-5.jpg)
![Jarvis march (assume no 3 points colinear) s p find the point that appears Jarvis march (assume no 3 points colinear) s p find the point that appears](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-6.jpg)
![Jarvis march (assume no 3 points colinear) Jarvis march (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-7.jpg)
![Jarvis march (assume no 3 points colinear) Jarvis march (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-8.jpg)
![Jarvis march (assume no 3 points colinear) s point with smallest x-coord p s Jarvis march (assume no 3 points colinear) s point with smallest x-coord p s](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-9.jpg)
![Jarvis march (assume no 3 points colinear) Running time = O(n. h) Jarvis march (assume no 3 points colinear) Running time = O(n. h)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-10.jpg)
![Graham scan (assume no 3 points colinear) O(n log n) homework start with a Graham scan (assume no 3 points colinear) O(n log n) homework start with a](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-11.jpg)
![Graham scan (assume no 3 points colinear) Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-12.jpg)
![Graham scan (assume no 3 points colinear) Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-13.jpg)
![Graham scan (assume no 3 points colinear) Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-14.jpg)
![Graham scan (assume no 3 points colinear) Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-15.jpg)
![Graham scan (assume no 3 points colinear) Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-16.jpg)
![Graham scan (assume no 3 points colinear) Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-17.jpg)
![Graham scan (assume no 3 points colinear) A start B next(A) C next(B) repeat Graham scan (assume no 3 points colinear) A start B next(A) C next(B) repeat](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-18.jpg)
![Closest pair of points Closest pair of points](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-19.jpg)
![Closest pair of points Closest pair of points](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-20.jpg)
![Closest pair of points 2 T(n/2) min(left, right) Closest pair of points 2 T(n/2) min(left, right)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-21.jpg)
![Closest pair of points 2 T(n/2) min(left, right) Closest pair of points 2 T(n/2) min(left, right)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-22.jpg)
![Closest pair of points 2 T(n/2) min(left, right) Closest pair of points 2 T(n/2) min(left, right)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-23.jpg)
![Closest pair of points pre-processing X sort the points by x-coordinate Y sort the Closest pair of points pre-processing X sort the points by x-coordinate Y sort the](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-24.jpg)
![Smallest enclosing disc Smallest enclosing disc](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-25.jpg)
![Smallest enclosing disc Smallest enclosing disc](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-26.jpg)
![Smallest enclosing disc Claim #1: The smallest enclosing disc is unique. Smallest enclosing disc Claim #1: The smallest enclosing disc is unique.](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-27.jpg)
![Smallest enclosing disc Claim #1: The smallest enclosing disc is unique. Smallest enclosing disc Claim #1: The smallest enclosing disc is unique.](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-28.jpg)
![Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-29.jpg)
![Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-30.jpg)
![Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-31.jpg)
![Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-32.jpg)
![Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-33.jpg)
![Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-34.jpg)
![Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-35.jpg)
![Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-36.jpg)
![Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-37.jpg)
![Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-38.jpg)
![Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-39.jpg)
- Slides: 39
![Convex hull smallest convex set containing all the points Convex hull smallest convex set containing all the points](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-1.jpg)
Convex hull smallest convex set containing all the points
![Convex hull smallest convex set containing all the points Convex hull smallest convex set containing all the points](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-2.jpg)
Convex hull smallest convex set containing all the points
![Convex hull 3 smallest convex set containing all the points 2 4 1 start Convex hull 3 smallest convex set containing all the points 2 4 1 start](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-3.jpg)
Convex hull 3 smallest convex set containing all the points 2 4 1 start = 1 1. next = 2 = 3. prev 2. next = 3 = 4. prev 3. next = 4 = 1. prev 4. next = 1 = 2. prev representation = circular doubly-linked list of points on the boundary of the convex hull
![Jarvis march assume no 3 points colinear s find the leftmost point Jarvis march (assume no 3 points colinear) s find the left-most point](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-4.jpg)
Jarvis march (assume no 3 points colinear) s find the left-most point
![Jarvis march assume no 3 points colinear s find the point that appears most Jarvis march (assume no 3 points colinear) s find the point that appears most](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-5.jpg)
Jarvis march (assume no 3 points colinear) s find the point that appears most to the right looking from s
![Jarvis march assume no 3 points colinear s p find the point that appears Jarvis march (assume no 3 points colinear) s p find the point that appears](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-6.jpg)
Jarvis march (assume no 3 points colinear) s p find the point that appears most to the right looking from p
![Jarvis march assume no 3 points colinear Jarvis march (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-7.jpg)
Jarvis march (assume no 3 points colinear)
![Jarvis march assume no 3 points colinear Jarvis march (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-8.jpg)
Jarvis march (assume no 3 points colinear)
![Jarvis march assume no 3 points colinear s point with smallest xcoord p s Jarvis march (assume no 3 points colinear) s point with smallest x-coord p s](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-9.jpg)
Jarvis march (assume no 3 points colinear) s point with smallest x-coord p s repeat PRINT(p) q point other than p for i from 1 to n do if i p and point i to the right of line (p, q) then q i p q until p = s
![Jarvis march assume no 3 points colinear Running time On h Jarvis march (assume no 3 points colinear) Running time = O(n. h)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-10.jpg)
Jarvis march (assume no 3 points colinear) Running time = O(n. h)
![Graham scan assume no 3 points colinear On log n homework start with a Graham scan (assume no 3 points colinear) O(n log n) homework start with a](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-11.jpg)
Graham scan (assume no 3 points colinear) O(n log n) homework start with a simple polygon containing all the points fix it in time O(n)
![Graham scan assume no 3 points colinear Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-12.jpg)
Graham scan (assume no 3 points colinear)
![Graham scan assume no 3 points colinear Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-13.jpg)
Graham scan (assume no 3 points colinear)
![Graham scan assume no 3 points colinear Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-14.jpg)
Graham scan (assume no 3 points colinear)
![Graham scan assume no 3 points colinear Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-15.jpg)
Graham scan (assume no 3 points colinear)
![Graham scan assume no 3 points colinear Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-16.jpg)
Graham scan (assume no 3 points colinear)
![Graham scan assume no 3 points colinear Graham scan (assume no 3 points colinear)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-17.jpg)
Graham scan (assume no 3 points colinear)
![Graham scan assume no 3 points colinear A start B nextA C nextB repeat Graham scan (assume no 3 points colinear) A start B next(A) C next(B) repeat](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-18.jpg)
Graham scan (assume no 3 points colinear) A start B next(A) C next(B) repeat 2 n times if C is to the right of AB then A. next C; C. prev A B A A prev(A) else A B B C C next(C)
![Closest pair of points Closest pair of points](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-19.jpg)
Closest pair of points
![Closest pair of points Closest pair of points](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-20.jpg)
Closest pair of points
![Closest pair of points 2 Tn2 minleft right Closest pair of points 2 T(n/2) min(left, right)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-21.jpg)
Closest pair of points 2 T(n/2) min(left, right)
![Closest pair of points 2 Tn2 minleft right Closest pair of points 2 T(n/2) min(left, right)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-22.jpg)
Closest pair of points 2 T(n/2) min(left, right)
![Closest pair of points 2 Tn2 minleft right Closest pair of points 2 T(n/2) min(left, right)](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-23.jpg)
Closest pair of points 2 T(n/2) min(left, right)
![Closest pair of points preprocessing X sort the points by xcoordinate Y sort the Closest pair of points pre-processing X sort the points by x-coordinate Y sort the](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-24.jpg)
Closest pair of points pre-processing X sort the points by x-coordinate Y sort the points by y-coordinate Closest-pair(S) if |S|=1 then return if |S|=2 then return the distance of the pair split S into S 1 and S 2 by the X-coord 1 Closest-pair(S 1), 2 Closest-pair(S 2) min( 1, 2) for points x in according to Y check 12 points around x, update if a closer pair found
![Smallest enclosing disc Smallest enclosing disc](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-25.jpg)
Smallest enclosing disc
![Smallest enclosing disc Smallest enclosing disc](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-26.jpg)
Smallest enclosing disc
![Smallest enclosing disc Claim 1 The smallest enclosing disc is unique Smallest enclosing disc Claim #1: The smallest enclosing disc is unique.](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-27.jpg)
Smallest enclosing disc Claim #1: The smallest enclosing disc is unique.
![Smallest enclosing disc Claim 1 The smallest enclosing disc is unique Smallest enclosing disc Claim #1: The smallest enclosing disc is unique.](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-28.jpg)
Smallest enclosing disc Claim #1: The smallest enclosing disc is unique.
![Smallest enclosing disc SEDS pick a random point x S c r SEDSx if Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-29.jpg)
Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if x Disc(c, r) then return (c, r) else return SED-with-point(S, x)
![Smallest enclosing disc SEDS pick a random point x S c r SEDSx if Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-30.jpg)
Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if x Disc(c, r) then return (c, r) else return SED-with-point(S, x) SED-with-point(S, y) pick a random point x S (c, r) SED-with-point(S-{x}, y) if x Disc(c, r) then return (c, r) else return SED-with-2 -points(S, y, x)
![Smallest enclosing disc SEDS pick a random point x S c r SEDSx if Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-31.jpg)
Smallest enclosing disc SED(S) pick a random point x S (c, r) SED(S-{x}) if x Disc(c, r) then return (c, r) else return SED-with-point(S, x) SED-with-point(S, y) pick a random point x S (c, r) SED-with-point(S-{x}, y) if x Disc(c, r) then return (c, r) else return SED-with-2 -points(S, y, x) SED-with-2 -point(S, y, z) pick a random point x S (c, r) SED-with-2 -points(S-{x}, y, z) if x Disc(c, r) then return (c, r) else return circle given by x, y, z
![Running time SEDS pick a random point x S c r SEDSx if Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-32.jpg)
Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if x Disc(c, r) then return (c, r) else return SED-with-point(S, x) SED-with-point(S, y) pick a random point x S (c, r) SED-with-point(S-{x}, y) if x Disc(c, r) then return (c, r) else return SED-with-2 -points(S, y, x) SED-with-2 -point(S, y, z) pick a random point x S (c, r) SED-with-2 -points(S-{x}, y, z) if x Disc(c, r) then return (c, r) else return circle given by x, y, z
![Running time SEDS pick a random point x S c r SEDSx if Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-33.jpg)
Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if x Disc(c, r) then return (c, r) else return SED-with-point(S, x) SED-with-point(S, y) pick a random point x S (c, r) SED-with-point(S-{x}, y) if x Disc(c, r) then return (c, r) else return SED-with-2 -points(S, y, x) SED-with-2 -point(S, y, z) pick a random point x S (c, r) SED-with-2 -points(S-{x}, y, z) if x Disc(c, r) then return (c, r) else return circle given by x, y, z O(n)
![Running time SEDS pick a random point x S c r SEDSx if Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-34.jpg)
Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if x Disc(c, r) then return (c, r) else return SED-with-point(S, x) SED-with-point(S, y) pick a random point x S (c, r) SED-with-point(S-{x}, y) if x Disc(c, r) then return (c, r) else return SED-with-2 -points(S, y, x) T(n) = T(n-1) + T(n) = O(n) 2 n SED-with-2 -points O(n)
![Running time SEDS pick a random point x S c r SEDSx if Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-35.jpg)
Running time ? SED(S) pick a random point x S (c, r) SED(S-{x}) if x Disc(c, r) then return (c, r) else return SED-with-point(S, x) T(n) = T(n-1) + T(n) = O(n) 2 n SED-with-point O(n)
![Smallest enclosing disc mdI B smallest enclosing disc with B on the boundary Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-36.jpg)
Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary and I inside Claim #2: if x is inside md(I, B) then md(I {x}, B) = md(I, B)
![Smallest enclosing disc mdI B smallest enclosing disc with B on the boundary Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-37.jpg)
Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary and I inside Claim #3: if x is outside of md(I, B) then md(I {x}, B) = md(I, B {x})
![Smallest enclosing disc mdI B smallest enclosing disc with B on the boundary Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-38.jpg)
Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary and I inside Claim #3: if x is outside of md(I, B) then md(I {x}, B) = md(I, B {x}) x md(I, B) md(l {x}, B)
![Smallest enclosing disc mdI B smallest enclosing disc with B on the boundary Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary](https://slidetodoc.com/presentation_image/b4fbaea732c4cec83f957c1063f941c5/image-39.jpg)
Smallest enclosing disc md(I, B) = smallest enclosing disc with B on the boundary and I inside Claim #3: if x is outside of md(I, B) then md(I {x}, B) = md(I, B {x}) Claim #2: if x is inside md(I, B) then md(I {x}, B) = md(I, B) Claim #1: md(I, B) is unique
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Jane dee hull elementary
Andy keels
Myepad
Bet relate thin heifer
Vehicle hull identification number
Advantage and disadvantage of transverse framing
Hull and propeller performance
Hull drive reduction theory
Apprendimento per associazionismo
Clark l. hull
Bullet bond
Dorure circuits imprimés
Coast guard hull identification number
For hull, drive reduction is ____.
Clark leonard hull teoria
How pin-up hits depot lease meaning
Corn minus the hull and germ.
Difference between o type and m type tubes
Sarkadi édes ősz
Wheat germ is the whole grain minus the husk.
Apply for secondary school hull