convex nails

Reference: http://www.dyn4j.org/2010/04/gjk-gilbert-johnson-keerthi/As with the SAT (split axis) method, the GJK can determine whether two convex shapes overlap. Compared to the SAT, GJK is able to handle all the graphics in the same way, while the SAT determines that two different shapes (polygon-polygon/polygon-circle/Circle-circle) are treated differently.GJK principle: If the Minkowski of two convex gra

Evaluate the length of the convex hull edge Solution: Standard convex bag GrahamAlgorithm Code highlighting produced by Actipro CodeHighlighter (freeware)http://www.CodeHighlighter.com/--> # Include Iostream > # Include Cmath > # Define Pi ACOs (-1, 1.0) Const Double EPS = 1e - 6 ; Int SGN ( Double A ){ Return ( > EPS) - ( EPS );} Struct Point { Double X, Y;Poin

Convex Polygon diameter We define the maximum distance between any two points on a polygon as the diameter of the polygon. The number of vertices that determine the diameter may be more than one pair. In factNPolygon of a vertex may haveNThere is a "diameter point. A simple example of a polygon diameter is shown in the left figure. The diameter point is shown as the Black Point (a red parallel line) that is passed by parallel lines in the figure

The Triangle division of the convex PolygonTest Instructions: How many methods of N convex polygon can be decomposed into disjoint triangles, the last value modulo m.idea: The example of Cattleya number, just die m is a headache, because m is not necessarily a prime, so there is not necessarily an inverse element.Solution: The equation is f (n) = (C (n-2), (n-2)) / (n-1))% m; p = n-2, the equation can be tr

Main topic: A convex hull, a random point makes it with the first two points of the area than the other two adjacent points small area of the probabilityAccording to the test Instructions column equation, the ratio of the intersection area of N lines to the area of the original convex hull is finally obtained.1#include 2 #defineMAXN 1000103 #defineEPS 1e-104 using namespacestd;5 Doubleans,s1,s2;6 structp{7

Links: Poj 1113Test Instructions : n vertices of a given polygon castle. Build a fence around the castle, surround all points,and the distance between the wall and all points is at least L. ask for the smallest length of the wall.Ideas : Minimum length = The total edge length of the convex hull consisting of the castle vertices + the circumference of the circle with a radius of LFirst, the convex hull is o

n (1≤ n ≤2x105). The next n lines contain the details of the competitors.  I-th line contains II integers si and Ri (1≤ s i, rI ≤104). OutputIn the first and the only line of output, print a sequence of numbers of possible winners in increasing order.Sample Test (s) input31 32 23 1OutputInput31 21 12 1OutputTest instructions: N individual competitions, swimming and racing, swimming distance s, running R. Each person corresponds to two speed (land and water), if present S, R, makes t

Link: http://uva.onlinejudge.org/index.php? Option = com_onlinejudge amp; Itemid = 8 page = show_problem amp; Category = amp; problem = 1006 Problem Useless tile Packers Input:Standard Input Output:Standard output Yes, as you have apprehendedUseless tile Packers(UTP) Pack tiles. the tiles are of uniform thickness and have simple polygonal shape. for each tile a container is M m-built. the floor of the container is a convex polygon and under this

Question: On the X axis, a person has tall buildings on both sides of the building. The horizontal coordinate XI of the building and the height Hi of the building are also POs, asking the person to see the maximum angle of the sky. Analysis: Sort the positions of buildings and people from left to right. Use the stack to find the convex hull of the building on the left of a person, find the smallest angle, and then symmetric it, find the minimum angle

Link: poj 1113 monotonic link convex bag Summary Question: we still use a convex bag to find the shortest perimeter. We only need to add the length of a circle. We can apply the template to solve this problem; AC code: 1 # include Poj 1113 wall convex hull Application

The Great Divide of The ultraviolet A 10256 to determine whether two convex packets are separated. Calculate Two convex packets from the given two vertex sets, Then determine whether the two convex packets are separated. # Include

11177 (intersection of Convex Polygon and circle) The coordinates of n points with a convex n-edge shape are given in clockwise or counterclockwise order, and then a center is placed at (0, 0) the intersection area of the circular and convex n-edges is greater than or equal to R.Question: This question is just a mess, and all kinds of details are wrong .. After o

The optimal triangle division and matrix concatenation are both of the same issues. They all belong to the expression brackets. A matrix concatenation is a group of matrices that multiply, but different sequences have different numbers of multiplications. This requires us to find the execution order with the least number of multiplications. The optimal triangle division and matrix concatenation of a convex polygon are the same problem. The optimal

Convex Polygon minimum perimeter external rectangle This problem is similar to the smallest area external rectangle. Our goal is to find an external polygon in the smallest box (for perimeter ).P. What is interesting is that the minimum area and the external rectangle of the minimum perimeter usually overlap. Some may wonder if this is always true. The following example answers this question: the polygon (Gray) and its smallest area external rectan

Question Link Question: Calculate the convex circumference + a complete circumference. Because the inner angle of the slice formed after the inflection point is 360 degrees, it is a complete circle. Idea: Find the convex bag and add the circle perimeter 1 #include View code Poj 1113 wall (Graham calculates the convex circumference)

Easy to view and reprint 1. How to determine whether a polygon is clockwise or counterclockwiseFor a convex polygon, you only need to calculate a certain point.Cross Product = (Xi-XI-1), (Yi-Yi-1) x (XI + 1-xi), (yi + 1-yi ))= (Xi-XI-1) * (yi + 1-yi)-(Yi-Yi-1) * (XI + 1-xi) If the value of the preceding formula is positive, it is counter-clockwise. If it is negative, it is clockwise. For a general simple polygon, the above value needs to be calcula

Convex hull: The smallest polygon that can surround all given points (personal understanding)Graham: Select the point with the lowest Y value, sort the other point angles, then add the 1~n points to the stack, judging the current point, the top of the stack, and the bottom of the stack.To judge with a cross product, i.e. to be sentenced (top--)In fact, it is not right oh, you have not reacted to it ~ by the angle of the order will not have this situat

0 0 0 1 1 1 1 0 Sample Output 2 Hint Farm 1 (0, 0) and Farm 3 (1, 1) have the longest distance (square root of 2) to give some points, to find the furthest point of the plane to the square of the distance. Thought: We know that the farthest point in the plane must be in the convex package that surrounds these points, so, we first use the Graham ' s scan algorithm to find all the points in the convex