úÎ51ð4      !"#$%&'()*+,-./0123 6Checking whether an angle is within a given interval. The sum of two angles. ?Linear interpolation between two angles along the smaller arc. AApplying a binary function to consecutive pairs in a vector with  wrap-around. ;The edge vectors of a polygon given as a list of vertices. AThe absolute angles (with respect to the x axis) of the edges of ( a polygon given as a list of vertices. AThe signed area of a simple polygon (positive if vertices are in  counter-clockwise order). "The centroid of a simple polygon. FThe moment of inertia of a simple polygon with respect to the origin. AThe convex hull of a collection of vertices in counter-clockwise  order. (Andrew's Monotone Chain Algorithm) ,Monotone decomposition of a simple polygon. %Triangulation of a monotone polygon. #Triangulation of a simple polygon.  A 5-tuple (d2,ds,sep,v1,v2)$ that provides distance information  on two convex polygons, where d2 is the square of the distance,  ds0 is its sign (negative in case of penetration), sep describes  the opposing features, while v1 and v2 are the absolute C coordinates of the deepest points within the opposite polygon. If  the third parameter is True, only negative distances are # reported, and the function yields Nothing for non-overlapping ? polygons. This is more efficient if we are only interested in E collisions, since the computation can be cancelled upon finding the 2 first separating axis. If the third parameter is False, the  result cannot be Nothing. (The vertices of the first polygon (vs1) )The vertices of the second polygon (vs2) .Whether we are only interested in overlapping         !2since there are a lot of triangulation algorithms * a triangulation function can be passed "#$ some triangulation algorithms on't support polygons with holes \ These polygons with (nested) holes have to be cut so that they consist of only one outline F I.e. the chars a,b,d,e,g,o,p,q contain holes tat have to be deleted. %&_cut a polygon at a good position and insert the contained hole-polygon with opposite direction 'mmake sure that direction (clockwise or ccw) of polygons alternates depending on the nesting number c of poly ( f should be the funtion to test contains ? the trees then are the hierarchy of containedness of outlines )*+,\how many positions to rotate a polygon until the start point is nearest to some other point 0 call i.e. with nearest (3,4) [(0,0),(1,2), ... ] 0 0 -.Sreturns True iff the first point of the first polygon is inside the second poylgon /nA point is inside a polygon if it has an odd number of intersections with the boundary (Jordan Curve theorem) 0Ithe direction of a polygon can be obtained by looking at a maximal point " returns True if counterclockwise  False if clockwise 12 !"#$%&'()*+4,-./01526 !"#$%&'()*+,-./012 !"#$%&'()*+,-./0127389:;333<      !"#$%&'()*+,-./0123456789:;<=>?triangulation-0.3'Graphics.Triangulation.GJPTriangulation$Graphics.Triangulation.Triangulation'Graphics.Triangulation.KETTriangulation SeparationMonotoneSegmentVertexVtxidxprevnextvtypepxpy VertexTypeSide BottomCupTopCup BottomCapTopCapbetween+<alerp pairsWithedgesanglesareacentroidmoment convexHullmonotoneDecompositionmonotoneTriangulation triangulationconvexSeparationTreeNodeTriangulationFunction triangulatev2sgjpTri deleteHolesflattenembed alternate generateTrees treesList insertTrees insertTree rotatePolynearest insidePoly pointInsidepolygonDirectionmaxim isLeftTurnketTricombinationsOfisRightTurnOrOnarea2V2iscanisEarreflexVertices