úÎ0Ç-³&      !"#$%None 7A class for applying geometric applications to objects NThe type of the transformation matrices used in all geometrical applications. The application of Matrix2 a b c d to vector (x,y) should be   (ax+by,cx+dy). 8Inverses an inversible matrix. If it is not inversible,  The behaviour is undefined. The matrix of a rotation  a b is the leftmost point between a and b.  a b is the rightmost point between a and b.   a b is the lower point between a and b.   a b is the upper point between a and b.  &'(    &'(None /The type for representing all types of curves. DThe basic constructor for lines : a line is a degree 1 Bezier curve HA shortcut to define degree 3 Bezier curves from points. If the control  points are a,b,c,d%, the function should be called with   xa ya xb yb xc yc xd yd. BGives the point corresponding to the given value of the parameter  c0 c12 is a list of all possible points of intersection  between curves c0 and c1 : if  (u,v,w,x) is returned by ,  then curve c0 may intersect with c1 between parameter values u  and v0, which corresponds to parameter values between w and x for  c1E. The implementation guarantees that all actual solutions are found, 4 but possibly false solutions may also be returned. :Pseudo-distance from a point to a curve. Is the result is A smaller than 1, the point is inside the curve. If it is greater * than 1, the point is outside. Else we don't know (as usual with  interval arithmetic). EOffsets a given Bezier curve with the given pen matrix. The original M pen is a circle of radius one, the matrix, if inversible, is applied to it. The leftmost point on a curve  The bottommost point on a curve The rightmost point on a curve The topmost point on a curve )*+, -./0    ),+*   -./0None Approximates a list of Curves+ with a list of degree 3 Bernstein curves. 1 2  1 2None3ECuts a curve into a list of consecutive non-selfintersecting curves. !! curves/ is the array of all the curves, cut such that & each part does not intersect itself. "<Computes the intersections between any pair of curves given $ as input, in parallel in GHC using +RTS -N. ##7 takes the curves and the intersections computed as in ", S and outputs a list of all simple closed paths defined by the curves in the input. $$! takes the curves, the output of #, and outputs  the list of remerged9 curves, i.e. where the parts free of self-intersections  are glued back to each other. %KTakes a list of curves, potentially offset, and outputs the relevants part  of the outlines. 456783!9:;"#$%!"#$%!"#$% 476583!9:;"#$%<      !"#$%&'()*+,-./0123425670/.89:;<typography-geometry-1.0Graphics.TypographyGraphics.Typography.Bezier!Graphics.Typography.ApproximationGraphics.Typography.Outlines Geometric translateapplyMatrix2inverserotationleftMost rightMost bottomMosttopMostCurveCirclecx0cy0OffsetmatrixBeziercxcyt0t1linebezier3 evalCurveinterdistanceoffsetleftbottomrighttop approximatecutAll intersectionscontourremergeoutlines $fGeometric[]$fIntervalizeMatrix2 $fNumMatrix2TopoDedans SurLaLigneDehorsanglernd derivRoots$fGeometricCurvedesintervalize cutNoSelfTopology!minsertmunionmdeleteFindMin