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The initial \ purpose was to blend geometric and symbolic aspects, so as to equip computer \ assisted design with symbolic capabilities. Nevertheless, this investigation \ aims more generally at providing a uniform treatment of analytical geometry \ and field analysis, in view of applications to physics, system modelling and \ morphology. This computational approach is based on a reification of \ parametric plotting commands. \ \>", "Abstract"], Cell["\<\ After a presentation of the data structure, the core of the paper \ describes a range of operators for the manipulation of manifolds. It stresses \ their potential use in shape design and scene description, in particular \ their ability to supersede several graphic packages. As such, the data type \ constitutes the foundations of a computational morphology. Then, various \ extensions are discussed: distributions and fields, mesh generation for \ finite element software and the prospect of an extension of the vector \ analysis package, with emphasis on tensors and differential forms. \ \>", \ "Abstract"], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell[TextData[{ "Computer algebra and symbolic programming have introduced analytical \ capabilities into many areas of scientific computing: discrete systems, \ algebra and summation, calculus and differential equations\[Ellipsis] \ Nevertheless, little benefit has been gained in shape design; researches in \ that domain have stimulated the evolution of computer assisted design but so \ far, these tools have included no or little symbolic capabilities and most \ CAD software is still developed with procedural languages and numerical \ methods. Besides, geometric problems have been tackled so far mainly by means \ of algebraic or theorem proving methods\[NonBreakingSpace][", CounterBox["Reference", "GaoWang"], "], thus leading to an underdevelopment of analytical methods." }], "Text"], Cell["\<\ Yet the analytical approach to geometry constitutes the foundations \ of many physical questions, especially those linked to space or space-time \ analysis by means of field theory. Hence the attempt to introduce analytical \ capabilities into geometry, initially in view of applications to shape \ description, then with the purpose to lay the foundations of further uses in \ differential geometry and field analysis. Although geometry is commonly \ thought of as the federating mathematical abstraction underlying those \ questions, morphology appears as an encompassing common denominator able to \ take into account questions outside the field of geometry, such as scene \ description, linkage design or finite element analysis.\ \>", "Text"], Cell[CellGroupData[{ Cell["Morphology as a Transverse Concept", "Subsection"], Cell["\<\ Although shape and form are more or less considered equivalent in \ common language, shape is rather devoted to geometric external aspects \ whereas form is rather devoted to more general internal structuring aspects \ (geometric or not). For instance, curves, surfaces and volumes as such are \ shapes, while considered together with some other characteristics, such as a \ field, they tend to be thought of as forms. So a form description is a piece \ of information about the way in which an object occupies and structures \ space. In practice, it is indissoluble from the way the object (or its form) \ is generated and can be transformed or combined with other ones. \ \>", "Text"], Cell[TextData[{ "Moreover, as a result of our cognitive capabilities, we tend to understand \ objects in contrast with a background, and also to perceive them as \ structured in container (wrapping structure) and content (internal structure)\ \[NonBreakingSpace][", CounterBox["Reference", "Lakoff"], "]. On the contrary, modern ideas about space or spacetime tend to identify \ space with its structuring content, space being constituted by the \ relationships between objects. To some extent, these opposite ideas can be \ made compatible by blending continuous aspects (figures as expansions) and \ discrete ones (figures as objects)," }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Mathematical and Algorithmic Requirements", "Subsection"], Cell[TextData[{ "Many form descriptions have been developed so far, in view of more or less \ specific applications: drawing software, geometric reasoning, computer \ assisted design, fractal image generation, data visualization\[Ellipsis]There \ is probably no universal form description, for those methods need always, to \ some extent, be optimized to best serve some specific problems. However, the \ trend to develop ad hoc optimized solutions for practical needs yields \ \[OpenCurlyDoubleQuote]a widely scattered conglomeration of disparate and, at \ first sight, unrelated methods\[CloseCurlyDoubleQuote]\[NonBreakingSpace][", CounterBox["Reference", "Lord&Wilson"], "]. This subsequently tends to severely decrease the so called \ orthogonality, i.e., the capability to cross fertilize disciplines by \ information exchange and object combinations thanks to generic types. " }], "Text"], Cell[TextData[{ "By quoting Lord and Wilson\[NonBreakingSpace][", CounterBox["Reference", "Lord&Wilson"], "], one may even stress the need for a mathematical foundation for a \ science of morphology unifying various approaches, a need that has not been \ fully recognized yet. Today, the requirement that the proposed method should \ lend itself well to an algorithmic treatment must be taken into account. It \ should also have a broader scope than the so called mathematical morphology, \ which is more or less restricted to the \[OpenCurlyDoubleQuote]pixel level\ \[CloseCurlyDoubleQuote] methods used for image processing. In the following, \ we actually focus on form synthesis rather than form analysis. The solution \ put forward derives from a common mathematical tool, slightly adapted to an \ algorithmic purpose, i.e., a new glance at a classical theory\ \[NonBreakingSpace][", CounterBox["Reference", "Barr\[EGrave]re"], "]. " }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Manifolds as a Unifying Approach to Morphology", "Subsection"], Cell["\<\ We bet on manifolds, because of their sound analytical foundation, \ their strong geometric flavor and their adaptation to the algorithmic \ treatment, especially computer algebra and symbolic programming. In \ particular, a manifold determines a codomain as a subset of some (often \ euclidean) space. By regarding the codomain as the object and the surrounding \ space as the background, it actually determines a shape. By considering \ various structuring elements such as a coordinate system (domain) or a field \ over the manifold, it determines as many forms. Moreover, the boundary of a \ manifold constitutes an element of a container-content approach. More \ generally, other structuring tools will be described below, such as atlases \ that enable scene descriptions.\ \>", "Text"], Cell[TextData[{ "Because of its visual aspects, shape design is in natural relationship \ with the underlying graphic capabilities\[NonBreakingSpace][", CounterBox["Reference", "Wickham-Jones"], ", ", CounterBox["Reference", "Trott"], "]. In Mathematica, these rely upon a few graphic primitives (", StyleBox["Line", "InlineInput"], ", ", StyleBox["Polygon", "InlineInput"], "\[Ellipsis]) and a range of standard plotting commands (", StyleBox["Plot", "InlineInput"], ", ", StyleBox["ParametricPlot\[Ellipsis]", "InlineInput"], "), plus a variety of complementary commands defined in various packages \ (", StyleBox["Shapes`", "InlineInput"], ", ", StyleBox["SolidOfRevolution`", "InlineInput"], "\[Ellipsis]). This leads to a functional approach where shapes are \ produced by plotting commands that build them by assembling low level graphic \ primitives, thus excluding higher level objects. " }], "Text"], Cell["\<\ On the contrary, resorting to manifolds leads to a reification of \ shape: these and other geometric entities like fields, can be defined as \ quite compact symbolic objects, rather than huge assemblies of raw graphic \ primitives resulting from plotting commands. This facilitates the \ introduction of both higher level entities, able to describe objects as \ wholes, and higher level symbolic functions able to manipulate and combine \ these entities. This also enables the consistent gathering of graphic tools \ scattered around various graphic packages and their extension not only to \ shape design but also to field analysis. \ \>", "Text"], Cell[BoxData[ \(Needs["\"]\)], "InputOnly"], Cell[TextData[{ "An experimental ", ButtonBox["set of packages"], " (", ButtonBox["available material", ButtonData:>"material", ButtonStyle->"Hyperlink"], ") is developed to investigate the ideas presented in the paper. ", StyleBox["Manifolds`Morphology`", "InlineInput"], " is simply intended to load the whole directory. Extracts or simplified \ versions, which should not be evaluated, are occasionally shown in the \ paper." }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["An Algorithmic Approach to Manifolds", "Section"], Cell[TextData[{ "Although a manifold is usually defined as a collection (called an atlas) \ of patches, i.e., of homeomorphisms from an open subset of ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^n\)]], " onto an open subset of a topological space \[ScriptCapitalM]\ \[NonBreakingSpace][", CounterBox["Reference", "GrayA"], "], the algorithmic approach will rather focus on ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^n\)]], " as a curvilinear coordinate systems on \[ScriptCapitalM], which in most \ cases will be some subset of ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^p\)]], ". Indeed, the notion of a manifold is deeply rooted in analytical \ geometry, i.e., in the practical need to describe curves, surfaces and \ volumes, or their n-dimensional generalizations, both from the analytical and \ the geometrical points of view." }], "Text"], Cell[CellGroupData[{ Cell["The Data Structure", "Subsection"], Cell[TextData[{ "As a reflect of this origin, the algorithmic approach aims at blending the \ analytical and geometric aspects, especially their graphic counterpart. \ Basically, the type ", StyleBox["Manifold", "InlineInput"], " introduced hereafter denotes a patch; then an atlas is simply a \ collection of manifolds, without any continuity or differentiability \ requirement. The type ", StyleBox["Manifold", "InlineInput"], " consists of two entities: a set of expressions that should be thought of \ as a list of parametric equations, together with a domain specification for \ the variables, which are the local coordinates on the manifold. The type \ being the head of the expression, this leads to the informal expression \ template\[NonBreakingSpace]: ", StyleBox["Manifold[list of expressions, domain specification]", "InlineInput"], ". The domain specification follows the syntax of continuous domains in \ plotting commands: a triple or a sequence of triples ", StyleBox["{c, cmin, cmax}", "InlineInput"], " denoting a coordinate symbol with a minimum value and a maximum value." }], "Text"], Cell[TextData[{ "This design is adapted from a first attempt by Gray\[NonBreakingSpace][", CounterBox["Reference", "GrayJ"], "] who actually adopted a more general viewpoint by considering mappings. \ Here is an example, which may be thought of as a parametrized parametric \ representation of a segment of a ring with the symbolic parameter r." }], "Text"], Cell[BoxData[ \(Manifold[{\[Rho]\ Cos[\[Theta]], \ \[Rho]\ Sin[\[Theta]]}, {\[Rho], \ 1, \ r}, {\[Theta], \ 0, 3\ \[Pi]/2}]\)], "InputOnly"], Cell[TextData[{ "In that case, the codomain is a subset of ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^2\)]], "and the expressions are usually interpreted as the parametric \ representation (equations) of a geometric domain. Nevertheless, manifolds \ describe in principle abstract entities that entail no assumption about their \ nature, except they are member of a topological space. In particular, the \ parametrized objects need not be points nor vectors. Any parametrized family \ of entities is susceptible of a description as a manifold, provided it has \ some differentiability or at least continuity properties. For instance, a \ parametrized family of matrices or a parametrized family of functions can be \ investigated as manifolds. However, there is no standard visualization \ procedure for such manifolds and their graphic representation may require \ assumptions or tricks." }], "Text"], Cell[TextData[{ "When the codomain is a subset of ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^p\)]], ", it needs not be euclidean; manifold theory is basically a relativistic \ theory of abstract spaces. Nevertheless, in many applications, manifolds are \ interpreted from an absolute point of view: the codomain is supposed to be \ some subset of an euclidean space with an orthogonal cartesian coordinate \ system and the domain is viewed as a curvilinear coordinate system for the \ codomain. Such an absolute interpretation is almost unavoidable when graphic \ representations are considered. " }], "Text"], Cell[TextData[{ "However this assumption is not mandatory and manifolds may have other \ interpretations: for instance, in another context, the codomain may be the \ subset of an euclidean space with a curvilinear coordinate system or even the \ subset of a space with no metric property. So we try to maintain flexibility \ by avoiding useless strong assumptions regarding the absolute or relative \ interpretations of manifolds, thus leaving the user choose the interpretation \ only when needed. In particular, commands like ", StyleBox["Connect", "InlineInput"], " are introduced, that facilitate the switching between the absolute and \ relative interpretations." }], "Text"], Cell[TextData[{ "Although it may be required in some reasonings, the distinction between \ open or closed intervals is useless in this algorithmic context\ \[NonBreakingSpace]; hence the use of lists for domains. As a remark, these \ algorithmic versions of manifolds need not be differentiable, i.e., they \ describe varieties as well (for instance, fractal varieties). Finally, a \ manifold with no domain is a point. Its syntax is ", StyleBox["Manifold[list of expressions]", "InlineInput"], ". Taking into account this limit case is useful in some generic \ applications. Actually, when working with manifolds, there is no longer any \ notion of point, curve, surface or volume as types since all are manifolds. \ The number of coordinates gives the nature of the figure, the dimension of \ the codomain specifying the immersion space. " }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["The Selectors", "Subsection"], Cell[TextData[{ "The selectors extract the various arguments of a typed expression\ \[NonBreakingSpace][", CounterBox["Reference", "MaederCSM"], "]. They were initially introduced in computer science to isolate the \ interface specification from the internal representation. Actually, when the \ representation is stable, argument extraction can be done directly with \ patterns in the left hand sides of transformation rules. Nevertheless, some \ generic programs are more easily designed by resorting to selectors. " }], "Text"], Cell[TextData[{ "By thinking of applications to geometry or field analysis, we use ", StyleBox["Coordinates", "InlineInput"], " for the variables, ", StyleBox["Domain", "InlineInput"], " for the coordinate ranges and ", StyleBox["Codomain", "InlineInput"], " for the parametric expressions (thus identifying the functions and their \ values)." }], "Text"], Cell[BoxData[{ \(Coordinates[Manifold[_, d__List]] ^:= Map[First, {d}]\), "\[IndentingNewLine]", \(Domain[Manifold[_, d__List]] ^:= {d}\), "\[IndentingNewLine]", \(\(\(Codomain[Manifold[e_, __]]\)\(^:=\)\(e\)\(\ \ \)\)\)}], "InputOnly"], Cell["\<\ There might be an ambiguity between domain and codomain, which in \ this context are the domain and codomain of the associated mapping, while the \ codomain can also be thought of as a domain in a geometric sense. We \ nevertheless maintain domain and codomain, because of their common use in \ mathematics as well as computer science and we will resort to patch or region \ to denote a geometric domain. \ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Variants", "Subsection"], Cell[CellGroupData[{ Cell["Atlases and geometric scenes", "Subsubsection"], Cell["\<\ In the frame of this algorithmic approach, an atlas is simply a \ list of manifolds; so one departs from the mathematical approach where a \ differentiable (at least continuous) overlapping is required. An atlas is \ basically a piecewise manifold; it is actually slightly more general for it \ enables the accumulation of manifolds with different dimensions. 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" }], "Text"], Cell[TextData[{ "Atlases are especially useful for the manipulation of sets of manifolds as \ wholes. As such, they constitute a natural data structure for compound shapes \ or geometric scenes, the atlas then being thought of as a set of figures. \ Manifolds then appear as the natural primitives for scene description, in \ association with the type ", StyleBox["Atlas", "InlineInput"], " as a composition tool. As such they enable the combination of continuous \ and discrete aspects." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Many-valued manifolds", "Subsubsection"], Cell["\<\ A many-valued manifold differs from an atlas in the sense that \ there is a common domain for a list of parametrizations; nevertheless, it can \ possibly be rewritten as an atlas of manifolds. The multiple parametrizations \ can not only be arranged in lists but also matrices or higher dimensional \ tables. Roughly, many-valued manifolds implement coverings.\ \>", "Text"], Cell["\<\ Many-valued manifolds are mainly used to parametrize figures with \ several branches (e.g. hyperbole), in particular in the case of manifolds \ computed as inverse mappings. Applications of many-valued manifolds to \ fractals are given below. 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of fields, coordinate systems should be \ regarded as particular cases of coordinate systems on manifolds. \ Nevertheless, for convenience and consistency with the vector analysis \ package, a specific data structure for usual coordinate systems is \ maintained, in the form of a type wrapping a list of coordinate symbols, \ e.g., ", StyleBox["Polar[{r, \[Theta]}]", "InlineInput"], ". There is nonetheless no default symbol for coordinates: freely chosen by \ the user, these are specified where needed. " }], "Text"], Cell[BoxData[{ \(SetAttributes[CoordinateRanges, \ HoldFirst]\), "\[IndentingNewLine]", \(SetAttributes[CoordinateSystemQ, \ HoldFirst]\), "\[IndentingNewLine]", \(CoordinateSystemQ[_Polar] := True\), "\[IndentingNewLine]", \(Polar[{r_, \[Theta]_}] := {r\ Cos[\[Theta]], r\ Sin[\[Theta]]}\), "\[IndentingNewLine]", \(CoordinateRanges[ Polar[{r_, \[Theta]_}]] ^:= {{r, 0, \[Infinity]}, {\[Theta], 0, 2 \[Pi]}}\)}], "InputOnly"], Cell[TextData[{ "The associated transformation rules must be given for every common \ coordinate system. A symbol like ", StyleBox["Polar", "InlineInput"], " may express either a coordinate system (absolute viewpoint) when \ processed as a type or a change of coordinates (relative viewpoint) when \ processed as a function. 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If need be, the \ auxiliary command ", StyleBox["ToManifold", "InlineInput"], " generates the associated manifold with the standard coordinate ranges." }], "Text"], Cell[TextData[{ "In particular, ", StyleBox["Manifold[Polar[{r, \[Theta]}]]", "InlineInput"], " yields ", StyleBox["Manifold[{r Cos[\[Theta]], r Sin[\[Theta]]}]", "InlineInput"], ", i.e., the cartesian coordinates of the point; so it is equivalent to the \ command ", StyleBox["CoordinatesToCartesian", "InlineInput"], " of the vector analysis package, the analog of ", StyleBox["CoordinatesFromCartesian", "InlineInput"], " being obtained by introducing reciprocal coordinate systems (respectively \ coordinate changes), e.g., ", StyleBox["InversePolar[{u, v}]", "InlineInput"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Manifold[InversePolar[{u, v}]]\)], "Input"], Cell[BoxData[ \(Manifold[{\@\(u\^2 + v\^2\), ArcTan[u, v]}]\)], "Output"] }, Open ]], Cell[TextData[{ "With these conventions, the expression ", StyleBox["Manifold[Polar[{f[t], g[t]}], {t,tmin,tmax}]", "InlineInput"], " describes the curve with parametric expressions ", StyleBox["f[t]", "InlineInput"], " and ", StyleBox["g[t]", "InlineInput"], " in polar coordinates. Surfaces in three dimensional coordinate systems \ can be described in a similar way. Although it is not common, this way of \ expressing manifolds by their parametric representations in some coordinate \ system is concise. 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A generic command ", StyleBox["Draw", "InlineInput"], " is introduced, in the form of polymorphic transformation rules." }], "Text"], Cell[CellGroupData[{ Cell["The Command Draw", "Subsection"], Cell[TextData[{ "Both the functions to be plotted and the domains being part of the data \ structure, manifolds require a single graphic command with a single argument \ plus possible options; let us call it ", StyleBox["Draw", "InlineInput"], ". Only manifolds the codomain of which have a geometric interpretation in \ a two or three dimensional space are drawn, the length of the first argument \ determining the dimension of the representation space. Then the number of \ variables determines the nature of the represented object: point, curve, \ surface, volume or higher dimensional object. Moreover, the codomain is \ supposed to be a subset of an euclidean affine space equipped with a \ canonical orthogonal cartesian coordinate system, which has consequently the \ statute of an \[OpenCurlyDoubleQuote]absolute\[CloseCurlyDoubleQuote] \ reference space. Then the domain is that of the curvilinear coordinate system \ of the manifold." }], "Text"], Cell["\<\ Most drawings are \[OpenCurlyDoubleQuote]subcontracted\ \[CloseCurlyDoubleQuote] to standard parametric plotting commands. The \ various combinations are summarized in the following table.\ \>", "Text"], Cell[BoxData[GridBox[{ {\(n\ \((domain)\)\), \(p\ \((codomain)\)\), \(plotting\ function\)}, {"0", "2", \(Show\ \((Graphics)\)\)}, {"0", "3", \(Show \((Graphics3D)\)\)}, {"1", "2", "ParametricPlot"}, {"1", "3", "ParametricPlot3D"}, {"2", "2", "SolidParametricPlot"}, {"2", "3", "ParametricPlot3D"}, {"3", "3", "SolidParametricPlot3D"} }]], "Text", TextAlignment->Center, TextJustification->0, GridBoxOptions->{ColumnAlignments->{Center, Center, Left}}], Cell[TextData[{ "Extensions of the family ", StyleBox["ParametricPlot", "InlineInput"], " are required for the 2-2 and 3-3 cases. They have been temporarily called \ ", StyleBox["SolidParametricPlot", "InlineInput"], " and ", StyleBox["SolidParametricPlot3D", "InlineInput"], ", although polymorphism should allow to process them as specific cases of \ ", StyleBox["ParametricPlot", "InlineInput"], " and ", StyleBox["ParametricPlot3D", "InlineInput"], ". ", StyleBox["SolidParametricPlot3D", "InlineInput"], " draws the boundary, which is valid only provided the jacobian of the \ parametric equations does not vanish. The case p=1 is not processed by ", StyleBox["Draw", "InlineInput"], " because it is of weak visual interest. Nevertheless, thanks to a lifting, \ it can be rearranged into a 2D or a 3D manifold so as to be visualized the \ same way functions are visualized with ", StyleBox["Plot", "InlineInput"], " or ", StyleBox["Plot3D", "InlineInput"], ". " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Lift[Manifold[{h[t]}, {t, \(-1\), 1}]]\)], "Input"], Cell[BoxData[ \(Manifold[{t, h[t]}, {t, \(-1\), 1}]\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Higher Dimensional Manifolds", "Subsection", CellTags->"Higher dimensional manifolds"], Cell["\<\ Higher dimensional manifolds are processed by means of the 2D or 3D \ projection of their boundary. Here is the example of the 4-dimensional unit \ hypercube.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(UnitHyperCube[s_List] := Manifold[s, Apply[Sequence, Thread[List[s, 0, 1]]]]\), "\[IndentingNewLine]", \(uhc4 = UnitHyperCube[{a, b, c, d}]\)}], "Input"], Cell[BoxData[ \(Manifold[{a, b, c, d}, {a, 0, 1}, {b, 0, 1}, {c, 0, 1}, {d, 0, 1}]\)], "Output"] }, Open ]], Cell["\<\ Below, a 3D projection of the 4D unit hypercube is drawn. \ Transparency effects would be welcome. 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Briefly, an iterated function system is a set of contracting affine \ transformations that are iteratively applied to any initial figure. The \ command ", StyleBox["ManifoldIFS", "InlineInput"], " uses the direct iteration\[NonBreakingSpace][", CounterBox["Reference", "Wagon"], "] rather than its variant called \[OpenCurlyDoubleQuote]chaos game\ \[CloseCurlyDoubleQuote]\[NonBreakingSpace][", CounterBox["Reference", "Wagon"], ", ", CounterBox["Reference", "IFS"], "]: it computes the nth approximation of an IFS, from any initial manifold, \ in the form of a many-valued manifold." }], "Text"], Cell[BoxData[{ \(\(OneStepIFS[ifs_]\)[s_] := Flatten[Map[Through[ifs[#]] &, s], 1]\), "\[IndentingNewLine]", \(IterateIFS[ifs_, init_, n_] := Nest[OneStepIFS[ifs], {init}, n]\), "\[IndentingNewLine]", \(ManifoldIFS[ifs_, Manifold[p_, c___], n_] := Manifold[IterateIFS[ifs, p, n], c]\)}], "InputOnly"], Cell[TextData[{ "Here is the example of a Sierpinsky sponge. Giving a low value to ", StyleBox["PlotPoints", "InlineInput"], " is necessary to avoid a lengthy computation. 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.30397 L .31806 .34626 L closepath p F P 0 g s .23 .175 .586 r .31806 .34626 m .3346 .34123 L .31786 .38303 L closepath p F P 0 g s .23 .175 .586 r .31786 .38303 m .33442 .37859 L .31766 .4199 L closepath p F P 0 g s .23 .175 .586 r .31766 .4199 m .33425 .41605 L .31746 .45687 L closepath p F P 0 g s .397 .802 .982 r .33514 .22975 m .35217 .22275 L .36845 .23373 L closepath p F P 0 g s .82 .657 .681 r .33514 .22975 m .36845 .23373 L .33496 .26681 L closepath p F P 0 g s .912 .958 .806 r .33496 .26681 m .35217 .22275 L .36845 .23373 L closepath p F P 0 g s .23 .175 .586 r .31746 .45687 m .33406 .45362 L .31726 .49393 L closepath p F P 0 g s .23 .175 .586 r .31726 .49393 m .33388 .49128 L .31706 .5311 L closepath p F P 0 g s .211 .159 .578 r .28509 .2326 m .30119 .22569 L .28485 .26941 L closepath p F P 0 g s .397 .802 .982 r .25091 .2286 m .2666 .22156 L .28509 .2326 L closepath p F P 0 g s .818 .656 .681 r .25091 .2286 m .28509 .2326 L .25061 .26575 L closepath p F P 0 g s .912 .946 .811 r .25061 .26575 m .2666 .22156 L .28509 .2326 L closepath p F P 0 g s .345 .786 .962 r .33478 .30397 m .35185 .29817 L .36819 .30727 L closepath p F P 0 g s .82 .657 .681 r .33478 .30397 m .36819 .30727 L .3346 .34123 L closepath p F P 0 g s .912 .965 .802 r .3346 .34123 m .35185 .29817 L .36819 .30727 L closepath p F P 0 g s .372 .795 .973 r .25061 .26575 m .26632 .25932 L .28485 .26941 L closepath p F P 0 g s .818 .656 .681 r .25061 .26575 m .28485 .26941 L .25032 .30301 L closepath p F P 0 g s .912 .95 .809 r .25032 .30301 m .26632 .25932 L .28485 .26941 L closepath p F P 0 g s .139 .68 .832 r .28313 .52991 m .29937 .52783 L .31706 .5311 L closepath p F P 0 g s .818 .656 .681 r .28313 .52991 m .31706 .5311 L .28288 .56753 L closepath p F P 0 g s .908 .978 .789 r .28288 .56753 m .29937 .52783 L .31706 .5311 L closepath p F P 0 g s .296 .23 .612 r .50225 .23203 m .52192 .2251 L .5023 .2689 L closepath p F P 0 g s .284 .761 .932 r .33442 .37859 m .35154 .374 L .36792 .3812 L closepath p F P 0 g s .82 .657 .681 r .33442 .37859 m .36792 .3812 L .33425 .41605 L closepath p F P 0 g s .91 .971 .796 r .33425 .41605 m .35154 .374 L .36792 .3812 L closepath p F P 0 g s .397 .802 .982 r .38586 .22686 m .40385 .21976 L .41892 .23089 L closepath p F P 0 g s .823 .659 .68 r .38586 .22686 m .41892 .23089 L .38575 .26416 L closepath p F P 0 g s .912 .965 .802 r .38575 .26416 m .40385 .21976 L .41892 .23089 L closepath p F P 0 g s .215 .726 .889 r .33406 .45362 m .35122 .45026 L .36766 .45553 L closepath p F P 0 g s .82 .657 .681 r .33406 .45362 m .36766 .45553 L .33388 .49128 L closepath p F P 0 g s .908 .978 .789 r .33388 .49128 m .35122 .45026 L .36766 .45553 L closepath p F P 0 g s .23 .175 .586 r .33514 .22975 m .35217 .22275 L .33496 .26681 L closepath p F P 0 g s .397 .802 .982 r .21607 .22452 m .23133 .21734 L .25091 .2286 L closepath p F P 0 g s .818 .656 .681 r .21607 .22452 m .25091 .2286 L .21572 .26203 L closepath p F P 0 g s .911 .943 .812 r .21572 .26203 m .23133 .21734 L .25091 .2286 L closepath p F P 0 g s .23 .175 .586 r .33478 .30397 m .35185 .29817 L .3346 .34123 L closepath p F P 0 g s .191 .142 .57 r .25091 .2286 m .2666 .22156 L .25061 .26575 L closepath p F P 0 g s .284 .761 .932 r .38542 .3767 m .4035 .37205 L .41866 .37934 L closepath p F P 0 g s .823 .659 .68 r .38542 .3767 m .41866 .37934 L .38531 .41441 L closepath p F P 0 g s .908 .978 .789 r .38531 .41441 m .4035 .37205 L .41866 .37934 L closepath p F P 0 g s .211 .159 .578 r .28313 .52991 m .29937 .52783 L .28288 .56753 L closepath p F P 0 g s .139 .68 .832 r .24855 .5287 m .26437 .52658 L .28313 .52991 L closepath p F P 0 g s .818 .656 .681 r .24855 .5287 m .28313 .52991 L .24825 .56668 L closepath p F P 0 g s .909 .975 .793 r .24825 .56668 m .26437 .52658 L .28313 .52991 L closepath p F P 0 g s .191 .142 .57 r .25061 .26575 m .26632 .25932 L .25032 .30301 L closepath p F P 0 g s .099 .652 .799 r .24825 .56668 m .26409 .56518 L .28288 .56753 L closepath p F P 0 g s .818 .656 .681 r .24825 .56668 m .28288 .56753 L .24795 .60476 L closepath p F P 0 g s .908 .978 .789 r .24795 .60476 m .26409 .56518 L .28288 .56753 L closepath p F P 0 g s .345 .786 .962 r .21538 .29964 m .23068 .29369 L .25032 .30301 L closepath p F P 0 g s .818 .656 .681 r .21538 .29964 m .25032 .30301 L .21504 .33735 L closepath p F P 0 g s .912 .95 .809 r .21504 .33735 m .23068 .29369 L .25032 .30301 L closepath p F P 0 g s .23 .175 .586 r .33442 .37859 m .35154 .374 L .33425 .41605 L closepath p F P 0 g s .248 .19 .593 r .38586 .22686 m .40385 .21976 L .38575 .26416 L closepath p F P 0 g s .397 .802 .982 r .35217 .22275 m .36977 .21551 L .38586 .22686 L closepath p F P 0 g s .823 .659 .68 r .35217 .22275 m .38586 .22686 L .35201 .26041 L closepath p F P 0 g s .912 .961 .804 r .35201 .26041 m .36977 .21551 L .38586 .22686 L closepath p F P 0 g s .23 .175 .586 r .33406 .45362 m .35122 .45026 L .33388 .49128 L closepath p F P 0 g s .372 .795 .973 r .35201 .26041 m .36963 .25379 L .38575 .26416 L closepath p F P 0 g s .823 .659 .68 r .35201 .26041 m .38575 .26416 L .35185 .29817 L closepath p F P 0 g s .912 .965 .802 r .35185 .29817 m .36963 .25379 L .38575 .26416 L closepath p F P 0 g s .397 .802 .982 r .2666 .22156 m .28282 .21428 L .30119 .22569 L closepath p F P 0 g s .82 .657 .681 r .2666 .22156 m .30119 .22569 L .26632 .25932 L closepath p F P 0 g s .912 .95 .809 r .26632 .25932 m .28282 .21428 L .30119 .22569 L closepath p F P 0 g s .397 .802 .982 r .48939 .22096 m .50936 .21366 L .52192 .2251 L closepath p F P 0 g s .827 .662 .678 r .48939 .22096 m .52192 .2251 L .48942 .25877 L closepath p F P 0 g s .908 .978 .789 r .48942 .25877 m .50936 .21366 L .52192 .2251 L closepath p F P 0 g s .248 .19 .593 r .38542 .3767 m .4035 .37205 L .38531 .41441 L closepath p F P 0 g s .169 .124 .56 r .21607 .22452 m .23133 .21734 L .21572 .26203 L closepath p F P 0 g s .284 .761 .932 r .35154 .374 m .36922 .36927 L .38542 .3767 L closepath p F P 0 g s .823 .659 .68 r .35154 .374 m .38542 .3767 L .35138 .41208 L closepath p F P 0 g s .909 .975 .793 r .35138 .41208 m .36922 .36927 L .38542 .3767 L closepath p F P 0 g s .397 .802 .982 r .18056 .22036 m .19538 .21305 L .21607 .22452 L closepath p F P 0 g s .818 .656 .681 r .18056 .22036 m .21607 .22452 L .18016 .25822 L closepath p F P 0 g s .911 .939 .813 r .18016 .25822 m .19538 .21305 L .21607 .22452 L closepath p F P 0 g s .251 .745 .912 r .35138 .41208 m .36909 .40797 L .38531 .41441 L closepath p F P 0 g s .823 .659 .68 r .35138 .41208 m .38531 .41441 L .35122 .45026 L closepath p F P 0 g s .908 .978 .789 r .35122 .45026 m .36909 .40797 L .38531 .41441 L closepath p F P 0 g s .372 .795 .973 r .18016 .25822 m .195 .25153 L .21572 .26203 L closepath p F P 0 g s .818 .656 .681 r .18016 .25822 m .21572 .26203 L .17977 .29619 L closepath p F P 0 g s .911 .943 .812 r .17977 .29619 m .195 .25153 L .21572 .26203 L closepath p F P 0 g s .139 .68 .832 r .2133 .52747 m .22869 .5253 L .24855 .5287 L closepath p F P 0 g s .818 .656 .681 r .2133 .52747 m .24855 .5287 L .21295 .56581 L closepath p F P 0 g s .91 .971 .796 r .21295 .56581 m .22869 .5253 L .24855 .5287 L closepath p F P 0 g s .191 .142 .57 r .24855 .5287 m .26437 .52658 L .24825 .56668 L closepath p F P 0 g s .191 .142 .57 r .24825 .56668 m .26409 .56518 L .24795 .60476 L closepath p F P 0 g s .169 .124 .56 r .21538 .29964 m .23068 .29369 L .21504 .33735 L closepath p F P 0 g s .345 .786 .962 r .17977 .29619 m .19461 .29013 L .21538 .29964 L closepath p F P 0 g s .818 .656 .681 r .17977 .29619 m .21538 .29964 L .17937 .33426 L closepath p F P 0 g s .912 .946 .811 r .17937 .33426 m .19461 .29013 L .21538 .29964 L closepath p F P 0 g s .316 .774 .948 r .17937 .33426 m .19423 .32884 L .21504 .33735 L closepath p F P 0 g s .818 .656 .681 r .17937 .33426 m .21504 .33735 L .17897 .37244 L closepath p F P 0 g s .912 .95 .809 r .17897 .37244 m .19423 .32884 L .21504 .33735 L closepath p F P 0 g s .057 .622 .762 r .2126 .60425 m .22802 .60337 L .24795 .60476 L closepath p F P 0 g s .818 .656 .681 r .2126 .60425 m .24795 .60476 L .21225 .64281 L closepath p F P 0 g s .908 .978 .789 r .21225 .64281 m .22802 .60337 L .24795 .60476 L closepath p F P 0 g s .23 .175 .586 r .35217 .22275 m .36977 .21551 L .35201 .26041 L closepath p F P 0 g s .23 .175 .586 r .35201 .26041 m .36963 .25379 L .35185 .29817 L closepath p F P 0 g s .191 .142 .57 r .2666 .22156 m .28282 .21428 L .26632 .25932 L closepath p F P 0 g s .139 .68 .832 r .26437 .52658 m .28074 .52438 L .29937 .52783 L closepath p F P 0 g s .82 .657 .681 r .26437 .52658 m .29937 .52783 L .26409 .56518 L closepath p F P 0 g s .908 .978 .789 r .26409 .56518 m .28074 .52438 L .29937 .52783 L closepath p F P 0 g s .281 .218 .606 r .48939 .22096 m .50936 .21366 L .48942 .25877 L closepath p F P 0 g s .397 .802 .982 r .45624 .21673 m .47585 .2093 L .48939 .22096 L closepath p F P 0 g s .827 .662 .678 r .45624 .21673 m .48939 .22096 L .45622 .25491 L closepath p F P 0 g s .909 .975 .793 r .45622 .25491 m .47585 .2093 L .48939 .22096 L closepath p F P 0 g s .372 .795 .973 r .45622 .25491 m .47586 .24811 L .48942 .25877 L closepath p F P 0 g s .827 .662 .678 r .45622 .25491 m .48942 .25877 L .45621 .29319 L closepath p F P 0 g s .908 .978 .789 r .45621 .29319 m .47586 .24811 L .48942 .25877 L closepath p F P 0 g s .397 .802 .982 r .14436 .21612 m .15871 .20866 L .18056 .22036 L closepath p F P 0 g s .818 .656 .681 r .14436 .21612 m .18056 .22036 L .14391 .25435 L closepath p F P 0 g s .91 .935 .814 r .14391 .25435 m .15871 .20866 L .18056 .22036 L closepath p F P 0 g s .23 .175 .586 r .35154 .374 m .36922 .36927 L .35138 .41208 L closepath p F P 0 g s .146 .104 .55 r .18056 .22036 m .19538 .21305 L .18016 .25822 L closepath p F P 0 g s .23 .175 .586 r .35138 .41208 m .36909 .40797 L .35122 .45026 L closepath p F P 0 g s .146 .104 .55 r .18016 .25822 m .195 .25153 L .17977 .29619 L closepath p F P 0 g s .169 .124 .56 r .2133 .52747 m .22869 .5253 L .21295 .56581 L closepath p F P 0 g s .139 .68 .832 r .17737 .52621 m .1923 .524 L .2133 .52747 L closepath p F P 0 g s .818 .656 .681 r .17737 .52621 m .2133 .52747 L .17697 .56492 L closepath p F P 0 g s .911 .968 .799 r .17697 .56492 m .1923 .524 L .2133 .52747 L closepath p F P 0 g s .397 .802 .982 r .36977 .21551 m .38796 .20803 L .40385 .21976 L closepath p F P 0 g s .825 .66 .679 r .36977 .21551 m .40385 .21976 L .36963 .25379 L closepath p F P 0 g s .912 .965 .802 r .36963 .25379 m .38796 .20803 L .40385 .21976 L closepath p F P 0 g s .099 .652 .799 r .17697 .56492 m .19191 .56337 L .21295 .56581 L closepath p F P 0 g s .818 .656 .681 r .17697 .56492 m .21295 .56581 L .17656 .60374 L closepath p F P 0 g s .91 .971 .796 r .17656 .60374 m .19191 .56337 L .21295 .56581 L closepath p F P 0 g s .146 .104 .55 r .17977 .29619 m .19461 .29013 L .17937 .33426 L closepath p F P 0 g s .146 .104 .55 r .17937 .33426 m .19423 .32884 L .17897 .37244 L closepath p F P 0 g s .169 .124 .56 r .2126 .60425 m .22802 .60337 L .21225 .64281 L closepath p F P 0 g s .057 .622 .762 r .17656 .60374 m .19152 .60284 L .2126 .60425 L closepath p F P 0 g s .818 .656 .681 r .17656 .60374 m .2126 .60425 L .17616 .64267 L closepath p F P 0 g s .909 .975 .793 r .17616 .64267 m .19152 .60284 L .2126 .60425 L closepath p F P 0 g s .015 .59 .722 r .17616 .64267 m .19113 .64243 L .21225 .64281 L closepath p F P 0 g s .818 .656 .681 r .17616 .64267 m .21225 .64281 L .17575 .6817 L closepath p F P 0 g s .908 .978 .789 r .17575 .6817 m .19113 .64243 L .21225 .64281 L closepath p F P 0 g s .284 .761 .932 r .14256 .36967 m .15696 .36478 L .17897 .37244 L closepath p F P 0 g s .818 .656 .681 r .14256 .36967 m .17897 .37244 L .1421 .40832 L closepath p F P 0 g s .912 .95 .809 r .1421 .40832 m .15696 .36478 L .17897 .37244 L closepath p F P 0 g s .284 .761 .932 r .36922 .36927 m .38751 .36436 L .4035 .37205 L closepath p F P 0 g s .825 .66 .679 r .36922 .36927 m .4035 .37205 L .36909 .40797 L closepath p F P 0 g s .908 .978 .789 r .36909 .40797 m .38751 .36436 L .4035 .37205 L closepath p F P 0 g s .397 .802 .982 r .19538 .21305 m .2107 .20548 L .23133 .21734 L closepath p F P 0 g s .82 .657 .681 r .19538 .21305 m .23133 .21734 L .195 .25153 L closepath p F P 0 g s .911 .943 .812 r .195 .25153 m .2107 .20548 L .23133 .21734 L closepath p F P 0 g s .191 .142 .57 r .26437 .52658 m .28074 .52438 L .26409 .56518 L closepath p F P 0 g s .397 .802 .982 r .42244 .21243 m .44166 .20484 L .45624 .21673 L closepath p F P 0 g s .827 .662 .678 r .42244 .21243 m .45624 .21673 L .42237 .25097 L closepath p F P 0 g s .91 .971 .796 r .42237 .25097 m .44166 .20484 L .45624 .21673 L closepath p F P 0 g s .265 .205 .6 r .45624 .21673 m .47585 .2093 L .45622 .25491 L closepath p F P 0 g s .265 .205 .6 r .45622 .25491 m .47586 .24811 L .45621 .29319 L closepath p F P 0 g s .12 .083 .538 r .14436 .21612 m .15871 .20866 L .14391 .25435 L closepath p F P 0 g s .345 .786 .962 r .19461 .29013 m .20997 .28386 L .23068 .29369 L closepath p F P 0 g s .82 .657 .681 r .19461 .29013 m .23068 .29369 L .19423 .32884 L closepath p F P 0 g s .912 .95 .809 r .19423 .32884 m .20997 .28386 L .23068 .29369 L closepath p F P 0 g s .397 .802 .982 r .10745 .2118 m .12131 .2042 L .14436 .21612 L closepath p F P 0 g s .818 .656 .681 r .10745 .2118 m .14436 .21612 L .10694 .2504 L closepath p F P 0 g s .909 .931 .815 r .10694 .2504 m .12131 .2042 L .14436 .21612 L closepath p F P 0 g s .372 .795 .973 r .10694 .2504 m .12082 .24344 L .14391 .25435 L closepath p F P 0 g s .818 .656 .681 r .10694 .2504 m .14391 .25435 L .10644 .2891 L closepath p F P 0 g s .91 .935 .814 r .10644 .2891 m .12082 .24344 L .14391 .25435 L closepath p F P 0 g s .139 .68 .832 r .14073 .52493 m .15519 .52268 L .17737 .52621 L closepath p F P 0 g s .818 .656 .681 r .14073 .52493 m .17737 .52621 L .14027 .56402 L closepath p F P 0 g s .912 .965 .802 r .14027 .56402 m .15519 .52268 L .17737 .52621 L closepath p F P 0 g s .146 .104 .55 r .17737 .52621 m .1923 .524 L .17697 .56492 L closepath p F P 0 g s .345 .786 .962 r .42231 .28962 m .44159 .28333 L .45621 .29319 L closepath p F P 0 g s .827 .662 .678 r .42231 .28962 m .45621 .29319 L .42225 .32838 L closepath p F P 0 g s .908 .978 .789 r .42225 .32838 m .44159 .28333 L .45621 .29319 L closepath p F P 0 g s .23 .175 .586 r .36977 .21551 m .38796 .20803 L .36963 .25379 L closepath p F P 0 g s .146 .104 .55 r .17697 .56492 m .19191 .56337 L .17656 .60374 L closepath p F P 0 g s .146 .104 .55 r .17656 .60374 m .19152 .60284 L .17616 .64267 L closepath p F P 0 g s .397 .802 .982 r .24711 .20993 m .26344 .20225 L .28282 .21428 L closepath p F P 0 g s .823 .659 .68 r .24711 .20993 m .28282 .21428 L .2468 .24868 L closepath p F P 0 g s .912 .95 .809 r .2468 .24868 m .26344 .20225 L .28282 .21428 L closepath p F P 0 g s .146 .104 .55 r .17616 .64267 m .19113 .64243 L .17575 .6817 L closepath p F P 0 g s .12 .083 .538 r .14256 .36967 m .15696 .36478 L .1421 .40832 L closepath p F P 0 g s .284 .761 .932 r .10542 .36684 m .11933 .36185 L .14256 .36967 L closepath p F P 0 g s .818 .656 .681 r .10542 .36684 m .14256 .36967 L .10491 .40587 L closepath p F P 0 g s .912 .946 .811 r .10491 .40587 m .11933 .36185 L .14256 .36967 L closepath p F P 0 g s .397 .802 .982 r .47585 .2093 m .49613 .2016 L .50936 .21366 L closepath p F P 0 g s .829 .664 .677 r .47585 .2093 m .50936 .21366 L .47586 .24811 L closepath p F P 0 g s .908 .978 .789 r .47586 .24811 m .49613 .2016 L .50936 .21366 L closepath p F P 0 g s .251 .745 .912 r .10491 .40587 m .11883 .40155 L .1421 .40832 L closepath p F P 0 g s .818 .656 .681 r .10491 .40587 m .1421 .40832 L .1044 .44501 L closepath p F P 0 g s .912 .95 .809 r .1044 .44501 m .11883 .40155 L .1421 .40832 L closepath p F P 0 g s .818 .656 .681 r .13889 .68195 m .17575 .6817 L .13843 .72148 L closepath p F P 0 g s .908 .978 .789 r .13843 .72148 m .1534 .68239 L .17575 .6817 L closepath p F P 0 g s .027 0 0 r .13889 .68195 m .1534 .68239 L .17575 .6817 L closepath p F P 0 g s .146 .104 .55 r .19538 .21305 m .2107 .20548 L .195 .25153 L closepath p F P 0 g s .23 .175 .586 r .36922 .36927 m .38751 .36436 L .36909 .40797 L closepath p F P 0 g s .248 .19 .593 r .42244 .21243 m .44166 .20484 L .42237 .25097 L closepath p F P 0 g s .139 .68 .832 r .1923 .524 m .20775 .52171 L .22869 .5253 L closepath p F P 0 g s .82 .657 .681 r .1923 .524 m .22869 .5253 L .19191 .56337 L closepath p F P 0 g s .91 .971 .796 r .19191 .56337 m .20775 .52171 L .22869 .5253 L closepath p F P 0 g s .397 .802 .982 r .38796 .20803 m .40679 .20029 L .42244 .21243 L closepath p F P 0 g s .827 .662 .678 r .38796 .20803 m .42244 .21243 L .38785 .24695 L closepath p F P 0 g s .911 .968 .799 r .38785 .24695 m .40679 .20029 L .42244 .21243 L closepath p F P 0 g s .397 .802 .982 r .06981 .2074 m .08316 .19964 L .10745 .2118 L closepath p F P 0 g s .818 .656 .681 r .06981 .2074 m .10745 .2118 L .06924 .24637 L closepath p F P 0 g s .908 .927 .815 r .06924 .24637 m .08316 .19964 L .10745 .2118 L closepath p F P 0 g s .146 .104 .55 r .19461 .29013 m .20997 .28386 L .19423 .32884 L closepath p F P 0 g s .093 .061 .525 r .10745 .2118 m .12131 .2042 L .10694 .2504 L closepath p F P 0 g s .372 .795 .973 r .38785 .24695 m .4067 .23987 L .42237 .25097 L closepath p F P 0 g s .827 .662 .678 r .38785 .24695 m .42237 .25097 L .38774 .28598 L closepath p F P 0 g s .91 .971 .796 r .38774 .28598 m .4067 .23987 L .42237 .25097 L closepath p F P 0 g s .093 .061 .525 r .10694 .2504 m .12082 .24344 L .10644 .2891 L closepath p F P 0 g s .12 .083 .538 r .14073 .52493 m .15519 .52268 L .14027 .56402 L closepath p F P 0 g s .057 .622 .762 r .19152 .60284 m .207 .60191 L .22802 .60337 L closepath p F P 0 g s .82 .657 .681 r .19152 .60284 m .22802 .60337 L .19113 .64243 L closepath p F P 0 g s .908 .978 .789 r .19113 .64243 m .207 .60191 L .22802 .60337 L closepath p F P 0 g s .139 .68 .832 r .10337 .52363 m .11732 .52132 L .14073 .52493 L closepath p F P 0 g s .818 .656 .681 r .10337 .52363 m .14073 .52493 L .10285 .5631 L closepath p F P 0 g s .912 .961 .804 r .10285 .5631 m .11732 .52132 L .14073 .52493 L closepath p F P 0 g s .248 .19 .593 r .42231 .28962 m .44159 .28333 L .42225 .32838 L closepath p F P 0 g s .345 .786 .962 r .38774 .28598 m .40661 .27956 L .42231 .28962 L closepath p F P 0 g s .827 .662 .678 r .38774 .28598 m .42231 .28962 L .38763 .32512 L closepath p F P 0 g s .909 .975 .793 r .38763 .32512 m .40661 .27956 L .42231 .28962 L closepath p F P 0 g s .099 .652 .799 r .10285 .5631 m .11682 .56148 L .14027 .56402 L closepath p F P 0 g s .818 .656 .681 r .10285 .5631 m .14027 .56402 L .10233 .60269 L closepath p F P 0 g s .912 .965 .802 r .10233 .60269 m .11682 .56148 L .14027 .56402 L closepath p F P 0 g s .345 .786 .962 r .06868 .28545 m .08205 .27902 L .10644 .2891 L closepath p F P 0 g s .818 .656 .681 r .06868 .28545 m .10644 .2891 L .06811 .32464 L closepath p F P 0 g s .91 .935 .814 r .06811 .32464 m .08205 .27902 L .10644 .2891 L closepath p F P 0 g s .316 .774 .948 r .38763 .32512 m .40652 .31937 L .42225 .32838 L closepath p F P 0 g s .827 .662 .678 r .38763 .32512 m .42225 .32838 L .38751 .36436 L closepath p F P 0 g s .908 .978 .789 r .38751 .36436 m .40652 .31937 L .42225 .32838 L closepath p F P 0 g s .169 .124 .56 r .24711 .20993 m .26344 .20225 L .2468 .24868 L closepath p F P 0 g s .397 .802 .982 r .2107 .20548 m .22656 .19766 L .24711 .20993 L closepath p F P 0 g s .823 .659 .68 r .2107 .20548 m .24711 .20993 L .21034 .24462 L closepath p F P 0 g s .912 .946 .811 r .21034 .24462 m .22656 .19766 L .24711 .20993 L closepath p F P 0 g s .372 .795 .973 r .21034 .24462 m .22621 .23746 L .2468 .24868 L closepath p F P 0 g s .823 .659 .68 r .21034 .24462 m .2468 .24868 L .20997 .28386 L closepath p F P 0 g s .912 .95 .809 r .20997 .28386 m .22621 .23746 L .2468 .24868 L closepath p F P 0 g s .139 .68 .832 r .24461 .52306 m .26108 .52074 L .28074 .52438 L closepath p F P 0 g s .823 .659 .68 r .24461 .52306 m .28074 .52438 L .24429 .5627 L closepath p F P 0 g s .908 .978 .789 r .24429 .5627 m .26108 .52074 L .28074 .52438 L closepath p F P 0 g s .284 .761 .932 r .06754 .36395 m .08094 .35886 L .10542 .36684 L closepath p F P 0 g s .818 .656 .681 r .06754 .36395 m .10542 .36684 L .06698 .40337 L closepath p F P 0 g s .911 .943 .812 r .06698 .40337 m .08094 .35886 L .10542 .36684 L closepath p F P 0 g s .093 .061 .525 r .10542 .36684 m .11933 .36185 L .10491 .40587 L closepath p F P 0 g s .265 .205 .6 r .47585 .2093 m .49613 .2016 L .47586 .24811 L closepath p F P 0 g s .093 .061 .525 r .10491 .40587 m .11883 .40155 L .1044 .44501 L closepath p F P 0 g s .12 .083 .538 r .13889 .68195 m .1534 .68239 L .13843 .72148 L closepath p F P 0 g s .818 .656 .681 r .10129 .6822 m .13889 .68195 L .10077 .72213 L closepath p F P 0 g s .909 .975 .793 r .10077 .72213 m .11529 .68265 L .13889 .68195 L closepath p F P 0 g s .027 0 0 r .10129 .6822 m .11529 .68265 L .13889 .68195 L closepath p F P 0 g s .397 .802 .982 r .12131 .2042 m .13566 .19632 L .15871 .20866 L closepath p F P 0 g s .82 .657 .681 r .12131 .2042 m .15871 .20866 L .12082 .24344 L closepath p F P 0 g s .91 .935 .814 r .12082 .24344 m .13566 .19632 L .15871 .20866 L closepath p F P 0 g s .818 .656 .681 r .10077 .72213 m .13843 .72148 L .10025 .76217 L closepath p F P 0 g s .908 .978 .789 r .10025 .76217 m .11478 .72327 L .13843 .72148 L closepath p F P 0 g s .069 0 0 r .10077 .72213 m .11478 .72327 L .13843 .72148 L closepath p F P 0 g s .215 .726 .889 r .0664 .4429 m .07982 .43917 L .1044 .44501 L closepath p F P 0 g s .818