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コッホ曲線 – Inkscape@JP

コッホ曲線


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パスからフラクタル画像を作成します。必ずしもコッホ曲線を描くのに最適化されているわけではなく、フラクタルな画像一般を作成するためのエフェクトです。実際にコッホ曲線を描くには、エクステンションの「Lシステム」を使う方が少ない手順で正確な画像が作成できます。

このエフェクトは、数学的に描くことのできない画像をフラクタル画像に加工するのに適しています。

もとの画像 コッホ曲線 適用
lpe-koch-flourish-orig lpe-koch-flourish-result

このエフェクトには、次の設定項目があります。

lpe-dialog-koch

「基準セグメント」は長さと角度のみ変更できるパスで、初期状態ではオリジナルパスの水平方向の中央に置かれています。このパスを変更することによって、複製されるパスとの大きさ比率と角度を変えることができます。

lpe-koch-reference-segment

「生成パス」は生成される子供のパスを定義するもので、初期状態ではオリジナルパスの幅の1/3の幅で、オリジナルパスの下側の境界線上の両端に置かれています。このパスは、普通のパスと同様にノードツールで変形などの編集ができます。生成パスが直線でない場合には、生成されるパスを変形させます。

lpe-koch-generating-path

最初に示した例での画像は、次のように生成パスを設定して描画しています。

lpe-koch-flourish-setting

ノードの編集には選択ツールが使えないため、生成パスの位置を移動したい場合、生成パス上のノードをすべて選択してから、いずれかのノードをドラッグします。

「同一変形のみ使用する」にチェックすると、生成パスで定義する変形のうち拡大/縮小の情報と、回転する角度の情報のみ使います。

「生成数」には、フラクタルの深さを指定します。指定する数が大きくなると等比級数的に処理が重くなるので、不用意に大きな値を指定しないよう注意してください。1ずつ大きくして様子を見ながら調整するのが安全です。

「全ての生成を描画する」にチェックすると、生成したすべてのオブジェクトを描画します。チェックをはずすと、最後に描画したもののみを画面に残します。

「最大複雑度」には、描画の複雑度の最大値を指定します。描画の複雑度がここで指定した値を超えたときには、エフェクトを適用せずにオリジナルパスをそのまま表示します。複雑度は、描画中のノード数合計とほぼ同じものです。生成数にうっかり大きな値を設定して画面が固まるのを防ぐための設定です。

上記の例ではノード数が33個のパスをオリジナルパスとして使用していますが、「最大複雑度」が1000のとき描画できるのは生成数3までです。生成数が4以上になると、複雑度が1000を超えるため描画されません。

最終更新: 2013-05-03 14:41:19