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集中線描画アルゴリズム

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漫画によくある集中線をコンピューターで描画する方法。

はじめに単純化した集中線を考える。中心から距離rまでは空白である。この、距離rの点をr1とする。中心からr1を通って外側に向かう直線を考え、その先の、中心からの距離r2の点を考える。線は、この描画開始位置r1から、r2まで引かれる。この線分をlとする。
lとX軸が作る角度をθとし、θを0から2π(ラジアン) まで変化させながら、その角度に応じた線分lを引けば、半径r1から半径r2までの直線がぐるりとウニの刺のように描かれた図形が出来上がる。任意のθにおける、r1とr1の位置(x1,y1), (x2, y2)は次のようになる。


x1 = r1 cosθ
y1 = r1 sinθ

x2 = r2 cosθ
y2 = r2 sin θ


たとえば、Macintosh用の REALbasicでは、以下のように書ける。

dim x1, y1, x2, y2, r1,r2 as integer // 座標
dim dig as double // 角度

dig = 0
r1 = 50
r2 = 100
while dig < 2* 3.141592 // 角度が2π(一回転分)になるまでくり返す
x1 = r1 * cos(dig)
y1 = r1 * sin(dig)
x2 = r2 * cos(dig)
y2 = r2 * cos(dig)
me.graphics.DrawLine x1,y1,x2,y2 // (x1,y1)から(x2,y2)まで線を引く
dig = dig + 0.05 // この数値が小さい程線の密度が上がる
wend


ただし、コンピューターの座標系では、一般に左上が原点になるため、このままでは集中線の右下90°の範囲しか描かれない。これを解決するためには、描画時にx1,y1,x2,y2それぞれに、中心にしたい位置の座標をそれぞれ足してやる必要がある。また、Y座標が下に行く程大きくなる事にも注意が必要。場合によってはYの符号を反転してやる必要がある。

この方法で描かれる集中線は、まるで太陽柄のスクリーントーンのように規則的で、とても集中線とは言えない。漫画の一般的な集中線に近付けるためにはどうしたらいいかを考える。

線の開始位置をランダムにずらす必要がある。以下のrnd関数は0から1の実数乱数を生成するとして、


r1 = 50 + rnd *10
r2 = r1+ 50

などとしてやれば、書きはじめの位置をランダムにずらす事ができる。また、同様にして、線と線の間隔(角度)もランダムにする。これらのパラメータは、ユーザーが任意に変更できるようにするべきである。

これでも実際の漫画に使えるような集中線は描けない。ペンで描かれた集中線は、外側は太く、中心近くで細くなっている。これを実現するためには、単純にr1からr2に直線を引く方法では対処できない。そこで、集中線ジェネレーターでは、中心から外側に向けて広がる二等辺三角形を描画する事にした。しかし、この方法では、実際にペンで描かれた物に比べ、直線的に太さが変わるため、機械的な印象が否めない。また、描画する距離が長くなると、必要以上に外側が太くなり、あきらかにペンのそれとは異なる様相を示す。これに改良を加えたバージョンでは、円弧の一部を切り取った図形を二つ張り合わせた多角形(筆の穂先のような形になる)*1を作り、これを回転させながらコピーする方法を取った。この方法は多少複雑だが、線の最大の太さが長さで決定できるため、どこまでのばしても、最大の太さが設定をこえる亊はない。このアルゴリズムを応用して、カーブした集中線も描けるようになった。
ある事情で、このバージョンは公開できなくなったが、近いうちに最低限これと同じ機能を持つソフトウエアが登場するはずである*2



*1:幾何学って難しいよなあ。僕は理系だが数学大嫌いだったのだ。この図形を描くための三角関数の組み合わせを考えるのにもう汗だらだら。図形としてはそんなに難しくはないんだけどね。


*2:要するに僕の手を離れたと言う事。より優れたるプログラマがプロ用ツールとして開発に当たっている。

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