Instruments and acoustics
Microphone directivity (three patterns are the two ends and the middle of one formula)
A polar plot of how much a microphone picks up from each direction. The three familiar shapes are not separate inventions but one formula at its ends and middle — omnidirectional, cardioid and figure-of-eight are A = 1, 0.5 and 0 in r = A + (1 - A)cos θ. Solving the same formula gives the dead angles: 180 degrees for a cardioid, 90 and 270 for a figure-of-eight.
This drawing comes from one YAML file. No shape was moved by hand.
Notes in the source (in Japanese)
指向性の図は、向き θ に対する感度 r(θ) を極座標で描いたもの。光の配光曲線（見本 264）と同じ読み方で、外側の破線が r ＝ 1。
無指向性（全指向性）は r ＝ 1。 どの向きも同じ感度 ——ただし可聴周波数の全部で無指向になるものは無い。
カーディオイドは r ＝（1 ＋ cos θ）／ 2。 正面に強く、真後ろが 0。特定の方向以外を拾いにくいのでハウリングとかぶりに強く、舞台のスピーチや楽器の拡声で多用される。
双指向性（Figure-8）は r ＝ cos θ。 正面と真後ろに強く、真横が 0。後ろ側は位相が逆になる。
式を並べると、1 つの family の両端と真ん中だと分かる。
r ＝ A ＋（1 − A）cos θ
A ＝ 1 で無指向性、A ＝ 0.5 でカーディオイド、A ＝ 0 で双指向性。スーパーカーディオイドとハイパーカーディオイドは、その間にある（A の値はこの図では確かめていないので、形は描いていない）。
カーディオイドは 1 ＋ cos θ ＝ 0 から θ ＝ 180°、双指向性は cos θ ＝ 0 から θ ＝ 90° と 270°。出典に書いていなくても、式があれば確かめられる。
図の輪は |r| を描いたもの（負の値は、向きではなく位相の反転）。型（ダイナミック／コンデンサ）と指向性は別の話で、どちらにも各指向性がある。
光の側は見本 264、PA の配置は見本 101、ホールの反射は見本 205。
Source (YAML)
examples/gallery/327-マイクの指向性.zumen.yaml
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