カメラから見える一定距離の範囲は錐台の四角形で定義されます。ある距離での四角形のサイズがどれぐらいであるか、またはある四角形のサイズでは距離がどれぐらいであるか、を計算すると役立つことがあります。例えば、動くカメラによりオブジェクトを常に追跡する(例えばプレイヤーなどを追跡する)必要がある場合、オブジェクトがカットオフされる距離まで近づいてはいけません。
ある距離での錐台の高さ(ともにワールド座標系の単位)は次の数式により計算できます:
var frustumHeight = 2.0f * distance * Mathf.Tan(camera.fieldOfView * 0.5f * Mathf.Deg2Rad);
… またこの処理を逆に行うことである錐台の高さから距離を計算することができます:
var distance = frustumHeight * 0.5f / Mathf.Tan(camera.fieldOfView * 0.5f * Mathf.Deg2Rad);
さらに高さと距離があるのときの FOV 角度を計算することができます:
var camera.fieldOfView = 2.0f * Mathf.Atan(frustumHeight * 0.5f / distance) * Mathf.Rad2Deg;
各々のこれらの計算は錐台の高さが関連しますすが、これは幅から簡単に計算できます(逆の場合も同様に計算できます):
var frustumWidth = frustumHeight * camera.aspect;
var frustumHeight = frustumWidth / camera.aspect;
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