JP4343564B2 - Graphic image rendering using radiance self-transmission in a low-frequency lighting environment - Google Patents

Description

【００３２】
と定義され、Ｐ_ｌ ^ｍは同伴ルジャンドル多項式であり、Ｋ_ｌ ^ｍは正規化定数である。
【００３３】
【数２】

【００３４】
上の定義は複素基底を形成し、実数値の基底は単純な変換
【００３５】
【数３】

【００３６】
によって与えられる。
【００３７】
低い値のｌ（バンドインデックスと呼ばれる）は、球面上の低周波数の基底関数を表す。帯域ｌの基底関数は、ｘ、ｙ、およびｚにおける次数ｌの多項式になる。評価は単純な漸化式で行うことができる（例えば、非特許文献１３、非特許文献１４参照）。
【００３８】
射影と再構築：ＳＨ基底は正規直交なので、積分（領域支持ライティング基底関数（area-supported basis function））
【００３９】
【数４】

【００４０】
を介して、Ｓ上に定義されたスカラー関数ｆをその係数に射影することができる。
【００４１】
それらの係数は、ｎ次の再構築関数
【００４２】
【数５】

【００４３】
を提供し、これは、帯域数ｎが増加するのにつれてｆへの近似の度合いが高まる。低周波信号は、数個のＳＨ帯域のみで正確に表すことができる。より高い周波数の信号は、低次の射影によって帯域制限する（すなわちエリアシングを生じさせずに滑らかにする）。
【００４４】
ｎ次への射影にはｎ^２個の係数が必要である。しばしば、１つずつインデックス付けされた射影係数のベクトルと基底関数について、
【００４５】
【数６】

【００４６】
を介して式（２）を書き換えると利便であり、ここでｉ＝ｌ（ｌ＋１）＋ｍ＋１である。この定式化により、再構築関数のｓにおける評価が、ｎ^２成分の係数ベクトルｆ_ｉと、評価された基底関数ｙ_ｌ（ｓ）のベクトルとの単純なドット積を表すことが明白になる。
【００４７】
基本的性質：ＳＨ射影の性質の１つはその回転不変性である。すなわち、ＱがＳ上における任意の回転であるときにｇ（ｓ）＝ｆ（Ｑ（ｓ））とすると、
【００４８】
【数７】

【００４９】
となる。
【００５０】
これは、１次元のフーリエ変換の推移不変の性質に類似する。実際、この性質は、回転したサンプル点セットにｆからのサンプルを集め、射影し、そして再度
【００５１】
【数８】

【００５２】
回転する際に、ＳＨ射影によってエリアシングアーチファクトが生じないことを意味する。
【００５３】
ＳＨ基底が正規直交であることにより、Ｓに対して任意の２つの関数ａおよびｂが与えられたときに、それらの射影が
【００５４】
【数９】

【００５５】
を満たすという有用な性質が得られる。すなわち、帯域制限した関数の積の積分が、それら関数の射影係数のドット積となる。
【００５６】
畳み込み：円対称の核関数ｈ（ｚ）への関数ｆの畳み込みはｈ^＊ｆと表される。上記の式（３）により、より次元が高い回転グループＳＯではなくＳに結果が定義されるように、ｈは円対称でなければならない（そして、したがってｓではなくｚの単純な関数として定義できる）ことに留意されたい。この畳み込みの射影は、
【００５７】
【数１０】

【００５８】
を満たす。換言すると、射影された畳み込みの係数は、単に個別に射影した関数のスケーリングした積になる。この性質は、ｈ（ｚ）＝ｍａｘ（ｚ，０）と定義される半球コサイン核を環境マップに畳み込んで放射照度マップを得るための高速の方式を提供する（例えば、非特許文献１２参照）。この場合、ｈの射影係数は解析的な式を用いて得ることができる。畳み込みの性質を使用して、より核が狭い予めフィルタリングされた環境マップを得ることもできる。ｈはｚを中心として円対称なので、その射影係数はｍ＝０のときのみ非ゼロになることに留意されたい。
【００５９】
積の射影：ａが分かっておりｂが分かっていない場合の球面関数ｃ（ｓ）＝ａ（ｓ）ｂ（ｓ）のペアの積の射影は、行列
【００６０】
【数１１】

【００６１】
【数１２】

【００６２】
を介した射影係数ｂ_ｊの線形変換と考えることができ、総和は複製されたｊインデックスに示される。
【００６３】
【数１３】

【００６４】
は対称行列であることに留意されたい。
【００６５】
回転：Ｑ，
【００６６】
【数１４】

【００６７】
によって回転した再構築関数を、ｆの射影係数ｆ_ｉの線形変換を使用して射影することができる。回転不変の性質により、この線形変換は各帯域の係数を個別に扱う。最も効率的な実装は、かなり複雑な漸化式を使用して回転Ｑのｚｙｚオイラー角の分解を使用して実現される（例えば、非特許文献１３、非特許文献１４、非特許文献１５参照）。低次関数のみを扱う際は、記号積分を使用してこれらの参考文献に記載される明白な回転式を実装することができる。
【００６８】
２．放射輝度の自己伝達
放射輝度の自己伝達は、オブジェクトＯがどのようにそれ自体にシャドーを作り、光を散乱するかを要約する。放射輝度の自己伝達は、ＳＨ基底を使用して、Ｌ_ｐ（ｓ）と表される点ｐ∈Ｏにおける入射ライティングを初めにパラメータ化することによって表す。したがって、入射ライティングはｎ^２個の係数のベクトル（Ｌ_ｐ）ｉとして表される。実際には、このライティングは、表面近くで、恐らくは単一の点のみで動的かつまばらにサンプリングすることができる。これは、Ｏ自体の存在に起因しないＯ上のライティングの変動が小さいことを前提とする（セクション４．１「入射放射輝度フィールドの空間サンプリング」を参照されたい）。放射輝度の自己伝達は伝達ベクトルまたは行列として事前に計算し、Ｏの上に高密度で格納しておくこともできる。
【００６９】
伝達ベクトル（Ｍ_ｐ）_ｉは拡散表面に使用することができ、ライティングベクトルに対する線形変換を表し、内積を介してＬ’_ｐと表すスカラー出射放射輝度を生成する。
【００７０】
【数１５】

【００７１】
すなわち、（Ｍ_ｐ）_ｉの各成分は、ライティング基底関数（Ｌ_ｐ）_ｉがｐでシェーディングに与える線形の影響を表す。
【００７２】
伝達行列（Ｍ_ｐ）_ｙは光沢表面に用いることができ、ライティングベクトルに対する線形変換を表し、この変換では、スカラーではなく伝達された放射輝度Ｌ’_ｐ（ｓ）の球面関数全体の射影係数が得られる。すなわち
【００７３】
【数１６】

【００７４】
入射する放射輝度と伝達された放射輝度の違いは、Ｌ’_ｐ（ｓ）はＯの存在に起因するシャドーイングと散乱の効果を含むのに対し、Ｌ_ｐ（ｓ）はＯがシーンから除去されたと仮定して入射ライティングを表す点である。（Ｍ_ｐ）_ｙの成分は、伝達された放射輝度Ｌ’_ｐ（ｓ）のｉ番目の係数に対する入射放射輝度（Ｌ_ｐ）ｊのｊ番目のライティング係数の線形の影響を表す。次のセクションでは、Ｏ上の自己散乱に起因する、拡散表面の伝達ベクトルと光沢表面の伝達行列をどのように求めるかについて述べる。
【００７５】
２．１ 拡散伝達
まずＯが拡散性であると想定する。点ｐ∈Ｏにおける最も単純な伝達関数は、スカラー関数
【００７６】
【数１７】

【００７７】
として定義されるシャドーを付けない拡散伝達を表し、これにより拡散表面に対するビュー角度によって変化しない出射放射輝度が得られる。ここで、ρ_ｐはｐにおけるオブジェクトのアルベドであり、Ｌ_ｐはＯがシーンから除去されたと仮定したｐにおける入射放射輝度であり、Ｎ_ｐは、ｐにおけるオブジェクトの法線であり、Ｈ_Ｎｐ（ｓ）＝ｍａｘ（Ｎ_ｐ［ｋ、０）はＮ_ｐを中心としたコサインの重みを付けた半球核である。Ｌ_ｐとＨ_Ｎｐを個別にＳＨ射影することにより、式（５）ではＴ_ＤＵがそれらの係数ベクトルの内積になる。これによって得られる因数をここではライト関数Ｌ_ｐおよび伝達関数Ｍ_ｐと呼ぶ。この最初の単純なケースでは、
【００７８】
【数１８】

【００７９】
となる。
【００８０】
Ｎ_ｐが既知なので、伝達関数
【００８１】
【数１９】

【００８２】
のＳＨ射影は事前に計算することができ、この結果伝達ベクトルが得られる。実際、Ｎ_ｐを与えられれば単純な解析式で伝達ベクトルが得られるので記憶は不要である。
【００８３】
【数２０】

【００８４】
は本質的にローパスフィルタなので、二次の射影（９つの係数）により、任意のライティング環境（滑らかでなくとも）で良好な精度が得られる。
【００８５】
シャドーを含めるために、シャドーを付けた拡散伝達を
【００８６】
【数２１】

【００８７】
と定義し、追加的な可視性関数Ｖ_ｐ（ｓ）→｛０，１｝は、方向ｓへのｐからの光線が再びＯと交差しない（すなわちシャドーができない）ときに１に等しくなる。シャドーを付けない伝達と同様に、この積分はＬ_ｐのＳＨ射影と、伝達関数
【００８８】
【数２２】

【００８９】
を使用して２つの関数に分解することができる。再びＬ_ｐとＭ_ｐを個別にＳＨ射影することにより、Ｔ_ＤＳ中の積分が係数ベクトルの内積になる。
【００９０】
この場合は伝達が重要である。放射輝度の自己伝達は伝播シミュレータを使用して事前に計算し（下記の「自己伝達の事前計算」のセクションで述べる）、その結果として得られる伝達ベクトル（Ｍ_ｐ）_ｉをＯ上の多くの点ｐに格納しておくことができる。先の場合と異なり、Ｖ_ｐは例えば「ピンホール」に自らシャドーを作るなどにより高周波数のライティングを局所的に生成する可能性があるので、
【００９１】
【数２３】

【００９２】
の２次射影は滑らかなライティング環境にも不正確になる可能性がある。４次または５次の射影を使用すると、滑らかなライティング環境の通常のメッシュで良好な結果が得られる。例えば、図９の拡散表面オブジェクトのシャドーを付けない画像とシャドーを付けた画像を比較されたい。
【００９３】
最後に、シャドーだけでなく拡散性の相互反射（例えば図９の相互反射を付けた画像を参照）を取り込むために、相互反射した拡散伝達を
【００９４】
【数２４】

【００９５】
と定義することができ、
【００９６】
【数２５】

【００９７】
は方向ｓにおけるＯ自体からの放射輝度である。問題点は、
【００９８】
【数２６】

【００９９】
はｐから任意の距離にある点の出射放射輝度によって決まり、またＯ上で局所的なライティングが変動するので、入射放射輝度が無限遠の光源から発されない限り、ｐだけで入射放射輝度を与えられても放射輝度
【０１００】
【数２７】

【０１０１】
が分からないことである。Ｏ上でライティングの変動が小さい場合は、Ｏが至るところでＬ_ｐによって照らされているかのように
【０１０２】
【数２８】

【０１０３】
に非常に近似する。したがって、Ｔ_ＤＩはＬ_ｐに線形に依存し、先の２つの事例と同様に、２つの射影した関数、すなわち光に依存する関数とジオメトリに依存する関数の積に因数分解することができる。
【０１０４】
事前に計算される相互反射には、Ｏ上の入射ライティングが空間的に変化しないことを前提としなければならないが、より単純なシャドー付きの伝達にはこの前提は必要でない。この違いは、シャドー付きの伝達がｐにおける入射ライティングだけに依存するのに対して、相互反射した伝達はＬ_ｑ≠Ｌ_ｐであるＯ上の多くの点ｑ≠ｐに依存する点である。したがって、入射放射輝度フィールドを十分に細かくサンプリングするのであれば（下記の「入射放射輝度フィールドの空間的サンプリング」のセクションで述べる）、局所的なライティングの変動を取り込むことができ、シャドーの付いた伝達が正確なものになる。
【０１０５】
【数２９】

【０１０６】
が存在すると、相互反射の伝達関数
【０１０７】
【数３０】

【０１０８】
を明示的に表すことが難しくなる。下記の「自己伝達の事前計算」のセクションでは、その射影係数を数的に計算する方法について述べる。
【０１０９】
２．２ 光沢伝達
光沢のあるオブジェクトの自己伝達は同様に定義することができるが、核関数を一般化して（固定の）法線Ｎではなく反射方向Ｒに依存する（ビューに依存する）ようにする。先のＨ核と同様に、放射輝度の自己伝達は光沢性の反射を核Ｇ（ｓ，Ｒ，ｒ）とモデル化することができ、スカラーｒは鏡面反応の「光沢度」あるいは広さを定義する。
【０１１０】
シャドーを付けない場合、シャドーを付ける場合、および相互反射する場合の類似する３つの光沢伝達関数を
【０１１１】
【数３１】

【０１１２】
と定義することができ、これらは、事前計算時にはどちらも未知の数量であるＬ_ｐとＲの関数として方向Ｒのスカラー放射輝度を出力する。伝達はもはや単にｓの関数ではないので、ＳＨ係数の単純なベクトルに置き換えることはできない。
【０１１３】
スカラー伝達をＲおよびｒでパラメータ化する代わりに、より有用な分解は、入射放射輝度Ｌ_ｐ（ｓ）を、Ｌ’_ｐ（ｓ）と表す伝達される放射輝度の球面全体に伝達するものである。光沢の核ＧがＲを中心として円対称であるとすると、Ｌ’_ｐ（ｓ）にＧ’_ｒ（ｚ）＝Ｇ（ｓ，（０，０，１），ｒ）を畳み込み、Ｒで評価して最終的な結果を得ることができる。
【０１１４】
今度はＬ’_ｐへの伝達をベクトルではなく行列として表す。例えば、光沢のシャドー付きの伝達は
【０１１５】
【数３２】

【０１１６】
と定義することができ、これは、そのＳＨ射影を式（７）を介して対称行列
【０１１７】
【数３３】

【０１１８】
として表すことのできるＬ_ｐに対する線形オペレータである。非常に滑らかなライティングの場合でも、Ｏの光沢度が増すのに従ってより多くのＳＨ帯域を
【０１１９】
【数３４】

【０１２０】
に使用し、そのような条件下では、低周波数のライティングをより高い周波数の伝達放射輝度に写像する非正方行列（例えば２５×９）が有用である。
【０１２１】
事前に計算する放射輝度の自己伝達の制限で重要なのは、Ｔ_ＤＩおよびＴ_ＧＩにおける相互反射に影響するＯの材料特性（アルベドや光沢度など）が、前処理された伝達に「焼きこまれ（baked in）」、実行時に変えることができない点である。これに対して、相互反射のないより単純なシャドー付きの伝達では、Ｏ上での材料特性の実行時の変更および／または空間的変動が可能である。障害物または光源がＯの凸包に入ると誤差が生じる。Ｏは剛体として移動することしかできず、ある構成要素を全体に相対的に変形または移動することはできない。また、正確な相互反射にはＯ上のライティングの変動が低いことが必要であるという前提を思い出されたい。
【０１２２】
最後に、上記で定義した拡散伝達は、すでにコサインの重みを付けた法線の半球を畳み込んであるので表面を離れた後の放射輝度を生成するのに対し、光沢伝達は表面に入射する放射輝度を生成し、局所的なＢＲＤＦを畳み込んで最終的な出射放射輝度を得ることに留意されたい。また、光沢のあるＯには固定されたＢＲＤＦを焼きこんでおき、実行時のＧの畳み込みを不要にし、しかし柔軟性を限定することも可能である。
【０１２３】
図９は、光沢表面オブジェクトのシャドーを付けない画像、シャドーを付けた画像、および相互反射させた画像を示す。
【０１２４】
３．自己伝達の事前計算
次いで図２を参照すると、イルミネーションシミュレータ１２０（図１）は、放射体（emitter）としての無限球（シミュレーションのための「基準ライティング環境」）にＳＨ基底を使用してオブジェクトＯに行うグローバルイルミネーションシミュレーション２００で、モデリングされたオブジェクトの放射輝度の自己伝達を事前に計算する（「自己伝達の事前計算」とも称する）。このシミュレーションは、入射光Ｌの未知の球面のｎ次のＳＨ射影によって、すなわちｎ^２個の未知の係数Ｌ_ｉによってパラメータ化する。シミュレーション結果は、ＳＨ基底関数ｙ_ｉ（ｓ）を放射体として用いてＬ_ｉごとに個別に計算することができるが、一度にすべてを計算するほうが効率的である。基準ライティング環境（無限遠の球面Ｌ）は、実行時にＯ周囲の実際の入射放射輝度Ｌ_ｐに置き換える。
【０１２５】
シミュレーション２００は、Ｌを発し直接サンプル点ｐ∈Ｏに到達する経路からの直接のシャドーをシミュレートするパス（「シャドーパス」２０２）から開始する。続くパス（「相互反射パス」２０４）では相互反射が追加され、ｐに達する前に複数回Ｏからはね返ったＬからの経路（Ｌｐ、ＬＤｐ、ＬＤＤｐなど）を表す。各パスで、ｐ表面上のすべてのサンプル点にエネルギーが集められる。大きな放射体（すなわち低周波数のＳＨ基底）では、エネルギーの集約がシューティング式の更新よりも効率的になる。
【０１２６】
サンプル点ｐ∈Ｏにおける方向の球面を取り込むために、シミュレーションでは大きな（１０ｋ〜３０ｋ）の準ランダムな方向の集合
【０１２７】
【数３５】

【０１２８】
を生成する。シミュレーションでは、各方向ｓ_ｄにおけるすべてのＳＨ基底関数の評価も事前に計算する。方向ｓ_ｄは、最初の２０面体を１→２の二等分で精製して等面積の球面三角形にすることによって形成される階層ビンに編成する（球面上では１→４の細分で平面の場合のように等面積の三角形を得ることができない）シミュレーションでは６〜８の細分レベルを使用し、５１２〜２０４８個のビン（bins）を生成する。階層の各レベルにあるビンはいずれもｓ_ｄのリストを含む。
【０１２９】
最初のパスすなわちシャドーパス２０２で、シミュレーション２００は、各ｐ∈Ｏについて、オブジェクトによってセルフオクルージョンの生じる（self-occlude）点ｐからの方向にタグを付ける（２１１）。シミュレーションは、階層を使用して半球の外側にある方向を排除（cull）して、ｐの法線Ｎ_ｐを中心とする半球中にシャドーレイを投影する。シミュレーションでは、オクルージョンビットを有する各方向ｓ_ｄすなわち１−Ｖ_ｐ（ｓ_ｄ）にタグを付け、ｓ_ｄが半球内にあり、再度Ｏと交差する（すなわちＯ自身によってシャドーができる）かどうかを示す。オクルージョンビットは階層ビンとも関連付けられており、ビン内にオクルージョンの生じるｓ_ｄがあるかどうかを示す。セルフオクルージョンがある方向とビンは、それらに対してさらなる相互反射パスを行えるようにタグ付けし、全くオクルージョンがないビン／サンプルは環境からの直接光だけを受ける。
【０１３０】
次いで、２１２でシミュレーション２００は点ｐの伝達放射輝度を積分する。拡散表面については、シミュレーションは、点ｐ∈Ｏごとに式（１０）のＭ_ｐのＳＨ射影によりさらに伝達ベクトルを計算する。光沢表面には、シミュレーションは式（１１）のＭ_ｐのＳＨ射影によって伝達行列を計算する。いずれの場合も、結果は、ｐで集められＬでパラメータ化された放射輝度を表す。伝達を計算するためのＳＨ射影を方向サンプルｓ_ｄに対する数値積分により行い、この合計は次の規則を使用して蓄積された伝達となる。
【０１３１】
【表１】

【０１３２】
上付文字０は反復回数を表す。各点ｐのベクトルＭ_ｐまたは行列Ｍ_ｐはシャドーパスの前に０に初期化し、シャドーパスではすべてのｐにおいてすべてのｓ_ｄを合計する。この規則は、拡散伝達積分の式（１）と光沢伝達積分の式（７）を使用して得られる。
【０１３３】
図７も参照すると、後の相互反射パス２０４ではシャドーパスでオクルージョンビットがセットされたビンをトラバースして、今度は２２１で相互反射伝達を積分する。シャドーレイの代わりに、シミュレーションでは出射照明からの伝達を戻す光線をＯに当てる。光線（ｐ、ｓ_ｄ）が別の点ｑ∈Ｏと交差する（ｑはｐに最も近い）場合は、ｑから方向−ｓ_ｄに出射する放射輝度をサンプリングする。次の更新規則を使用し、この中で下付文字ｂははね返りパスの反復回数である。
【０１３４】
【表２】

【０１３５】
シャドーパス２０２と同様に、相互反射パス２０４は、方向ｓ_ｄにわたって伝達を累積する前に伝達ベクトルまたは行列を０に初期化することによって開始する。拡散の規則は、Ｔ_ＤＩの定義と式（１）から得られ、光沢の規則はＴ_ＧＩの規則と式（６）および（７）から得られる。光沢伝達の定義中の真中の因数は、１つ前のはね返りパスｂ−１のｑから発しｐに戻る放射輝度を表す。Ｍ_ｑは入射する放射輝度を格納するので、それにｑにおけるＯのＢＲＤＦを畳み込んで
【０１３６】
【数３６】

【０１３７】
の方向への出射放射輝度を得、ｋにわたる総和を得なければならない。ａ_ｋは、１つずつインデックス付けされた表記法で表されるｋ番目の畳み込み係数であることを思い出されたい。「ｒｅｆｌｅｃｔ」オペレータは、単に、その最初のベクトル引数をその２番目のベクトル引数について反映させる。式（７）は、（Ｍ_ｐ）_ｙは２つの球面関数の積によって形成されるのでシャドーを付けた光沢のある伝達の対称行列となることを意味することに注意されたい。これは、相互反射した光沢のある伝達には当てはまらない。
【０１３８】
２３０に示すように、相互反射パス２０４は、所与のパスの合計エネルギーが重要な閾値を下回るなどの終了条件が満たされるまで反復される。標準的なマテリアルでは相互反射はかなり急速に減少する。すべてのはね返りパスからの伝達の合計が相互反射に相当する。
【０１３９】
あるいは、このシミュレーションに単純な強化を加えることによりＯ内の鏡様の表面が可能になる。このシミュレーションでは、そのような表面における伝達は記録しない。代わりに、鏡状の表面に当たる光線は常に反射され、鏡状でない表面に達するまで伝播する。したがって、連続した反復における経路は（Ｌ［Ｓ］^*ｐ、Ｌ［Ｓ］^*Ｄ［Ｓ］^*ｐ、Ｌ［Ｓ］^*Ｄ［Ｓ］^*Ｄ［Ｓ］^*ｐなど）と表すことができ、Ｄは拡散性または光沢性のはね返りであり、Ｓは鏡面のはね返りである。これにより、ライティングの変化に動的に反応する拡散性または光沢の対象物へのコースティック（caustic）が取り込まれる。
【０１４０】
４．放射輝度伝達の実行時レンダリング
上述のシミュレーション２００（図２）は、ベクトルまたは行列として表されるオブジェクト表面上の多数の点ｐにおける放射輝度の伝達を取り込んだモデルを提供する。次いで図３を参照すると、リアルタイム画像レンダリングエンジン１４０（図１）は実行時手順３００でこのモデルを使用して、オブジェクトのリアルタイムの画像レンダリング時に、選択されたライティング環境とビュー方向でオブジェクトの自己伝達放射輝度を計算する。図４および図５はそれぞれ、拡散表面と光沢表面についての実行時手順３００による処理の流れを表す。
【０１４１】
手順３００で、レンダリングエンジン１４０は次の動作を実行時に行う。３１０で、Ｏに近い１つまたは複数のサンプル点Ｐ_ｉにおける入射ライティング｛Ｌ_ｐｉ｝をＳＨ基底について計算する。３２０でそのＬ_ＰｉをＯの座標枠に合わせて回転し、それらをブレンドして（下記参照）Ｏ上の入射ライティングＬ_ｐのフィールドを得る。３３０〜３９０で、Ｏ上の各点ｐで（Ｌ_ｐ）_ｉに線形変換を行って出射放射輝度を得る。この線形変換は、アクション３５０の拡散表面（式（８））の（Ｍｐ）ｉとのドット積か、またはアクション３６０の光沢表面（式（９））の（Ｍ_ｐ）_ｉｊとの行列ベクトル乗算である。光沢表面にはさらにアクション３７０および３８０があり、ここで乗算３６０によって得られる放射輝度ベクトルにｐにおけるＯのＢＲＤＦを畳み込み、ビューに依存する反射方向Ｒで評価する。
【０１４２】
アクション３１０のために、レンダリングエンジン１４０は、選択されたライティング環境の入射ライティングの表現として、事前に計算した環境マップをロードする、ソフトウェアで分析的ライティングモデルを評価する、あるいはグラフィックハードウェアを用いて放射輝度をサンプリングすることができる。アクション３２０の回転についてはセクション１の「球面調和関数の概略」で概説しており、これは点ｐごとではなく１つのオブジェクトにつき１回行われる。この回転を行うのは、伝達がＯについての共通の座標系を使用して記憶されるためである。Ｏが剛体として動いている場合は、Ｏの多数の伝達関数を回転するよりも、Ｏと整合するようにＬ_ｐｉ中の数個の放射輝度サンプルを回転する方が効率的である。
【０１４３】
拡散表面の場合、アクション３５０の単純な実装は、頂点ごとに伝達ベクトルを格納し、頂点シェーダでドット積を行うものである。伝達ベクトルは頂点ごとに格納するのではなくテクスチャマップに格納し、ピクセルシェーダを使用して評価することもできる。これらの係数は常に［−１，１］の範囲にあるとは限らない符号付きの数量なので、［−８、８］というより広い範囲を提供するＤｉｒｅｃｔＸ８．１ピクセルシェーダ（Ｖ１．４）またはそれらに相当するＯｐｅｎＧＬ（拡張はＡＴＩによる）を使用することができる。一実装では、ピクセルシェーダはドット積を実行するのに８命令しか必要とせず、Ｌ_ｐの射影係数を定数レジスタに格納する。
【０１４４】
色を付けた環境またはＯでのカラーブリーディングのシミュレーションには３回のパスを行い、各パスでｒ、ｇ、およびｂチャネルに個別のドット積を行う。それ以外の場合は１回のパスで十分である。
【０１４５】
光沢の自己伝達の場合は、伝達行列が現在の頂点シェーダまたはピクセルシェーダのどちらで操作するにも大きすぎる可能性があるので、式（９）の行列変換をソフトウェアで行うことができる。この結果は（Ｌ’_ｐ）_ｉ、すなわちＯ上の点ｐにおける伝達放射輝度のＳＨ係数になる。そしてピクセルシェーダで、Ｇ^*の単純な余弦べき乗（Ｐｈｏｎｇローブ）の核を用いて畳み込み３７０を行い、結果を反射方向Ｒで評価することができる。この結果は
【０１４６】
【数３７】

【０１４７】
と書くことができる。現在のグラフィックハードウェアでは５次までのＳＨ射影を評価することができる。
【０１４８】
４．１ 入射放射輝度フィールドの空間サンプリング
入射放射輝度を動的にサンプリングするための単純かつ有用なアプローチは、Ｏの中心点で入射放射輝度をサンプリングするものである。Ｏ上の局所的なライティングの変動に対処するために、より精密な技術では複数の点で入射ライティングをサンプリングする。望ましい数の点を入力として与えられた場合に、ＩＣＰ（反復最近傍点）アルゴリズムを使用して適切なサンプル点のセットを前処理として得ることができる（例えば、非特許文献１６参照）。これにより、入射ライティングを実行時にサンプリングできるＯに近くＯ上に均一に分散した点Ｐ_ｉの代表的なセットが生成される。レンダリングエンジン１４０は、結果得られるサンプリングされた放射輝度の各球面Ｌ_ｐｉからの寄与をブレンドするＯ上の各点ｐにおける係数を事前に計算して、上でＬ_ｐと表したＯ上の入射放射輝度フィールドを得ることもできる。
【０１４９】
図１１は、単一の点、ＩＣＰ点、および複数のサンプルにおける入射放射輝度のサンプリングと、図３の実行時手順３００を使用したレンダリングから得られる画像を表す。
【０１５０】
４．２ グラフィックハードウェアによるＳＨ放射輝度のサンプリング
グラフィックハードウェアは、動的なシーンで放射輝度サンプル｛Ｌ_Ｐｉ｝を取り込むのに有用である。これを行うには、キューブマップの球面パラメータ化の６面に対応する各Ｐ_ｉから６つの画像をレンダリングする。Ｏ自体はそのレンダリングから除去しなければならない。次いで式（１）の積分を使用してキューブマップ画像を各自のＳＨ係数に射影する。
【０１５１】
効率面から、それぞれｓのキューブマップのパラメータ化に対して評価した差分立体角で重みを付けた基底関数についてテクスチャを事前に計算しておく
【０１５２】
【数３８】

【０１５３】
。すると、この結果得られる積分は、取り込まれたＬ_ｐ（ｓ）のサンプルとテクスチャ
【０１５４】
【数３９】

【０１５５】
の単純なドット積になる。
【０１５６】
この計算はグラフィックハードウェアで行うのが理想的である。あるいは、精度の問題と、ハードウェアでは内積を行うことができないことから、サンプリングした放射輝度画像を読み戻し、ソフトウェアで射影してもよい。この場合は読み戻す画像の解像度を可能な限り下げると有用である。
【０１５７】
低次のＳＨ射影は、適切に帯域制限されていることを前提として非常に低解像度のキューブマップを用いて計算することができる。例えば、すでに６次に帯域制限された球面信号は６４×４の画像を使用して射影することができ、べき乗単位信号（すなわち球面上での積分平方が１である信号）を想定することによって誤差を正規化した場合、平均ケースの二乗誤差が約０．３％、最悪ケースの二乗誤差が約１％である。（より正確には、平均ケースの誤差は、すべてのべき乗単位信号（unit-power signal）にわたって平均した基準信号と再構築信号との積分した二乗差である。最悪ケースの誤差はそれと同じ積分誤差であるが、最悪ケースのべき乗単位信号についての誤差である）６×８×８のマップでは、この誤差は平均で０．００３％、最悪ケースで０．０２％に低下する。不都合なのは、典型的な信号は球形に帯域制限されないことである。別の分析によると、サンプリングした２Ｄ画像に対する連続的な双一次の再構築を想定すると、６×８×８の画像を使用した６次への射影では平均ケースの二乗誤差が０．７％、最悪ケースの誤差が２％であり、６×１６×１６の画像ではそれぞれ０．２％と０．５％の誤差となる。
【０１５８】
例示的な実装ではハードウェアから６×１６×１６の画像を抽出する。点でサンプリングを行うレンダリングで常にそうであるように、上述の分析では点サンプルからの双一次の再構築を基準として使用するので、２Ｄ画像のエリアシングがなお問題となる。エリアシングを軽減するために、キューブマップ画像を各次元でスーパーサンプリング（例えば２倍）し、読み出しと射影の前にボックスフィルタリングしたデシメーションをハードウェアで行うことができる。同様に、前処理として基底関数テクスチャもスーパーサンプリングし、デシメーションすることができる。読み戻しとＳＨ射影を含む放射輝度サンプルの場合、この例示的な実装はＡＴＩ Ｒａｄｅｏｎ８５００搭載のＰＩＩＩ−９３３ＰＣで約１．１６ｍｓを要する。
【０１５９】
４．３ ボリュームモデルの自己伝達
ボリュームの自己伝達データには表面の場合と同じフレームワークを使用する。これにより得られる事前計算モデルはライティングの実行時の変更を可能にし、任意の低周波数ライティング環境で正確なシャドーイングと相互反射が得られる。図１２は、雲のモデルがどのようにそれ自体にシャドーを作り、光を散乱するかを捉えるために実行時手順３００のボリューム自己伝達向けの変形（以下に説明する）でボリュームでの自己伝達を使用した雲モデルの画像を表す。
【０１６０】
表面の伝達と同様に、前処理ステップでＳＨ基底関数を放射体として使用してボリュームへのライティングをシミュレートする。相互反射のないシャドー付きの伝達（すなわち直接シャドーイング）の場合、シミュレータは、ボリュームを貫通するその経路によって減衰される、放射体からボリュームのすべてのボクセルｐへのエネルギーを集める。方向ｓ_ｄに必要な数値積分は
【０１６１】
【数４０】

【０１６２】
と表すことができ、Λ（ｐ→ｑ）は、ｐからｑへの経路に沿ったボリュームの積分した減衰であり、Ｄは光線（ｐ，ｓ_ｄ）がボリュームを出るまでの距離である。相互反射を含めるために、シミュレーションはあらゆるボクセルｐをトラバースし、無作為の方向ｓ_ｄに沿ってその伝達を前方に散乱する。伝達は、規則
【０１６３】
【数４１】

【０１６４】
を使用して、ボリュームを出るまでｓ_ｄに沿ったすべてのボクセルｑに置かれる。ボリュームにより多くのパスを行うと、さらに多くの間接的なはね返りが生成される。
【０１６５】
レンダリングは従来の方式で、すなわち透明度を考慮するアルファブレンディングを使用して３Ｄボリュームを貫通するスライスを後ろから前への順序で描画することによって行う。各スライスは、伝達ベクトルのサンプルを含む２Ｄ画像である。ピクセルシェーダは、ライティングの係数と、各スライスに陰影を付けるのに必要な伝達ベクトルとのドット積を計算する。
【０１６６】
５．放射輝度の近傍伝達
近傍伝達では、パラメータ化された低周波数ライティングについて、オブジェクトＯがそれに近接する環境に与える影響を事前に計算する。図１３は、シミュレーション２００（図２）の近傍伝達向けの変形（以下で説明する）と実行時レンダリング手順３００（図３）を用いて捉えた、ハンググライダーが近接する凹凸のある地形にぼんやりしたシャドーを投じている画像を示す。伝播のシミュレーションはセクション３「自己伝達の事前計算」の自己伝達のシミュレーションと同じであるが、Ｏの上ではなくＯを取り巻く３Ｄ空間内の点に行われる。実行時にこのボリューム中に任意の対象物Ｒを配置して、事前にＲを知らなくともＯによってＲの上に投じられるシャドー、反射、およびコースティックを捉えることができる。例えば、移動する乗り物Ｏが地面Ｒにシャドーを投じることができる。投じられたシャドーとライティングはライティングの変化にも反応する。例えば、ライトを動かすとＲ上のぼんやりしたシャドーが移動する。これは、光沢のある伝達を考慮し、動的なライティングを可能にすることにより放射照度ボリュームを一般化する（例えば、非特許文献１７参照）。
【０１６７】
Ｒは事前計算のステップでは未知なので、Ｏの近傍ボリュームは、ベクトルではなく伝達行列を格納する。Ｒの法線が事前に分からないので、これは拡散対象物にも当てはまる。
【０１６８】
一実装では、シミュレータは、Ｏの周囲の単純な３Ｄグリッド内の各点における伝達行列Ｍ_ｐを事前に計算しておく。実行時にレンダリングエンジンはボリューム中の各点で式（９）の行列変換をソフトウェアで実行し、結果をグラフィックハードウェアにアップロードする。この結果は、伝達された放射輝度（Ｌ’_ｐ）の係数を含むボリュームテクスチャであり、これをＲに適用する。
【０１６９】
次いで、ピクセルシェーダで、この伝達された放射輝度を使用して対象物にライトを当てる。拡散対象物は、式（６）を使用して放射輝度に余弦の重みを付けた半球Ｈ^*を畳み込み、そして得たＳＨ射影をＲの法線ベクトルで評価する。光沢のある対象物は式（１２）を行う。
【０１７０】
自己伝達が予め計算された対象物には、ＯとＲが共通の座標系を共有しないという問題が生じる。このため、２つのオブジェクトのうち１つの伝達サンプルの稠密な集合を動的に回転してもう一方と整合させなければならない。その複雑さはＯ（ｎ^４）であり、式（９）の行列変換を行う複雑さと同じであるが、より高次の射影の回転はその演算に比べてかなり負荷が高い。ハードウェアの改良によりこの問題はほどなく軽減されよう。
【０１７１】
自己伝達と比べると、近傍伝達ではいくつかの追加的な近似誤差が生じる。複数の近傍伝達オブジェクトから同一の対象物に投じられるシャドーまたは光は組み合わせるのが難しい。ＯまたはＲの存在に起因しない局所的なライティングの変動も問題となる。すなわち、正確な結果を提供するには、Ｏの近傍全体にわたってライティングがかなり一定でなければならない。詳細には、ＯおよびＲ以外のオブジェクトがＯの近傍に入りこむと、あるべきシャドーが欠けるなどのエラーが生じる。また、Ｏの近傍は、ＯがＲに投じ得るシャドーまたは光をいずれも包含するのに十分な大きさでなければならない。それでも、近傍伝達は、従来の方法ではリアルタイムで得ることができない効果を取り込む。
【０１７２】
６．コンピューティング環境
図６は、例示的な実施形態を実装することが可能な適切なコンピューティング環境６００の概略的な一例である。本発明は様々な汎用または特殊目的のコンピューティング環境で実装できることから、コンピューティング環境６００は本発明の使用または機能性の範囲に関して何らの制限を示唆するものではない。
【０１７３】
図６を参照すると、コンピューティング環境６００は、少なくとも１つの処理装置６１０およびメモリ６２０を含む。図６では、この最も基本的な構成６３０を点線内に含めている。処理装置６１０は、コンピュータ実行可能命令を実行し、実際のプロセッサであっても仮想プロセッサであってもよい。多重処理システムでは複数の処理装置でコンピュータ実効命令を実行して処理力を増大する。メモリ６２０は、揮発性メモリ（例えばレジスタ、キャッシュ、ＲＡＭ）、不揮発性メモリ（例えばＲＯＭ、ＥＥＰＲＯＭ、フラッシュメモリなど）、あるいはこれら２種の何らかの組合せであってよい。メモリ６２０は、放射輝度の自己伝達を用いるグラフィック画像レンダリングを実装するソフトウェア６８０を格納する。
【０１７４】
コンピューティング環境は、この他の機能を備えることが可能である。例えば、コンピューティング環境６００は、ストレージ６４０、１つまたは複数の入力装置６５０、１つまたは複数の出力装置６６０、および１つまたは複数の通信接続６７０を含む。バス、コントローラ、あるいはネットワークなどの相互接続機構（図示せず）は、コンピューティング環境６００の構成要素を相互に接続する。通例、オペレーティングシステムソフトウェア（図示せず）は、コンピューティング環境６００で実行される他のソフトウェアのための動作環境を提供し、コンピューティング環境６００の構成要素のアクティビティを調整する。先に述べたように、コンピューティング環境は、ＤｉｒｅｃｔＸおよびＯｐｅｎＧＬの関数ライブラリ、ＡＴＩ ＲａｄｅｏｎやＮＶｉｄｉａ ＧｅＦｏｒｃｅビデオカードなどのグラフィック処理ハードウェアおよびソフトウェアを含むことが望ましい。
【０１７５】
ストレージ６４０は取り外し可能でも取り外し不能でもよく、磁気ディスク、磁気テープまたはカセット、ＣＤ−ＲＯＭ、ＣＤ−ＲＷ、ＤＶＤ、あるいは情報の記憶に使用することができ、コンピューティング環境６００内でアクセスが可能な任意の他の媒体を含む。ストレージ６４０は、画像レンダリングシステム（図１）を実装するソフトウェア６８０の命令を記憶する。
【０１７６】
入力装置６５０は、キーボード、マウス、ペン、トラックボールなどのタッチ入力装置、音声入力装置、スキャニング装置、あるいはコンピューティング環境６００に入力を提供する他の装置でよい。オーディオには、入力装置６５０はサウンドカード、あるいはアナログまたはデジタル形態のオーディオ入力を受け付ける同様の装置でよい。出力装置６６０は、ディスプレイ、プリンタ、スピーカ、あるいはコンピューティング環境６００からの出力を提供する他の装置でよい。
【０１７７】
通信接続６７０は、通信媒体を通じた別のコンピューティングエンティティとの通信を可能にする。通信媒体は、コンピュータ実行命令、圧縮されたオーディオまたはビデオ情報、あるいはその他のデータなどの情報を変調データ信号で伝搬する。変調データ信号とは、その信号中に情報を符号化するような形でその特性の１つまたは複数を設定または変更した信号である。例として、これらに限定しないが、通信媒体には、電気、光学、ＲＦ、赤外線、音響、あるいは他の搬送波を用いて実装される配線式または無線式の技術が含まれる。
【０１７８】
本発明は、コンピュータ可読媒体の一般的な文脈で説明することができる。コンピュータ可読媒体は、コンピューティング環境内でアクセスできる任意の利用可能な媒体である。例として、これらに限定しないが、コンピューティング環境６００ではコンピュータ可読媒体はメモリ６２０、ストレージ６４０、通信媒体、および上述の媒体の任意の組合せを含む。
【０１７９】
本発明は、プログラムモジュールに含まれ、コンピューティング環境で実際あるいは仮想のターゲットプロセッサで実行されるコンピュータ実行可能命令の一般的な文脈で説明することができる。一般に、プログラムモジュールには、特定タスクを行う、あるいは特定の抽象データタイプを実装するルーチン、プログラム、ライブラリ、オブジェクト、クラス、コンポーネント、データ構造などが含まれる。プログラムモジュールの機能は、各種の実施形態で必要に応じてプログラムモジュール間で組み合わせるか、または分割することができる。プログラムモジュールのコンピュータ実行可能命令は、ローカルな、または分散したコンピューティング環境で実行することができる。
【０１８０】
提示のために、この詳細な説明ではコンピューティング環境内のコンピュータ動作を説明するために「判定する（determine）」、「入手する（get）」、「調整する（adjust）」、および「適用する（apply）」といった語を使用している。これらの語は、コンピュータによって行われる動作の高レベルの抽象であり、人間によって行われる行為と混同すべきではない。これらの語に対応する実際のコンピュータ動作は実装によって異なる。
【０１８１】
例示的実施形態を参照して本発明の原理を説明し、例示したが、この例示的実施形態は上記のような原理から逸脱することなく構成と詳細を変更できることを認識されよう。特に指摘しない限りは、本明細書に記載するプログラム、プロセス、あるいは方法は任意の特定タイプのコンピューティング環境に関連しない、あるいは制限されないことを理解されたい。各種タイプの汎用または特殊化コンピューティング環境は、本明細書に記載する教示による動作とともに使用することができ、あるいはその動作を行うことができる。ソフトウェアとして示した例示的実施形態の要素はハードウェアに実装してもよく、その逆も同様である。
【０１８２】
本発明の原理を応用することが可能な多くの可能な実施形態に照らし、頭記の特許請求の範囲およびその均等物の範囲および精神に含まれ得る実施形態はすべて本発明として請求する。
【図面の簡単な説明】
【図１】動的な低周波数のライティング環境におけるリアルタイム画像レンダリングのための事前計算された放射輝度自己伝達を取り入れるコンピュータグラフィックソフトウェアアーキテクチャのブロック図である。
【図２】図１の画像レンダリングシステムにおける自己伝達の事前計算の流れ図である。
【図３】図１の画像レンダリングシステムにおける放射輝度伝達のリアルタイムレンダリングの流れ図である。
【図４】図３のリアルタイムレンダリングにおける実行時の拡散表面自己伝達を処理する流れ図である。
【図５】図３のリアルタイムレンダリングにおける実行時の光沢表面自己伝達を処理する流れ図である。
【図６】図１の画像レンダリングシステムに適したコンピューティング環境のブロック図である。
【図７】図２の自己伝達の事前計算でシミュレートした相互反射を表す図である。
【図８】ともにシャドーを付けず、図３のリアルタイムレンダリングを介して生成された画像の図である。
【図９】ともにシャドーを付けず、図３のリアルタイムレンダリングを介して生成された、拡散表面の自己伝達の効果を示す画像の図である。
【図１０】ともにシャドーを付けず、図３のリアルタイムレンダリングを介して生成された、光沢表面の自己伝達の効果を示す画像の図である。
【図１１】それぞれ単一の点、反復最近傍点アルゴリズム（ＩＣＰ）の点、および複数のサンプルで入射放射輝度をサンプリングした、図３のリアルタイムレンダリングを介して生成された画像の図である。
【図１２】図３のリアルタイムレンダリングを介して生成されたボリュームの自己伝達の画像の図である。
【図１３】図３のリアルタイムレンダリングを介して生成された近傍伝達の画像の図である。
【符号の説明】
１００ コンピュータグラフィック画像レンダリングシステム
１１０ 幾何学的オブジェクトモデル
１３０ 放射輝度自己伝達データ
１２０ グローバルイルミネーションシミュレータ
１４０ リアルタイム画像レンダリングエンジン
１５０ ライティング環境
１６０ ビュー方向
１７０ ユーザコントロール
１８０ グラフィックディスプレイドライバ
６００ コンピューティング環境
６１０ 処理装置
６２０ メモリ
６４０ ストレージ
６５０ 入力装置
６６０ 出力装置
６７０ 通信接続
６８０ ソフトウェア[0001]
BACKGROUND OF THE INVENTION
The present invention relates to computer graphic image rendering techniques, and more particularly to lighting and shadowing of modeled objects in a rendered image.
[0002]
[Prior art]
A portion of the disclosure of this patent document contains material that is subject to copyright protection. The copyright owner has no objection to any reproduction of this patent disclosure contained in the US Patent and Trademark Office patent file or record by any party, but otherwise retains all copyrights.
[0003]
Lighting from surface light sources, soft shadows, and interreflection are important effects for realistic image composition. Unfortunately, general methods for integrating over large lighting environments, including Monte Carlo ray tracing, radiosity, or multi-pass rendering summing over multiple point sources, are impractical for real-time rendering. (There are representative literatures on Monte Carlo ray tracing (see, for example, Non-Patent Document 1, Non-Patent Document 2, and Non-Patent Document 3). (For example, refer to Non-Patent Document 5, Non-Patent Document 6, and Non-Patent Document 7).
[0004]
[Non-Patent Document 1]
Cook, R. Porter, T and Carpenter, L, Distributed Ray Tracing, SIGGRAPH'84, 137-146
[0005]
[Non-Patent Document 2]
Jensen, H, Global Illumination using Photon Maps, Eurographics Workshop on Rendering 1996, 21-30
[0006]
[Non-Patent Document 3]
Kajiya, J, The Rendering Equation, SIGGRAPH '86, 143-150
[0007]
[Non-Patent Document 4]
Cohen, M and Wallace, J, Radiosity and Realistic Image Synthesis, Academic Press Professional, Cambridge, 1993
[0008]
[Non-Patent Document 5]
Haeberli, P and Akeley, K, The Accumulation Buffer: Hardware Support for High-Quality Rendering, SIGGRAPH'90, 309-318
[0009]
[Non-Patent Document 6]
Keller, A, Instant Radiosity, SIGGRAPH '97, 49-56
[0010]
[Non-Patent Document 7]
Segal, M, Korobkin, C, van Widenfelt, R, Foran, J and Haeberli, P, Fast Shadows and Lighting Effects Using Texture Mapping, SIGGRAPH'92, 249-252
[0011]
[Non-Patent Document 8]
Cabral, B, Olano, M and Nemec, P, Reflection Space Image Based Rendering, SIGGRAPH'99, 165-170
[0012]
[Non-patent document 9]
Greene, N, Environment Mapping and Other applications of World Projections, IEEE CG & A, 6 (11): 21-29, 1986
[0013]
[Non-Patent Document 10]
Heidrich, W, Seidel H, Realistic, Hardware-Accelerated Shading and Lighting, SIGGRAPH'99, 171-178
[0014]
[Non-Patent Document 11]
Kautz, J, Vazquez, P, Heidrich, W and Seidel, H, A Unified Approach to Pre-filtered Environment Maps, Eurographics Workshop on Rendering 2000, 185-196
[0015]
[Non-Patent Document 12]
Ramamoorthi, R and Hanrahan, P, An Efficient Representation for Irradiance Environment Maps, SIGGRAPH'01, 497-500
[0016]
[Non-Patent Document 13]
Edmonds, A, Angular Momentum in Quantum Mechanics, Princeton University, Princeton, 1960
[0017]
[Non-Patent Document 14]
Zare, R, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics, Wiley, New York, 1987
[0018]
[Non-Patent Document 15]
Chirikjian, G and Stein, D, Kinematic Design and Communication of a Spherical Stepper Motor, IEEE Transactions on Mechatronics, 4 (4), Dec. 1999
[0019]
[Non-Patent Document 16]
Linde, Y, Buzo and Gray, R, An algorithm for Vector Quantizer Design, IEEE Transaction on Communication COM-28, 1980, 84-95
[0020]
[Non-Patent Document 17]
Greger, G., Shirley, P, Hubbard, P, and Greenberg, D, The Irrandiance Volume, IEEE Computer Graphics and Applications, 6 (11): 21-29, 1986
[0021]
[Problems to be solved by the invention]
There are three difficulties associated with real-time, realistic global illumination. That is, the complex and spatially varying bidirectional reflection distribution function (BRDF) of real material must be modeled (BRDF complexity), and the integration over the hemisphere in the lighting direction at each point (light integration) Necessary and the bouncing / occlusion effects such as shadows due to inclusions in the light path from the light source to the receiver must be taken into account (light propagation complexity). Many studies have focused on solving the problem of light integration by expanding the complexity of BRDF (eg glossy anisotropic reflection) and representing incident lighting as a sum of directions or points. It was. Thus, the integration of light results in just the same sampling of analytical or tabular BRDFs at a few points, but is cumbersome for large light sources. In the second line of research, radiance is sampled and kernels of various sizes are convoluted in advance. (For example, refer to the following (for example, see Non-Patent Document 8, Non-Patent Document 9, Non-Patent Document 10, Non-Patent Document 11, Non-Patent Document 12)) This method solves the problem of light integration, Since convolution is premised on the incident reflection brightness not being shielded and scattered, the complexity of light propagation such as shadow is ignored. And there are clever ways to increase the propagation of light, especially the shadow complexity. The problem is light integration, and most of the methods described above are not suitable for very large light sources.
[0022]
[Means for Solving the Problems]
The real-time image rendering techniques described herein better consider the complexity of light integration and light propagation in real time. This technique is intended for low-frequency lighting environments (area-supported basis functions) and does not cause aliasing using low-order spherical harmonic (SH) bases. Efficient environment. One aspect of this technique is to represent how an object scatters its light into the object itself or adjacent space in a way that separates the scatter from incident lighting. For example, in FIG. 8, the modeled image of the human head without shadow is compared with the image generated in the manner described herein using radiance self-transmission.
[0023]
To briefly describe the technique described here, first assume that there is a convex diffuse object illuminated by an infinitely distant environment map. The object's shaded “response” to its environment can be thought of as a transfer function that maps the incoming radiance to the outgoing radiance, which in some cases simply performs a cosine weighted integration. More complex integrations capture how concave objects create shadows themselves, in this case multiplying the integrand by an additional propagation factor that represents visibility in each direction.
[0024]
The technical approach described here pre-calculates a high load propagation simulation required by a complex transfer function such as shadowing for a given object. The resulting transfer function is represented as a dense set of vectors or matrices on the object surface. On the other hand, it is not necessary to calculate the incident radiance in advance. During subsequent real-time rendering, the graphics hardware can dynamically sample the incident radiance at a limited number of points, and this technique converts it to a spherical harmonic (SH) basis with a fast computation. . Analytical models such as skylight models and simple geometric shapes such as circles can also be used.
[0025]
By representing both the incident radiance and the transfer function in the SH basis, the technique described here allows the integration of light through a simple dot product (diffuse object) between each coefficient vector, or through a small transfer matrix. Let it be a simple linear transformation (glossy object) of the lighting coefficient vector. Very few coefficients (9-25) are required in a low frequency lighting environment, and the graphics hardware can calculate the result in a single pass. Unlike the Monte Carlo method or the multi-pass optical integration method, the run-time calculation with this technique can be kept constant no matter how many or even the light sources. Retaining a certain amount of runtime calculations relies on large, smooth lighting to limit the number of SH coefficients required.
[0026]
The technique described here represents complex propagation effects in the transfer function, such as interreflection and caustic. Since all of these are simulated as preprocessing, only the basis coefficient of the transfer function changes, and the calculation at run time does not change. The technical approach described here deals with both surface and volume based geometry. With higher SH coefficients, this technique can handle glossy (but not highly specular) objects including not only diffusion but also interreflection. For example, 25 SH coefficients are sufficient to obtain a useful glossy effect. In addition to the transmission from the rigid object, called self-transmission, to itself, this technique is generalized to proximity transmission from the rigid object to the space adjacent to it, thrown soft shadows, glossy reflections, And allows caustic on moving objects.
[0027]
DETAILED DESCRIPTION OF THE INVENTION
Referring to FIG. 1, the software architecture of the computer graphic image rendering system 100 is modeled with interreflection and self-shadowing using the radiance self-transmitting image rendering technique described herein. Provides real-time image rendering of objects. In general, the software architecture includes a global illumination simulator 120, a real-time image rendering engine 140, and a graphic display driver 180. In the radiance self-propagating rendering technique described more fully below, the global illumination simulator 120 performs a pre-processing stage of the technique where the radiance self-propagating data 130 is pre-calculated from the geometric object model 110. deep. The geometric object model 110 may be a triangular mesh, wavelet synthesis, or any other representation of the geometry of the object being modeled. The real-time image rendering engine 140 then renders an image of the object modeled for the dynamically varying lighting environment 150 and view direction 160 using pre-calculated radiance self-propagating data, and the lighting environment 150 and view direction 160. Can be selectively changed or set by user control 170. The graphic display driver 180 outputs an image to an image output device (for example, a monitor, a projector, or a printer).
[0028]
In some embodiments of the graphic image rendering system, the pre-calculation of radiance self-transmission by the simulator 120 and the image rendering by the engine 140 are implemented on a single computer as described in Section 6 “Computing Environment” below. can do. More generally, the simulator 120 can be run on another computer and the resulting data can be transferred to a computer that runs the rendering engine 140 to generate a graphic image.
[0029]
Summary of Radiance Self-Transmission Technique: As a pre-processing, the global illumination simulator 120 performs a lighting simulation on the model 110 to capture how the modeled object shadows itself and scatters light. This result is recorded in the radiance self-transmitted data 130 as a dense set of vectors (in the case of diffusion) or matrices (in the case of gloss) on the model. During image rendering, the rendering engine 140 projects the incident radiance corresponding to the lighting environment 150 onto a spherical harmonic (SH) basis (this is described below). The model transfer vector or matrix field is then applied to the lighting coefficient vector. When the object is diffusive, the dot product of the transfer vector and the lighting coefficient at a plurality of points on the object is obtained, and the self-scattered shading is accurately generated. If the object is glossy, a transfer matrix is applied to the lighting coefficients to obtain a spherical function coefficient representing the self-scattered incident radiance at those points. This function is convolved with the object's bi-directional reflection distribution function (BRDF) and then evaluated in a view-dependent reflection direction to produce the final shading of the object in the rendered image.
[0030]
1. Overview of spherical harmonics
Definition: A spherical harmonic function defines an orthonormal group for a sphere S, similar to a Fourier transform for a one-dimensional circle. Parameterization
s = (x, y, z) = (sin θ cos φ, sin θ sin φ, cos θ)
Then the basis function is
[0031]
[Expression 1]

[0032]
Defined as P_l ^mIs the associated Legendre polynomial, K_l ^mIs a normalization constant.
[0033]
[Expression 2]

[0034]
The above definition forms a complex basis, and a real-valued basis is a simple transformation
[0035]
[Equation 3]

[0036]
Given by.
[0037]
A low value of l (called the band index) represents a low frequency basis function on the sphere. The basis function of band l is a polynomial of degree l in x, y, and z. The evaluation can be performed with a simple recurrence formula (see, for example, Non-Patent Document 13 and Non-Patent Document 14).
[0038]
Projection and reconstruction: SH base is orthonormal, so integration (area-supported basis function)
[0039]
[Expression 4]

[0040]
The scalar function f defined on S can be projected onto its coefficients via
[0041]
Their coefficients are nth order reconstruction functions
[0042]
[Equation 5]

[0043]
Which increases the degree of approximation to f as the number of bands n increases. Low frequency signals can be accurately represented in only a few SH bands. Higher frequency signals are band limited (ie, smooth without aliasing) by lower order projections.
[0044]
n for n-th projection²Number of coefficients is required. Often, for a vector of projection coefficients and basis functions indexed one by one,
[0045]
[Formula 6]

[0046]
It is convenient to rewrite equation (2) via, where i = 1 (l + 1) + m + 1. With this formulation, the evaluation of the reconstruction function at s is n²Component coefficient vector f_iAnd the evaluated basis function y_lIt becomes clear to represent a simple dot product with the vector of (s).
[0047]
Basic property: One of the properties of SH projection is its rotational invariance. That is, when Q is an arbitrary rotation on S and g (s) = f (Q (s)),
[0048]
[Expression 7]

[0049]
It becomes.
[0050]
This is similar to the transition invariant nature of the one-dimensional Fourier transform. In fact, this property collects samples from f into a rotated sample point set, projects them, and again
[0051]
[Equation 8]

[0052]
This means that no aliasing artifacts are produced by SH projection when rotating.
[0053]
Because the SH basis is orthonormal, given any two functions a and b for S, their projections are
[0054]
[Equation 9]

[0055]
The useful property of satisfying is obtained. That is, the integral of the product of the band-limited functions becomes the dot product of the projection coefficients of those functions.
[0056]
Convolution: The convolution of the function f into the circularly symmetric kernel function h (z) is h^*expressed as f. According to equation (3) above, h must be circularly symmetric (and thus can be defined as a simple function of z rather than s, so that the result is defined in S rather than the higher dimensional rotation group SO) Note that) The projection of this convolution is
[0057]
[Expression 10]

[0058]
Meet. In other words, the projected convolution coefficients are simply scaled products of individually projected functions. This property provides a high-speed method for obtaining an irradiance map by convolving a hemispherical cosine nucleus defined as h (z) = max (z, 0) into an environment map (see, for example, Non-Patent Document 12). ). In this case, the projection coefficient of h can be obtained using an analytical expression. The convolution property can also be used to obtain a pre-filtered environment map with narrower nuclei. Note that since h is circularly symmetric about z, its projection coefficient is non-zero only when m = 0.
[0059]
Projection of product: The projection of the product of a pair of spherical functions c (s) = a (s) b (s) when a is known and b is unknown is a matrix
[0060]
## EQU11 ##

[0061]
[Expression 12]

[0062]
Projection coefficient b via_jAnd the sum is shown in the replicated j-index.
[0063]
[Formula 13]

[0064]
Note that is a symmetric matrix.
[0065]
Rotation: Q,
[0066]
[Expression 14]

[0067]
The reconstructed function rotated by is the projection coefficient f of f_iCan be projected using a linear transformation of Due to the rotation invariant nature, this linear transformation treats each band coefficient individually. The most efficient implementation is realized using a zyz Euler angle decomposition of the rotation Q using a fairly complex recurrence formula (see, for example, Non-Patent Document 13, Non-Patent Document 14, and Non-Patent Document 15). ). When dealing with low-order functions only, symbolic integration can be used to implement the explicit rotation formula described in these references.
[0068]
2. Self-transmission of radiance
The self-transmission of radiance summarizes how object O shadows itself and scatters light. The self-transmission of radiance is calculated using L_pWe represent by first parameterizing the incident lighting at the point pεO, denoted as (s). Therefore, the incident lighting is n²Vector of coefficients (L_p) I. In practice, this lighting can be sampled dynamically and sparsely near the surface, perhaps only at a single point. This assumes that the variation in lighting on O that is not due to the presence of O itself is small (see Section 4.1 “Spatial Sampling of the Incident Radiance Field”). The radiance self-transmission can be pre-calculated as a transfer vector or matrix and stored on O at high density.
[0069]
Transfer vector (M_p)_iCan be used for a diffusing surface and represents a linear transformation to the lighting vector, L ′ through the inner product_pA scalar emission radiance expressed as follows is generated.
[0070]
[Expression 15]

[0071]
That is, (M_p)_iEach component of is a lighting basis function (L_p)_iP represents the linear effect on shading.
[0072]
Transfer matrix (M_p)_yCan be used for glossy surfaces and represents a linear transformation to the lighting vector, in which the transmitted radiance L 'rather than a scalar is transmitted._pThe projection coefficient of the entire spherical function (s) is obtained. Ie
[0073]
[Expression 16]

[0074]
The difference between the incident radiance and the transmitted radiance is L '_p(S) includes the effects of shadowing and scattering due to the presence of O, while L_p(S) is a point representing incident lighting assuming that O has been removed from the scene. (M_p)_yOf the transmitted radiance L '_pIncident radiance (L) for the i-th coefficient of (s)_p) Represents the linear effect of the jth lighting coefficient of j. The next section describes how to determine the diffusion surface transfer vector and the glossy surface transfer matrix due to self-scattering on O.
[0075]
2.1 Spreading transmission
First, assume that O is diffusive. The simplest transfer function at the point p∈O is a scalar function
[0076]
[Expression 17]

[0077]
Represents diffuse transmission without shadows, defined as, which results in an outgoing radiance that does not vary with view angle relative to the diffusing surface. Where ρ_pIs the albedo of the object at p and L_pIs the incident radiance at p assuming that O has been removed from the scene, and N_pIs the normal of the object at p and H_Np(S) = max (N_p[K, 0) is N_pIt is a hemispherical nucleus with cosine weights centered on. L_pAnd H_NpBy SH projecting individually, in Equation (5), T_DUIs the inner product of those coefficient vectors. The factor obtained by this is the light function L_pAnd transfer function M_pCall it. In this first simple case,
[0078]
[Formula 18]

[0079]
It becomes.
[0080]
N_pIs known, so the transfer function
[0081]
[Equation 19]

[0082]
Can be calculated in advance, resulting in a transfer vector. In fact, N_pSince a transfer vector can be obtained with a simple analytical expression, storage is not necessary.
[0083]
[Expression 20]

[0084]
Is essentially a low-pass filter, so the quadratic projection (9 coefficients) provides good accuracy in any lighting environment (even if not smooth).
[0085]
To include shadows, use diffusive transmission with shadows.
[0086]
[Expression 21]

[0087]
And an additional visibility function V_p(S) → {0,1} is equal to 1 when the ray from p in direction s does not intersect O again (ie cannot be shadowed). Like the unshaded transmission, this integral is L_pSH projection and transfer function
[0088]
[Expression 22]

[0089]
Can be decomposed into two functions. L again_pAnd M_pBy projecting SH individually_DSThe integral inside is the inner product of the coefficient vectors.
[0090]
In this case, communication is important. The self-transmission of radiance is pre-calculated using a propagation simulator (described in the section “Pre-calculation of self-transmission” below) and the resulting transfer vector (M_p)_iCan be stored at many points p on O. Unlike the previous case, V_pCan generate high frequency lighting locally, for example by creating a shadow in the “pinhole”,
[0091]
[Expression 23]

[0092]
Can be inaccurate even in smooth lighting environments. Using a 4th or 5th order projection gives good results with a regular mesh in a smooth lighting environment. For example, compare the unshaded image of the diffuse surface object of FIG. 9 with the shadowed image.
[0093]
Finally, in order to capture not only shadows but also diffusive interreflections (see, for example, the image with interreflections in Figure 9)
[0094]
[Expression 24]

[0095]
Can be defined as
[0096]
[Expression 25]

[0097]
Is the radiance from O itself in direction s. The problem is
[0098]
[Equation 26]

[0099]
Is determined by the outgoing radiance of a point at an arbitrary distance from p, and since local lighting fluctuates on O, the incident radiance is given only by p unless the incident radiance is emitted from a light source at infinity. Even if radiance
[0100]
[Expression 27]

[0101]
I don't know. If the variation in lighting on O is small, L is everywhere O_pAs if illuminated by
[0102]
[Expression 28]

[0103]
Very close to. Therefore, T_DIIs L_pCan be factored into a product of two projected functions, a light-dependent function and a geometry-dependent function, as in the previous two cases.
[0104]
Pre-calculated interreflection must assume that the incident lighting on O does not change spatially, but this assumption is not necessary for simpler shadowed transmissions. The difference is that the shadowed transmission depends only on the incident lighting at p, whereas the interreflected transmission is L_q≠ L_pIt depends on many points q ≠ p on O. Therefore, if the incident radiance field is sampled sufficiently fine (as described in the section “Spatial sampling of the incident radiance field” below), local lighting variations can be captured and shadowed. Transmission is accurate.
[0105]
[Expression 29]

[0106]
Is present, the interreflection transfer function
[0107]
[30]

[0108]
Is difficult to express explicitly. The section “Pre-calculation of self-transmission” below describes how to calculate the projection coefficient numerically.
[0109]
2.2 Gloss transmission
Glossy object self-transmission can be defined similarly, but generalizes the kernel function to depend on the reflection direction R (depending on the view) rather than the (fixed) normal N. Similar to the previous H nucleus, the self-transmission of radiance can model the glossy reflection as the nucleus G (s, R, r), and the scalar r is the “glossiness” or breadth of the specular reaction. Define.
[0110]
Three similar gloss transfer functions with no shadow, with shadow, and with interreflection
[0111]
[31]

[0112]
Which are both unknown quantities when precalculated_pAnd a scalar radiance in the direction R as a function of R. Since transfer is no longer just a function of s, it cannot be replaced by a simple vector of SH coefficients.
[0113]
Instead of parameterizing the scalar transmission with R and r, a more useful decomposition is the incident radiance L_p(S) to L '_pIt is transmitted to the entire spherical surface of the transmitted radiance represented by (s). If the gloss core G is circularly symmetric about R, then L ′_pG ’in (s)_r(Z) = G (s, (0, 0, 1), r) can be convolved and evaluated with R to obtain the final result.
[0114]
This time L ’_pThe transmission to is represented as a matrix rather than a vector. For example, transmission with glossy shadows
[0115]
[Expression 32]

[0116]
Which defines its SH projection via equation (7) as a symmetric matrix
[0117]
[Expression 33]

[0118]
L which can be expressed as_pIs a linear operator. Even in the case of very smooth lighting, as the glossiness of O increases, more SH bands are used.
[0119]
[Expression 34]

[0120]
Under such conditions, a non-square matrix (eg, 25 × 9) that maps low frequency lighting to higher frequency transmitted radiance is useful.
[0121]
What is important in limiting the self-transmission of the radiance calculated in advance is T_DIAnd T_GIThe material properties (such as albedo and glossiness) of O that affect the mutual reflection in the are “baked in” to the preprocessed transmission and cannot be changed at runtime. In contrast, simpler shadowed transmission without interreflection allows for on-the-fly material property changes and / or spatial variations on O. An error occurs when an obstacle or light source enters the convex hull of O. O can only move as a rigid body and cannot deform or move certain components relative to the whole. Also recall the premise that accurate interreflection requires low lighting variation on O.
[0122]
Finally, the diffuse transfer defined above produces a radiance after leaving the surface because it has already folded the cosine-weighted normal hemisphere, whereas the gloss transfer is incident on the surface. Note that the radiance is generated and the local BRDF is convolved to obtain the final exit radiance. Further, it is possible to burn in a fixed BRDF in glossy O so that the G convolution at the time of execution is unnecessary, but the flexibility can be limited.
[0123]
FIG. 9 shows an unshaded image, a shadowed image, and an interreflected image of the glossy surface object.
[0124]
3. Pre-calculation of self-transmission
Referring now to FIG. 2, the illumination simulator 120 (FIG. 1) is a global illumination simulation performed on an object O using an SH infinite sphere (“reference lighting environment” for simulation) as an emitter. At 200, the self-transmission of the radiance of the modeled object is pre-calculated (also referred to as “pre-calculation of self-transmission”). This simulation is based on an nth-order SH projection of an unknown spherical surface of incident light L, i.e. n²Unknown coefficients L_iParameterized by The simulation result is the SH basis function y_iL using (s) as radiator_iEach can be calculated individually, but it is more efficient to calculate all at once. The reference lighting environment (spherical surface L at infinity) is the actual incident radiance L around O at run time._pReplace with
[0125]
The simulation 200 starts with a path simulating a direct shadow from a path that emits L and directly reaches the sample point pεO (“shadow path” 202). In the subsequent path (“interreflection path” 204), mutual reflection is added, representing a path (Lp, LDp, LDDp, etc.) from L that bounces back from O multiple times before reaching p. In each pass, energy is collected at every sample point on the p-surface. For large radiators (ie low frequency SH bases), energy aggregation is more efficient than shooting-type updates.
[0126]
A large (10k-30k) set of quasi-random directions in the simulation to capture the sphere in the direction at the sample point pεO
[0127]
[Expression 35]

[0128]
Is generated. In the simulation, each direction s_dThe evaluation of all SH basis functions in is also calculated in advance. Direction s_dIs organized into hierarchical bins formed by refining the first icosahedron in 1 → 2 bisectors to equal area spherical triangles (as in the case of 1 → 4 subdivision on the sphere as a flat surface) In the simulation, 6-8 subdivision levels are used to generate 512-2048 bins. Any bin at each level of the hierarchy is s_dContains a list of
[0129]
In the first pass or shadow pass 202, the simulation 200 tags (211) for each pεO the direction from the point p that self-occludes by the object. The simulation uses the hierarchy to cull directions that are outside the hemisphere, so that the normal N of p_pProjects a shadow ray in a hemisphere centered at. In the simulation, each direction s with an occlusion bit_dIe 1-V_p(S_d)_dIs in the hemisphere and crosses O again (ie, O can shadow itself). Occlusion bits are also associated with hierarchical bins, and the occurrences of occlusion within bins_dIndicates whether there is Directions and bins with self-occlusion are tagged to allow further interreflection paths for them, and bins / samples without any occlusion receive only direct light from the environment.
[0130]
Next, at 212, the simulation 200 integrates the transmitted radiance at point p. For a diffusing surface, the simulation shows that for each point pεO, M in equation (10)_pFurther, a transfer vector is calculated by the SH projection. For a glossy surface, the simulation is M in equation (11)._pThe transfer matrix is calculated by SH projection of In either case, the result represents the radiance collected at p and parameterized at L. Directional sample s SH projection to calculate transmission_dThis sum is the accumulated transfer using the following rule:
[0131]
[Table 1]

[0132]
Superscript 0 represents the number of iterations. Vector M of each point p_pOr matrix M_pIs initialized to 0 before the shadow path, and in the shadow path all s in all p_dTo sum. This rule is obtained using the diffusion transfer integral equation (1) and the gloss transfer integral equation (7).
[0133]
Referring also to FIG. 7, the subsequent interreflection path 204 traverses the bin in which the occlusion bit is set in the shadow path, and this time, 221 integrates the interreflection transmission. Instead of shadow rays, the simulation places a ray on O that returns the transmission from the outgoing illumination. Rays (p, s_d) Intersects another point qεO (q is closest to p), the direction from q to −s_dThe radiance emitted to is sampled. The following update rule is used, where the subscript b is the number of iterations of the rebound path.
[0134]
[Table 2]

[0135]
Similar to the shadow path 202, the inter-reflection path 204 has a direction s._dStart by initializing the transmission vector or matrix to 0 before accumulating the transmission over. The diffusion rule is T_DIAnd the rule of gloss is T_GIAnd the formulas (6) and (7). The middle factor in the definition of gloss transmission represents the radiance originating from q of the previous rebound path b-1 and returning to p. M_qStores the incident radiance, so convolve O BRDF in q
[0136]
[Expression 36]

[0137]
The emission radiance in the direction of, and the sum over k must be obtained. a_kRecall that is the kth convolution coefficient expressed in notation indexed one by one. The “reflect” operator simply reflects its first vector argument with respect to its second vector argument. Equation (7) is expressed as (M_p)_yNote that is formed by the product of two spherical functions, thus resulting in a symmetric matrix of glossy transmission with shadows. This is not the case for interreflective glossy transmissions.
[0138]
As shown at 230, the interreflective path 204 is repeated until a termination condition is met, such as the total energy of a given path being below a critical threshold. With standard materials, the interreflection decreases quite rapidly. The sum of the transmissions from all rebound paths corresponds to the mutual reflection.
[0139]
Alternatively, a simple enhancement to this simulation allows a mirror-like surface in O. This simulation does not record the transmission at such surfaces. Instead, light rays that strike a mirrored surface are always reflected and propagate until they reach a non-mirrored surface. Thus, the path in successive iterations is (L [S]^*p, L [S]^*D [S]^*p, L [S]^*D [S]^*D [S]^*p is a diffusive or glossy rebound, and S is a specular rebound. This introduces caustic to diffusive or glossy objects that react dynamically to lighting changes.
[0140]
4). Runtime rendering of radiance transfer
The simulation 200 described above (FIG. 2) provides a model that incorporates the transmission of radiance at a number of points p on the object surface, represented as a vector or matrix. Referring now to FIG. 3, the real-time image rendering engine 140 (FIG. 1) uses this model in the runtime procedure 300 to self-propagate the object in the selected lighting environment and view direction during real-time image rendering of the object. Calculate the radiance. 4 and 5 respectively show the flow of processing according to the run-time procedure 300 for the diffusing surface and the glossy surface.
[0141]
In step 300, the rendering engine 140 performs the following operations at runtime. One or more sample points P close to O at 310_iIncident lighting at L_pi} For the SH basis. 320 that L_PiRotate to fit the coordinate frame of O, blend them (see below), incident lighting L on O_pGet the field. 330-390, at each point p on O (L_p)_iThe output radiation radiance is obtained by performing a linear transformation on. This linear transformation is either the dot product of the diffuse surface of action 350 (equation (8)) with (Mp) i or the glossy surface of action 360 (equation (9)) (M_p)_ijAnd matrix vector multiplication. There are further actions 370 and 380 on the glossy surface, where the BRDF of O at p is convolved with the radiance vector obtained by multiplication 360 and evaluated in a view-dependent reflection direction R.
[0142]
For action 310, the rendering engine 140 loads a pre-calculated environment map, evaluates an analytical lighting model in software, or uses graphics hardware as a representation of incident lighting for the selected lighting environment. The radiance can be sampled. The rotation of action 320 is outlined in Section 1, “Spherical Harmonic Overview”, which is done once per object, not per point p. This rotation is done because the transmission is stored using a common coordinate system for O. If O is moving as a rigid body, it will align with O rather than rotate many transfer functions of O._piIt is more efficient to rotate several radiance samples in it.
[0143]
For a diffuse surface, a simple implementation of action 350 is to store a transfer vector for each vertex and do a dot product with a vertex shader. The transfer vector can be stored in a texture map instead of stored for each vertex and evaluated using a pixel shader. Since these coefficients are not always in the range [-1, 1], they are signed quantities, so the DirectX 8.1 pixel shader (V1.4) that provides a wider range [-8, 8] or those OpenGL corresponding to (extension by ATI) can be used. In one implementation, the pixel shader requires only 8 instructions to perform the dot product and L_pIs stored in the constant register.
[0144]
The color bleeding simulation in the colored environment or O is performed three times, and individual dot products are performed on the r, g, and b channels in each pass. In other cases, a single pass is sufficient.
[0145]
In the case of gloss self-transmission, the matrix transformation of equation (9) can be done in software because the transfer matrix may be too large to operate with either the current vertex shader or pixel shader. The result is (L ’_p)_iThat is, it becomes the SH coefficient of the transmitted radiance at the point p on O. And with pixel shader, G^*The convolution 370 can be performed using a simple cosine power (Phong lobe) kernel, and the result can be evaluated in the reflection direction R. This result is
[0146]
[Expression 37]

[0147]
Can be written. Current graphics hardware can evaluate up to 5th order SH projection.
[0148]
4.1 Spatial sampling of incident radiance field
A simple and useful approach to dynamically sample the incident radiance is to sample the incident radiance at the O center point. To deal with local lighting variations on O, more precise techniques sample incident lighting at multiple points. Given a desired number of points as input, an appropriate set of sample points can be obtained as a pre-process using an ICP (iterative nearest neighbor) algorithm (see, for example, Non-Patent Document 16). As a result, the points P that are uniformly distributed on O close to O where incident lighting can be sampled at the time of execution._iA representative set of is generated. Rendering engine 140 calculates each resulting spherical radiance sphere L_piPre-compute the coefficient at each point p on O that blends the contribution from_pAn incident radiance field on O can be obtained.
[0149]
FIG. 11 represents an image obtained from sampling incident radiance at a single point, ICP point, and multiple samples and rendering using the runtime procedure 300 of FIG.
[0150]
4.2 Sampling of SH radiance with graphics hardware
The graphics hardware uses radiance samples {L_Pi} Is useful. To do this, each P corresponding to the six surfaces of the spherical parameterization of the cube map._iTo render six images. O itself must be removed from the rendering. The cube map image is then projected onto its own SH coefficient using the integration of equation (1).
[0151]
From the viewpoint of efficiency, textures are calculated in advance for basis functions weighted by the difference solid angle evaluated for the parameterization of each s cube map.
[0152]
[Formula 38]

[0153]
. The resulting integral is then taken into L_pSample and texture of (s)
[0154]
[39]

[0155]
Is a simple dot product.
[0156]
This calculation is ideally done with graphics hardware. Or, since the inner product cannot be performed by the problem of accuracy and the hardware, the sampled radiance image may be read back and projected by software. In this case, it is useful to reduce the resolution of the read back image as much as possible.
[0157]
The low order SH projection can be calculated using a very low resolution cube map, assuming that it is properly bandlimited. For example, a spherical signal that has already been band-limited to the 6th order can be projected using a 64 × 4 image, by assuming a power unit signal (ie, a signal whose integral square on the sphere is 1). When the error is normalized, the mean case square error is about 0.3%, and the worst case square error is about 1%. (To be more precise, the average case error is the integrated squared difference of the reference signal and the reconstructed signal averaged over all unit-power signals. The worst case error is the same integral error. In a 6 × 8 × 8 map (which is the error for the worst case power unit signal), this error is reduced to 0.003% on average and 0.02% in the worst case. The disadvantage is that typical signals are not band limited to a sphere. According to another analysis, assuming continuous bilinear reconstruction of the sampled 2D image, the 6th order projection using 6 × 8 × 8 image has a mean case square error of 0.7%, The worst case error is 2%, and for a 6 × 16 × 16 image, the errors are 0.2% and 0.5%, respectively.
[0158]
An exemplary implementation extracts a 6 × 16 × 16 image from hardware. As is always the case with rendering with point sampling, the above analysis still uses bilinear reconstruction from point samples as a reference, so aliasing of 2D images is still a problem. To reduce aliasing, cube map images can be supersampled (eg, doubled) in each dimension, and box-filtered decimation can be performed in hardware before readout and projection. Similarly, basis function textures can also be supersampled and decimated as preprocessing. For radiance samples including readback and SH projection, this exemplary implementation takes about 1.16 ms on a PIII-933 PC with an ATI Radeon 8500.
[0159]
4.3 Self-transmission of volume model
The same framework is used for volume self-transmission data as for the surface. The resulting pre-computation model allows lighting to be changed at run time, resulting in accurate shadowing and interreflection in any low frequency lighting environment. FIG. 12 shows a self-transmission in volume with a variant for volume self-transmission (described below) of the runtime procedure 300 to capture how the cloud model shadows itself and scatters light. Represents an image of a cloud model using.
[0160]
Similar to surface transfer, the preprocessing step uses SH basis functions as radiators to simulate lighting on the volume. In the case of shadowed transmission without interreflection (ie direct shadowing), the simulator collects energy from the radiator to all voxels p of the volume that is attenuated by its path through the volume. Direction s_dThe numerical integration required for
[0161]
[Formula 40]

[0162]
Λ (p → q) is the integrated attenuation of the volume along the path from p to q, and D is the ray (p, s_d) Is the distance to leave the volume. In order to include interreflection, the simulation traverses every voxel p and generates a random direction s_dScatters its transmission forward along. Communication, rules
[0163]
[Expression 41]

[0164]
To exit the volume using_dIs placed in all voxels q. As more passes are made to the volume, more indirect rebounds are generated.
[0165]
Rendering is done in a conventional manner, i.e. by drawing slices through the 3D volume in back-to-front order using alpha blending that takes transparency into account. Each slice is a 2D image containing a sample of transfer vectors. The pixel shader calculates the dot product of the lighting coefficient and the transfer vector needed to shade each slice.
[0166]
5). Near-field transmission of radiance
In the neighborhood transmission, the influence of the object O on the environment adjacent to the parameterized low frequency lighting is calculated in advance. FIG. 13 blurs the uneven terrain near the hang glider, captured using the simulation 200 (FIG. 2) deformation for near transmission (described below) and the runtime rendering procedure 300 (FIG. 3). Shows a shadowed image. The simulation of propagation is the same as the simulation of self-transmission in Section 3, “Self-Transmission Precalculation”, but is performed on points in 3D space surrounding O, not on O. Arbitrary objects R can be placed in this volume at runtime to capture shadows, reflections, and caustics that are thrown onto R by O without knowing R in advance. For example, a moving vehicle O can cast a shadow on the ground R. Thrown shadows and lighting react to lighting changes. For example, if you move the light, the blurred shadow on R will move. This generalizes the irradiance volume by taking into account glossy transmission and enabling dynamic lighting (see, for example, Non-Patent Document 17).
[0167]
Since R is unknown in the precomputation step, the neighborhood volume of O stores a transfer matrix, not a vector. This is also true for diffusion objects since the normal of R is not known in advance.
[0168]
In one implementation, the simulator transmits a transfer matrix M at each point in a simple 3D grid around O._pIs calculated in advance. At runtime, the rendering engine performs the matrix transformation of equation (9) in software at each point in the volume and uploads the results to the graphics hardware. The result is the transmitted radiance (L '_p), And this is applied to R.
[0169]
The pixel shader then uses the transmitted radiance to light the object. The diffusing object is a hemisphere H that cosine weights the radiance using equation (6).^*And the resulting SH projection is evaluated with the R normal vector. A glossy object performs equation (12).
[0170]
An object for which self-transmission is calculated in advance has a problem that O and R do not share a common coordinate system. For this reason, a dense set of transmission samples of one of the two objects must be dynamically rotated and aligned with the other. Its complexity is O (n⁴), Which is the same as the complexity of performing the matrix transformation of Equation (9), but the higher-order projection rotation is considerably more burdensome than the operation. Hardware improvements will soon alleviate this problem.
[0171]
Compared to self-transmission, neighborhood transmission introduces some additional approximation errors. Shadows or light cast from a plurality of nearby transmission objects onto the same object are difficult to combine. Local lighting fluctuations not due to the presence of O or R are also a problem. That is, the lighting must be fairly constant across the neighborhood of O to provide accurate results. Specifically, when an object other than O and R enters the vicinity of O, an error such as lack of a desired shadow occurs. Also, the vicinity of O must be large enough to contain any shadow or light that O can cast on R. Nevertheless, proximity transmission captures effects that cannot be obtained in real time with conventional methods.
[0172]
6). Computing environment
FIG. 6 is a schematic example of a suitable computing environment 600 in which example embodiments may be implemented. Since the present invention can be implemented in various general purpose or special purpose computing environments, the computing environment 600 does not imply any limitation as to the scope of use or functionality of the invention.
[0173]
With reference to FIG. 6, the computing environment 600 includes at least one processing unit 610 and memory 620. In FIG. 6, this most basic configuration 630 is included within a dotted line. The processing unit 610 executes computer-executable instructions and may be an actual processor or a virtual processor. In a multi-processing system, a computer effective instruction is executed by a plurality of processing devices to increase processing power. Memory 620 may be volatile memory (eg, registers, cache, RAM), non-volatile memory (eg, ROM, EEPROM, flash memory, etc.), or some combination of the two. Memory 620 stores software 680 that implements graphic image rendering using radiance self-transmission.
[0174]
The computing environment can include other functions. For example, the computing environment 600 includes a storage 640, one or more input devices 650, one or more output devices 660, and one or more communication connections 670. An interconnection mechanism (not shown) such as a bus, controller, or network interconnects the components of the computing environment 600. Typically, operating system software (not shown) provides an operating environment for other software running on the computing environment 600 and coordinates the activities of the components of the computing environment 600. As noted above, the computing environment preferably includes DirectX and OpenGL function libraries, graphics processing hardware and software such as ATI Radeon and NVidia GeForce video cards.
[0175]
Storage 640 may be removable or non-removable and may be used to store magnetic disks, magnetic tapes or cassettes, CD-ROMs, CD-RWs, DVDs, or information and is accessible within computing environment 600. Including any other media. Storage 640 stores instructions for software 680 that implements the image rendering system (FIG. 1).
[0176]
Input device 650 may be a touch input device such as a keyboard, mouse, pen, trackball, voice input device, scanning device, or other device that provides input to computing environment 600. For audio, the input device 650 may be a sound card or a similar device that accepts analog or digital audio input. Output device 660 may be a display, printer, speaker, or other device that provides output from computing environment 600.
[0177]
Communication connection 670 allows communication with another computing entity over a communication medium. The communication medium propagates information such as computer-executed instructions, compressed audio or video information, or other data in a modulated data signal. A modulated data signal is a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media includes wired or wireless technology implemented using electrical, optical, RF, infrared, acoustic, or other carrier waves.
[0178]
The invention can be described in the general context of computer-readable media. Computer readable media can be any available media that can be accessed within a computing environment. By way of example, and not limitation, in computing environment 600, computer-readable media include memory 620, storage 640, communication media, and any combination of the above-described media.
[0179]
The invention may be described in the general context of computer-executable instructions contained in program modules and executed on a real or virtual target processor in a computing environment. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The functions of the program modules can be combined or divided among the program modules as required in various embodiments. Computer-executable instructions for program modules may be executed in local or distributed computing environments.
[0180]
For presentation purposes, this detailed description includes "determine", "get", "adjust", and "apply" to describe computer behavior within the computing environment. (Apply) ". These terms are high-level abstractions of actions performed by computers and should not be confused with actions performed by humans. The actual computer operations corresponding to these words vary depending on the implementation.
[0181]
While the principles of the invention have been described and illustrated with reference to exemplary embodiments, it will be appreciated that the exemplary embodiments can be modified in arrangement and detail without departing from the principles set forth above. Unless otherwise indicated, it is to be understood that the programs, processes, or methods described herein are not related or limited to any particular type of computing environment. Various types of general purpose or specialized computing environments can be used in conjunction with, or can perform, the operations according to the teachings described herein. Elements of the exemplary embodiment shown as software may be implemented in hardware and vice versa.
[0182]
In light of the many possible embodiments to which the principles of the present invention may be applied, all embodiments that fall within the scope and spirit of the following claims and their equivalents are claimed as the present invention.
[Brief description of the drawings]
FIG. 1 is a block diagram of a computer graphics software architecture that incorporates precomputed radiance self-transmission for real-time image rendering in a dynamic low frequency lighting environment.
FIG. 2 is a flow diagram of self-calculation precomputation in the image rendering system of FIG.
3 is a flow diagram of real-time rendering of radiance transfer in the image rendering system of FIG.
4 is a flow diagram for processing diffuse surface self-transmission at runtime in the real-time rendering of FIG.
5 is a flow diagram for processing glossy surface self-transmission at runtime in the real-time rendering of FIG.
FIG. 6 is a block diagram of a computing environment suitable for the image rendering system of FIG.
7 is a diagram showing mutual reflection simulated by the pre-computation of self-transmission in FIG. 2;
8 is a diagram of an image generated through the real-time rendering of FIG. 3 without shadowing.
9 is an image showing the effect of self-transmission on the diffusing surface generated through the real-time rendering of FIG. 3 with no shadowing.
10 is an image showing the effect of self-transmission of a glossy surface generated through the real-time rendering of FIG. 3 with no shadowing.
11 is a diagram of an image generated via the real-time rendering of FIG. 3, each sampling the incident radiance at a single point, an iterative nearest point algorithm (ICP) point, and multiple samples.
12 is an illustration of a volume self-transmission image generated via the real-time rendering of FIG. 3. FIG.
13 is a diagram of a neighborhood transmission image generated via the real-time rendering of FIG. 3. FIG.
[Explanation of symbols]
100 Computer graphic image rendering system
110 Geometric Object Model
130 Radiance self-transmission data
120 Global Illumination Simulator
140 Real-time image rendering engine
150 Lighting environment
160 view direction
170 User control
180 graphic display driver
600 computing environment
610 processor
620 memory
640 storage
650 input device
660 output device
670 Communication connection
680 software

Claims (65)

A computer-implemented method for rendering a computer graphic image of a geometrically modeled object comprising:
A radiation that represents the radiation response of the object including a global transfer effect on a linear combination of region-supporting lighting basis functions at the plurality of locations, simulating self-shadowing and interreflection at a plurality of locations on the modeled object Generating luminance transfer data; and
Evaluating the radiance transfer of the modeled object at the location for a view direction, which is a lighting environment, based on the radiance transfer data;
Generating an image of the modeled object shaded according to the radiance transfer assessment.   The method of claim 1, wherein the step of simulating includes simulating the modeled object illuminated in a reference low frequency lighting environment.   The method of claim 1, wherein the radiance transfer data represents a transfer of a source radiance of the modeled object at the location to an outgoing radiance.   The method of claim 1, wherein the radiance transfer data represents a transfer of a source radiance of the modeled object at the location to a transmitted incident radiance.   The method of claim 1, wherein the step of simulating lighting is performed as a pre-processing, and the step of evaluating and generating is performed in real time. Evaluating the radiance transfer comprises:
Calculating light source lighting data for at least one sampling point in a lighting environment;
A linear transformation is performed on the calculated light source lighting data in accordance with pre-calculated radiance transfer data for a plurality of positions on the surface of the modeled object to obtain exit radiance data from the position for a view. And the radiance transfer data includes representing a radiance response including a global propagation effect of the modeled object to source light at the location under a reference lighting environment. Item 2. The method according to Item 1. The radiance transfer data includes a radiance transfer vector representing a radiance response at a location on the diffusing surface of the modeled object, and evaluating the radiance transfer includes the diffusion of the modeled object. About the surface
Calculating a light source radiance vector for at least one sampling point in a lighting environment;
The method of claim 1 including calculating a dot product of the light source radiance vector and the radiance transfer vector. The radiance transfer data includes data representing a radiance response at a location on the glossy surface of the modeled object, and the step of evaluating the radiance transfer is for the glossy surface of the modeled object,
Calculating a light source radiance vector for at least one sampling point in a lighting environment;
Determining an exit radiance from the position for a view direction as a function of the light source radiance vector, the data representing the radiance response of the position, and a bidirectional reflection distribution function of the position. The method of claim 1, characterized in that: The radiance transfer data includes data representing a radiance response at a location on the glossy surface of the modeled object, and the step of evaluating the radiance transfer is for the glossy surface of the modeled object,
Calculating a light source radiance vector for at least one sampling point in a lighting environment;
Determining the transmitted radiance of the position based on the light source radiance vector and the data representing the radiance response of the position;
2. The method of claim 1, comprising determining an exit radiance from the position for a view direction based on the transmitted radiance and a bidirectional reflection distribution function of the position. The radiance transfer data includes a radiance transfer matrix that represents a radiance response at a location on the glossy surface of the modeled object, and evaluating the radiance transfer includes the gloss of the modeled object. About the surface
Calculating a light source radiance vector for at least one sampling point in a lighting environment;
Performing matrix vector multiplication of the light source radiance vector and the radiance transfer matrix;
The product of the matrix-vector multiplication includes convolving a bi-directional reflection distribution function of the location on the glossy surface of the modeled object and evaluating the result of the convolution for a view direction. The method of claim 1. A computer-implemented method for real-time rendering of a computer graphic image of a surface of a geometrically modeled object, comprising:
Calculating light source lighting data for at least one sampling point in a lighting environment;
Radiation radiance data from the position for a view direction that has been linearly transformed into the calculated light source lighting data according to pre-calculated radiance transfer data for a plurality of positions on the surface of the modeled object Wherein the radiance transfer data represents a radiance response including a radiance response including a global propagation effect of the modeled object to source light at the location under a reference lighting environment. Steps,
See containing and generating said shading according emitted radiance, images of the being the modeled for a view direction in the lighting environment object from said position,
Performing the linear transformation in the case of an extended surface of the modeled object is
Calculating a dot product of a source radiance vector and a pre-calculated radiance transfer vector, wherein the source radiance vector represents source light at a sampling point and the pre-calculated radiance The transfer vector represents the radiance response at a position on the diffusing surface of the modeled object,
Performing the linear transformation in the case of the glossy surface of the modeled object is
Performing a matrix vector multiplication of a source radiance vector representing source light at a sampling point and a pre-calculated radiance transfer matrix representing a radiance response at a position on the glossy surface of the modeled object; ,
Convolving a product of the matrix vector multiplication with a bi-directional reflection distribution function of the position on the glossy surface of the modeled object;
Evaluating the result of the convolution for a view direction;
Wherein the free Mukoto a. A computer-implemented method for real-time rendering of a computer graphic image of a diffusing surface of a geometrically modeled object comprising:
Projecting a radiance under a lighting environment onto a spherical harmonic basis to generate a lighting coefficient vector for at least one location of the modeled object;
Calculating the dot product of the lighting coefficient vector and a pre-calculated radiance transfer vector for at least one position on the diffusing surface, so that the diffusion of the modeled object for the lighting environment and view direction; Generating an exit radiance at the at least one location on a surface, wherein the pre-calculated radiance transfer vector is the at least one for source light under a reference low frequency lighting environment; Representing a radiance response including a global propagation effect of the diffusing surface at a location;
Calculating shading of the diffuse surface of the modeled object at the at least one location;
Applying the shading to generate an image of the diffusing surface of the modeled object. A computer-implemented method for real-time rendering of a computer graphic image of a glossy surface of a geometrically modeled object comprising:
Projecting radiance under a lighting environment onto a spherical harmonic basis to generate a lighting coefficient vector for at least one location of the modeled object;
Pre-calculated radiance transfer matrix data representing a radiance response including a global propagation effect of the glossy surface to source light at the at least one location under a reference low frequency lighting environment; Determining an exit radiance from the at least one position on the glossy surface for a view direction as a function of a bi-directional reflection distribution function of the at least one position;
Calculating a shading of the glossy surface of the modeled object at the at least one location;
Generating the glossy surface image of the modeled object with the shading. Determining the outgoing radiance for a view direction is
Matrix vector multiplication of the lighting coefficient vector and a pre-computed radiance transfer matrix for at least one location on the glossy surface is performed, the pre-computed radiance transfer matrix being a reference low Representing a radiance response including a global propagation effect of the glossy surface to source light at the at least one location in a frequency lighting environment;
Convolving the product of the matrix vector multiplication with a bi-directional reflection distribution function at the location on the glossy surface of the modeled object;
The method of claim 1 3, characterized in that it comprises a evaluating the results of the convolution said for a view direction. Determining the exit radiance for a view direction comprises:
Calculating the exit radiance based on a matrix vector multiplication of the lighting coefficient vector and a radiance transfer matrix pre-calculated for at least one position on the glossy surface, the pre-calculation The radiance transfer matrix determined includes representing a radiance response including a global transfer effect of the glossy surface to source light under the reference low frequency lighting environment at the at least one location. the method according to claim 1 3. A computer-implemented method for generating radiance self-transmitting data for use in real-time rendering and display of computer graphic images of modeled objects comprising:
Performing a global illumination simulation on the modeled object for a reference low frequency lighting environment expressed as a linear combination of region-supported lighting basis functions, the simulation comprising a plurality of sample points on the modeled object Calculating the radiance transfer of the model, wherein the simulation incorporates self-shadowing and interreflection of the modeled object;
For use in generating a graphical image of the modeled object by rendering radiance transfer over the modeled object, the global illumination simulation for the plurality of sample points, the area supporting lighting basis functions Recording as a linear transformation of the coefficients. The method of claim 16 , wherein the reference low frequency lighting environment is parameterized as a projection of a spherical harmonic basis of a spherical surface of incident light. Performing the global illumination simulation on the modeled object in multiple passes;
Simulating direct illumination of a plurality of sample points on the modeled object in a first shadowing pass, including self-shadowing of the modeled object, wherein the simulation of direct illumination is About sample points
Evaluating at the sample points a plurality of directions from the sample points in the hemisphere centered on the normal direction to the surface of the modeled object;
Tagging as occlusion occurs in a direction from the sample point that intersects the modeled object, and accumulating radiance transfer from direct illumination of the sample point in the plurality of directions, Generating radiance transfer data of:
Simulating the interreflective illumination of the plurality of sample points on the modeled object in a subsequent interreflective path, the simulated interreflective illumination comprising:
Accumulating radiance transfer from the inter-reflected illumination of the sample points in the plurality of directions tagged as causing occlusion to generate radiance transfer data for the sample points;
Repeating the interreflection path until the condition is met;
Summing the radiance transfer data accumulated in the first shadowing pass and the subsequent interreflection pass for a sample point to generate a total radiance transfer for the sample point. The method of claim 16 . The method of claim 16 , wherein the condition is that the total inter-reflection illumination energy of the current inter-reflection path is below a certain threshold level. The method of claim 16 , further comprising representing radiance transfer data of sampling points on the diffusing surface of the modeled object as a vector of spherical harmonic basis coefficients. The method of claim 16 , further comprising representing radiance transfer data of sampling points on the glossy surface of the modeled object as a matrix of spherical harmonic basis coefficients. A method for real-time rendering of a computer graphic image of a surface of a geometrically modeled object comprising:
In the pre-computation stage of radiance transmission performed on the first computer,
Performing a lighting simulation of the modeled object in a reference low frequency lighting environment to calculate a radiance transfer of a plurality of sample points on the modeled object, the simulation comprising the modeled object Incorporating steps of self-shadowing and interreflection,
Recording the calculated radiance transfer as a radiance transfer vector of spherical harmonic basis coefficients for sample points on the diffusing surface of the modeled object;
Recording the calculated radiance transfer as a radiance transfer matrix of spherical harmonic basis coefficients for sample points on the glossy surface of the modeled object;
Rendering an image of the modeled object in an image rendering stage performed in a second computer, the rendering step comprising:
Sampling light source light of the modeled object in a lighting environment at the time of rendering to obtain a light source radiance vector of spherical harmonic basis coefficients of the plurality of sample points on the modeled object;
Obtaining an exit radiance in the view direction that is a dot product of the light source radiance vector and the radiance transfer vector for sample points on the diffusing surface of the modeled object;
For sample points on the glossy surface of the modeled object, the outgoing radiance for a view direction based on the light source radiance vector, the radiance transfer matrix, and the bidirectional reflection distribution function of the glossy surface A step of seeking
And shading the modeled object at the plurality of sample points based on the emitted radiance of the plurality of sample points in the view direction individually. Determining an outgoing radiance for the view direction;
Multiplying the light source radiance vector by the radiance transfer matrix;
Evaluating the convolution of the glossy surface's bidirectional reflection distribution function to the product of the light source radiance vector and the radiance transfer matrix at the sample point for the view direction to obtain an exit radiance in the view direction the method of claim 2 2, characterized in that it comprises and. At the image rendering stage performed on the second computer,
Selecting a lighting environment for the rendering under user control;
The method of claim 2 2, characterized in that it further comprises a rendering further images of the modeled object for various lighting environments selected by the user control. At the image rendering stage performed on the second computer,
Changing the view direction under user control;
The method of claim 2 2, characterized in that it further comprises a rendering further images of the modeled object for various view direction is controlled by the user. A memory for storing a geometric model of the object;
Simulate self-shadowing and interreflection of lighting at multiple locations on the modeled object to represent the radiation response of the object, including global transfer effects on linear combinations of region-supported lighting basis functions at multiple locations An illumination simulator that generates radiance transfer data;
Based on the radiance transfer data, evaluate a radiance transfer at the plurality of locations of the modeled object in a lighting environment for a view, and image the modeled object shaded according to the radiance transfer evaluation. A real-time image rendering engine to generate,
A computer graphic image rendering system comprising: an image output device for presenting the image. 27. The computer graphic image rendering system of claim 26 , wherein the radiance transfer data represents a transfer of a source radiance of the modeled object to an outgoing radiance at the plurality of locations. 27. The computer graphic image rendering system of claim 26 , wherein the radiance transfer data represents a transfer of a source brightness of the modeled object to a transmitted light source radiance at the plurality of locations. A memory for storing a geometric model of the object;
An illumination simulator for calculating a radiance response to a reference low frequency lighting environment, including self-shadowing and interreflection by the object, parameterized with a spherical harmonic basis at a plurality of points on the surface of the object;
Calculate the light source radiance at the points parameterized by the spherical harmonic basis and process the transformation combining the light source radiance and the radiance response to the exit radiance from the points to a view A real-time image rendering engine that generates an image of the object that is shaded of the object at the plurality of points according to an individual exit radiance of the plurality of points to the view;
A computer graphic image rendering system comprising: an image output device for presenting the image. Multiple points on the surface of the object, including self-shadowing and interreflection by the object, simulated in a reference low-frequency lighting environment expressed as a linear combination of the object's geometric model and a region-supported lighting basis function A memory for storing radiance response data of
Calculating a light source radiance at the plurality of points, obtaining an outgoing radiance from the plurality of points for the view being processed for a transformation combining the light source radiance and a radiance response; A real-time image rendering engine that generates an image of the object shaded at the plurality of points according to the individual exit radiance of the point;
A real-time graphic rendering system comprising: an image output device for presenting the image. The real-time graphics rendering system according to claim 3 0 radiance response data, characterized in that it is parameterized by spherical harmonics basis. Real-time graphics rendering system according to claim 3 0 wherein the source radiance is characterized in that it is parameterized by spherical harmonics basis. Computer readable data carrying program code for processing data including a geometric model of the object and radiance self-transfer reactions of a plurality of points on the object, thereby rendering an image of the geometrically modeled object A carrier medium, wherein the program code is:
Program code means for calculating light source lighting at one or more sample points close to the object in a reference low frequency lighting environment expressed as a linear combination of region support lighting basis functions;
Computer readable data carrier comprising program code means for combining said light source lighting data and said radiance self-transmission response data to obtain exit radiance from said point on said object in a view direction Medium. The radiance self-transfer response data includes a radiance self-transfer response vector of a region-supported lighting basis for points on the diffusing surface of the object, and the program code further includes the point of the point on the diffusing surface of the object. And a program code means for obtaining the emitted radiance from the point on the object in the view direction by performing a dot product of a light source light vector and the radiance self-transfer reaction vector. the computer-readable data carrying medium according to claim 3 3. The computer-readable data carrying medium according to claim 3 4, characterized in that the region supporting lighting basis is a base of spherical harmonics. The radiance self-transfer response data includes a spherical harmonic-based radiance self-transfer response matrix for points on the glossy surface of the object, and the program code further includes the point of the points on the gloss surface of the object. Program code means for determining the exit radiance from the point on the object in a view direction based on a source light vector, the radiance self-transfer reaction matrix, and a bidirectional reflection distribution function. the computer-readable data carrying medium of claim 3 3, wherein. Obtaining the exit radiance;
Matrix vector multiplication of the light source light vector and the radiance self-transfer reaction matrix is performed, and a bidirectional reflection distribution function evaluated for the view direction is convolved with a product of the matrix vector multiplication, so that the view direction is changed. 37. The computer readable data bearing medium of claim 36 , comprising obtaining the exit radiance from the point on an object. Determining the exit radiance;
Convolving a product of the matrix vector multiplications with a bi-directional reflection distribution function evaluated for the view direction to obtain the exit radiance from the point on the object in the view direction, 38. The computer readable data carrier medium of claim 37 . The radiance self-transfer response data includes a radiance self-transfer response matrix, and the program code further performs matrix vector multiplication of the light source light vector and the radiance self-transfer response matrix to obtain a view direction. the computer-readable data carrying medium of claim 3 3, characterized in that it comprises program code means for determining the exit radiance from a point on the object. A computer-implemented method for evaluating an incident radiance field of the lighting environment for use in rendering and displaying a computer graphic image of a modeled object in a low frequency lighting environment, comprising:
Generating an image of light source radiance in a plurality of directions from a point in the lighting environment;
Transforming an image into a representation as a linear combination of region support lighting basis functions of the light source radiance field at the point of the lighting environment;
Shading the modeled object with the points using a lighting basis representation in rendering an image of the modeled object in the lighting environment;
Visually presenting the image of the modeled object in the lighting environment. The method of claim 4 0, characterized in that said lighting basis representation is spherical harmonics basis representation. Method of capturing radiance samples for use in rendering and displaying computer graphic images of modeled objects in a dynamic scene using graphics hardware on a computer using the lighting environment in the dynamic scene Because
Storing a pre-computed set of texture images representing region support lighting basis functions;
Rendering, with the graphics hardware, a set of images from sample points in the dynamic scene, wherein the images represent source light from the lighting environment of the dynamic scene;
Projecting light source radiance at the sample points as a function of a set of source light images and the pre-calculated texture image set at the graphics hardware, and the source radiance at the sample points is the region support lighting. Getting to the base,
Shading the modeled object at the points using the light source radiance of the sample points in rendering an image of the modeled object in the lighting environment;
Visually presenting the image of the modeled object in the lighting environment. The pre-computed texture image A method according to claim 4 2, characterized in that represent a set of basis functions of spherical harmonic (SH). Wherein the set of basis functions of spherical harmonics method of claim 4 3, the difference solid angle weighted, characterized in that it is evaluated through the cube map spherical parameterization of the angle. The method according to claim 4 2, wherein the rendered image, characterized in that corresponding to the face of the cube map sphere parameters of the light source light from the low-frequency lighting environment of the dynamic scene. Method of capturing radiance samples for use in rendering and displaying computer graphic images of modeled objects in a dynamic scene using graphics hardware on a computer using the lighting environment in the dynamic scene Because
Storing a set of texture images pre-computed for a set of spherical harmonic (SH) basis functions weighted by a difference solid angle and evaluated via a cube map spherical parameterization of said angle;
Rendering a set of images from sample points in the dynamic scene with the graphics hardware, wherein the image is a cube map spherical parameterization surface of source light from the low frequency lighting environment of the dynamic scene Steps corresponding to
The graphic hardware projects the light radiance of the sample point to a spherical harmonic function coefficient as a dot product of the set of light source light images and the set of SH basis function texture images, and emits light source at the sample points. Obtaining luminance on the SH basis;
Shading the modeled object at the point using the light radiance of the SH basis at the sample point in rendering an image of the modeled object in the lighting environment;
Visually presenting the image of the modeled object of the lighting environment. The method of claim 46 , further comprising repeating rendering and projecting operations for a plurality of spatially different sample points in the dynamic scene. 47. The method of claim 46 , further comprising supersampling and box filter decimation of the source light image prior to projection to SH coefficients, thereby reducing aliasing. The method of claim 46 , further comprising supersampling and box filter decimation of the SH basis function texture image prior to projection onto SH coefficients. A computer system for graphic rendering,
Memory storing a set of texture images pre-computed for a set of basis functions of spherical harmonics (SH) weighted by a difference solid angle and evaluated via a cube map spherical parameterization of said angle;
A graphics processing board that operates to render a set of images from sample points in a dynamic scene having a lighting environment, the image being a cube-map sphere of light source light from the lighting environment of the dynamic scene Corresponding to the parameterization surface, and further, as a dot product of the set of the light source light image and the set of the SH basis function texture image, the light source radiance at the sample point is projected onto a spherical harmonic function coefficient to A graphics processing board that operates to obtain the light source radiance at the SH base;
Real-time image rendering that operates to shade the modeled object at the point using the light source radiance of the SH basis at the sample point when rendering an image of the modeled object in the lighting environment A system processor running the engine;
A system comprising: an image output device that presents the image. Uses computer graphics hardware to carry program code that captures radiance samples used to render and display computer graphic images of modeled objects in a dynamic scene using a lighting environment in the scene A computer-readable data carrier medium, wherein the program code is
Let the graphics hardware render a set of images from sample points in the dynamic scene, the image corresponding to the cube map spherical parameterization surface of the source light from the low frequency lighting environment of the dynamic scene Program code means to
The graphic hardware was pre-computed for a set of source light images and a set of spherical harmonic (SH) basis functions weighted by the difference solid angle and evaluated via cube map spherical parameterization of the angles. Program code means for projecting the incident radiance at the sample point onto a spherical harmonic function coefficient as a dot product with a set of SH basis function texture images to obtain the incident radiance of the sample point on the SH basis;
Program code means for shading the modeled object at the point using the incident radiance of the SH basis at the sample point when rendering an image of the modeled object in the lighting environment;
A computer readable data bearing medium comprising program code means for visually presenting the image of the modeled object in the writing environment. A computer-implemented method for generating radiance self-transmitted data for use in real-time rendering and display of a computer graphic image of a volume model comprising:
Simulate lighting self-shadowing and interreflection on illuminated volumes to produce radiance responses including global transfer effects for linear combinations of region-supported lighting basis functions for multiple volume elements of the volume model Generating radiance transfer data representing;
Evaluating radiance transfer of the plurality of volume elements in a lighting environment for a view based on the radiance transfer data;
Generating an image of the volume model shaded according to the evaluation of the radiance transfer. A computer-implemented method for generating radiance self-transmitted data for use in real-time rendering and display of a computer graphic image of a volume model comprising:
Performing global illumination simulation on the volume for a reference low frequency lighting environment expressed as a linear combination of region-supported lighting basis functions, the simulation calculating radiance transfer for a plurality of volume elements of the volume model; The simulation incorporates self-shadowing and interreflection of the volume model;
A global illumination simulation for the plurality of volume elements is recorded as a linear transformation of the basis function coefficients for use in rendering a radiance transfer on the volume model to generate a graphic image of the volume model. A method comprising the steps of: The method of claim 3, characterized in that parameterizing the reference low-frequency lighting environment as a projection of spherical harmonics basis of the spherical surface of the source light. Performing the global illumination simulation on the volume model in multiple passes;
Simulating direct illumination of a plurality of volume elements of the volume model in the reference low frequency lighting environment including attenuation along a path through the volume model in a first shadowing path;
Simulating the interreflective illumination of the volume element of the volume model by other volume elements of the volume model including attenuation through the volume model in a subsequent interreflection path;
Repeating the interreflection path until the condition is met;
Summing the radiance transfer data accumulated in the first shadowing pass and the subsequent interreflection pass for a sample point to generate a total radiance transfer at the sample point. the method according to claim 3. A computer graphic image rendering system for real-time rendering of a computer graphic image of a volume model,
Memory to store the volume model;
Simulating lighting self-shadowing and inter-reflection on a plurality of volume elements of the volume model illuminated in a reference lighting environment, so that the radiance from the light source light to the emitted light of the volume elements of the volume model An illumination simulator that generates data representing the transmission,
Based on the radiance transfer data, evaluate the radiance transfer with the volume element of the volume model in a second lighting environment for a view direction, and generate an image of the volume model shaded according to the evaluation of the radiance transfer A real-time image rendering engine to
A system comprising: an image output device that presents the image. A computer-readable program-carrying medium carrying a program, wherein the program can be executed by a computer to perform a method for generating radiance self-transmitted data for use in real-time rendering and display of a computer graphic image of a volume model The method
Performing a global illumination simulation on the volume for a reference low frequency lighting environment parameterized as a projection of the spherical harmonic basis of the spherical surface of the source light, the projection having a spherical harmonic coefficient, the simulation comprising: Calculating radiance transfer of a plurality of volume elements of the volume model, wherein the simulation incorporates self-shadowing and interreflection of the volume model;
The global illumination simulation for the plurality of volume elements is linearly transformed to the spherical harmonic function coefficients of the source light for use in rendering a radiance transfer on the volume model to generate a graphic image of the volume model. And recording as a medium. The method further includes:
Performing the global illumination simulation on the volume model in multiple passes;
Simulating direct illumination of a plurality of volume elements of the volume model in the reference low frequency lighting environment including attenuation along a path through the volume model in a first shadowing path;
Simulating the interreflective illumination of the volume element of the volume model by other volume elements of the volume model including attenuation through the volume model in a subsequent interreflection path;
Repeating the interreflection path until the condition is met;
Summing the radiance transfer data accumulated in the first shadowing pass and the subsequent interreflection pass for a sample point to generate a total radiance transfer for the sample point. 58. The medium of claim 57 . A computer-readable program-carrying medium carrying a program, wherein the program can be executed by a computer to perform a method of real-time rendering of a computer graphic image of a volume model, the method comprising:
Calculating light source lighting data for at least one sampling point in a lighting environment;
According to radiance transfer data calculated in advance for a plurality of volume elements of the volume model, linear conversion is performed on the calculated light source lighting data to obtain emission radiance data from the volume element for a certain view direction. The radiance transfer data represents a radiance response including a global transfer effect on a linear combination of area support lighting basis functions of the volume elements of the volume model; and
Generating the image of the modeled object for the view in the lighting environment, shaded according to the exit radiance from the location. The method further includes:
As a pre-calculation, performing a global illumination simulation on the volume for a reference low frequency lighting environment parameterized as a projection of a spherical harmonic basis of a spherical surface of the source light, the projection having a spherical harmonic coefficient The simulation calculates radiance transfer of a plurality of volume elements of the volume model, the simulation taking into account the self-shadowing and interreflection of the volume model;
Wherein the plurality of the global illumination simulation for the volume elements recorded as linear transformation coefficients of the spherical harmonic of the source light, to claim 59, characterized in that it comprises the steps of forming the radiance transfer data The computer-readable program carrier medium described. The method further includes:
Performing the global illumination simulation on the volume model in multiple passes;
Simulating direct illumination of a plurality of volume elements of the volume model in the reference low frequency lighting environment including attenuation along a path through the volume model in a first shadowing path;
Simulating the interreflective illumination of the volume element of the volume model by other volume elements of the volume model including attenuation through the volume model in a subsequent interreflection path;
Repeating the interreflection path until the condition is met;
Summing the radiance transfer data accumulated in the first shadowing pass and the subsequent interreflection pass for a sample point to generate a total radiance transfer for the sample point. computer readable program carrying medium of claim 6 0. A computer graphic image rendering system for real-time rendering of a computer graphic image of a modeled object in a scene containing modeled objects,
A memory for storing the object and a model of the object;
Simulating lighting self-shadowing and interreflection for a plurality of sample points in the near space around the modeled object illuminated in a reference lighting environment, and the plurality of samples from the modeled object An illumination simulator for generating data representing radiance transmission from the light source light to the transfer incident light for the sample point;
Based on the radiance transfer data, a radiance transfer from the modeled object to the modeled object in a second lighting environment for a view is evaluated at the plurality of sample points, and the radiance transfer of A real-time image rendering engine for generating an image of the modeled object shaded according to the evaluation;
A system comprising: an image output device that presents the image. The program to program a computer to perform a method of generating a radiance Doden who data used for real-time rendering and display of modeled objects computer graphic image in the scene from the modeled object in the scene A computer readable program carrying medium for carrying, the method comprising:
Performing a global illumination simulation on the modeled object in a reference low frequency lighting environment represented as a linear combination of basis functions, the simulation comprising a plurality of sample points in a close space around the modeled object Calculating the radiance transfer of the self-shadowing and interreflection reflected from the modeled object to the plurality of sample points;
The global illumination simulation for the plurality of sample points is recorded as a linear transformation of the basis function coefficients for use in rendering a radiance transfer on the volume model to generate a graphic image of the volume model. And a computer-readable program carrying medium. The method
Performing the global illumination simulation on the modeled object in multiple passes;
The plurality of sample points in the near space around the modeled object in the reference low frequency lighting environment, including a shadowing of the plurality of sample points from the modeled object in a first shadowing pass Simulating direct lighting of
Simulating reflected illumination of the plurality of sample points in the near space around the modeled object from the modeled object in a subsequent interreflection path;
Repeating the interreflection path until the condition is met;
Summing the radiance transfer data accumulated in the first shadowing pass and the subsequent interreflection pass for a sample point to generate a total radiance transfer for the sample point. 64. A computer-readable program carrying medium according to claim 63 . The global illumination simulation record of the plurality of sample points as a linear transformation is in the form of a transfer matrix for a plurality of points in a three-dimensional grid centered on the modeled object. 64. A computer-readable program carrying medium according to 64 .

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