JP4155425B2 - Skeleton model intermediate frame shape derivation method, skeleton model shape deformation method, image generation apparatus, and information storage medium - Google Patents

Description

また添え字の順序と符号との関係は以下の通りである。
【００９３】
【数２】

４.１ 基本式
図１５において、ノードＮ_iの座標を（ｘ_i、ｙ_i、ｚ_i）とする。またアークには、３次元空間内での回転を表すために、アーク法線ベクトルを設ける。アークＡ_ij（ノードＮ_i、ノードＮ_jを結ぶアーク）の法線ベクトルをｎ_ij（ｕ_ij、ｖ_ij、ｗ_ij）とする。本実施形態では、これらの基本変数を用いてスケルトンモデルの形状を表す。アークごとに次の基本式が成り立つ。
【００９４】
【数３】

式(1)は、アークＡ_ijの長さがＬ_ijであることを意味する。式(2)は、法線ベクトルの大きさが1であることを意味する。式(3)は、アーク法線ベクトルとアークが垂直であることを意味する。
【００９５】
４.２ 基本式の解法
式(1)(2)(3)は非線形方程式であり、また式の数が変数の数より少ない。そこで、ニュートン法とラグランジュの乗数法を組み合わせて解くことにする。
【００９６】
なお、特に指示する必要のない場合は、変数の添え字を省略して表記する。
【００９７】
４.２.１ ニュートン法の適用
ループ１回ごとの各変数の変化量を、次のように定義する。
【００９８】
【数４】

上記の基本式(1)にニュートン法を適用すると、次式が得られる。
【００９９】
【数５】

これを整理すると、次式になる。
【０１００】
【数６】

ｌ_ijはアーク長さの現在値で、次式で表される。計算が収束した状態では、ｌ_ij＝Ｌ_ijとなる。
【０１０１】
【数７】

また、λはスケールファクターである。λの値としては、次式のようにアーク長Ｌ_ijの平均値を用いることにする。なおＮ_arcは、スケルトンを構成するアークの本数である。
【０１０２】
【数８】

式(2),(3)及び変数ｕ，ｖ，ｗについては、解くべき方程式の未知数を減らすために、ニュートン法を使わず、以下に述べる１変数ρによる１次近似を用いる。
【０１０３】
４.２.２ アーク法線ベクトル変化量の１次近似
アーク法線ベクトルｎ_ijはアークＡ_ijに垂直で、大きさ１であるため、成分ｕ_ij、ｖ_ij、ｗ_ijは、３変数でありながら、図１４（Ａ）に示すように変化の自由度は１である。そこで、解くべき方程式の未知数を減らすために、１変数による１次近似を行う。
【０１０４】
図１５に示すように、アークの始点ノードＮ_iから終点ノードＮ_jに向かう単位ベクトルを、アーク方向ベクトルａ_ijと定義する。また、同図に示すようにアークＡ_ij上にベクトルｓ_ijを作る。
【０１０５】
【数９】

式(2),(3)を微分して整理すると、次式のように、ｎ_ij（ｕ_ij，ｖ_ij，ｗ_ij） の変化量Δｎ_ij（Δｕ_ij，Δｖ_ij，Δｗ_ij）を、新たに導入した未知変数ρ_ijの１次式として近似できる。
【０１０６】
【数１０】

ｎ_ijが、次のイベントサイクルでとる値をｎ′_ijとする。ｎ′_ijは、本来アークＡ_ijに垂直で大きさ１となるべきであるが、変化量の２乗のオーダーで誤差を生じてしまう。そこで、次式のように、まず方向を修正し、更に大きさを１に修正したものをｎ′_ijとする。ただし、ａ′_ijは、ａ_ijが次のイベントサイクルでとる値である。
【０１０７】
【数１１】

４.２.３ ラグランジュの乗数法の適用
式(6)は、式の数が変数の数より少なく、また変数ρを含まないので、これだけではスケルトンモデルの変形を一意的に定めることはできない。そこで、ρを含む評価式を用意し、この式を極小化するという条件のもとで、ラグランジュの乗数法を適用して解を求める。評価式は、式Ｕ₁，Ｕ₂，Ｕ₃，… の総和Ｕ_eとして構成する。未定乗数α_ijを導入し、次式のようにＵを定義する。
【０１０８】
【数１２】

式(6)と次式(14)を連立させて、これを解くことにより、解ξ，η，ζ，ρを得る。
【０１０９】
【数１３】

得られた解に基づき、次式によりｘ，ｙ，ｚの新しい値ｘ′，ｙ′，ｚ′を求め、ノードの座標が決まる。
【０１１０】
【数１４】

そして式(11), (12)によりｎ（ｕ，ｖ，ｗ）の新しい値ｎ′（ｕ′，ｖ′，ｗ′）を求め、アーク法線ベクトルが決まる。
【０１１１】
４.３ アークの方向固定
４.３.１ アークの方向固定の意味
アークの方向を固定した場合、そのアークは次のような拘束を受けるものとする。
【０１１２】
即ち、両端のノードが固定されていない場合には、平行移動のみが可能になる（アーク法線ベクトルの向きも変化できない）。一方、両端のノードのうち少なくとも一方が固定されている場合には、移動も回転もできない（完全固定状態）。
【０１１３】
４.３.２ Trans group
隣接する複数のアークが方向固定されており、これらのアークが移動する場合には、これらのアークは一体となって平行移動することになる。このような１本以上のアーク（あるいは２個以上のノード）のグループをtrans groupと呼ぶことにする。
【０１１４】
trans groupの中のノードの１つを代表ノードとすると、trans groupの中の代表ノード以外のノードの移動量は、代表ノードの移動量と等しくなる。
【０１１５】
方向固定されたアークについては、式(1)、(6)は不要となり、変数ρも消え去る。trans groupの中の代表ノード以外のノードについては、式(14)から変数ξ，η，ζが消え去る。このように変数の数が減ることで、計算負荷を軽くすることができる。
【０１１６】
４.４ 評価式の作成
前述のように、ラグランジュの乗数法を適用するには、極小化すべき評価式を用意する必要がある。評価式としては、図１４（Ｂ）で説明したように、アーク間角度の変化量、ノード座標の変化量、ノード座標の速度変化量等を含む種々の評価式を考えることができる。これらの評価式の詳細については特開平10-208072に開示されている。
【０１１７】
４.４.１ ラバーバンドの設定
ラバーバンドは、収縮しようとする性質を持った仮想的なアークである。ここで、ラバーバンドの一端を（ｘ_i，ｙ_i，ｚ_i）とし、他端を（ｘ_ci，ｙ_ci，ｚ_ci）とする。特開平10-208072に開示されるように、このラバーバンドを用いて、ユーザーは、スケルトンモデルを所望の形状に変形できる。この場合に、ラバーバンドの一端（ｘ_i，ｙ_i，ｚ_i）は、ユーザーがマウス等でピックしたノードＮ_iになり、他端（ｘ_ci，ｙ_ci，ｚ_ci）は、ユーザーのマウスの動きに合わせて移動する。
【０１１８】
また、このラバーバンドは、前述のようにノードpullerにも利用できる。この場合には、一端（ｘ_i，ｙ_i，ｚ_i）は、パスカーブ指定されたノードＮ_iになり、他端（ｘ_ci，ｙ_ci，ｚ_ci）は、制御点（パスカーブ上の所与の位置）になる。
【０１１９】
式(13)の評価式Ｕ_eに、次式Ｕ₂を加えることで、ラバーバンドの収縮性を表現できる。Ｗ_rは、ラバーバンドの収縮性（張力）の強さを表すウェイト値（重み係数）である。
【０１２０】
【数１５】

Ｕ_2iの偏微分は以下のようになる。
【０１２１】
【数１６】

４.４.２ ラバーバンドのウェイト値の適応可変
ラバーバンドの張力が強くなると暴れが発生する傾向がある。そこで、ラバーバンドのウェイト値Ｗ_rを、スケルトンモデルの状態に応じて可変にする。この際、単にウェイト値に上限を設けるだけでは不十分であり、次の場合を考慮する必要がある。
【０１２２】
第１に、複数のノードをピックし、同一方向に引っ張った場合には、個々のラバーバンドの張力は小さくても、全ラバーバンドの張力の総和は大きくなってしまう（図１０（Ａ）参照）。
【０１２３】
第２に、複数のノードを異なる方向に引っ張った場合には、単純にラバーバンドの張力に上限を設けたのでは、次のような不具合が生じる。即ち、ラバーバンドが伸びた状態でスケルトンモデルの形状が収束した場合に、釣り合い状態が一意的に定まらない場合が生じる。例えば図１６（Ａ）のように、１本のアークを左右に引っ張ったとする。ここで、ラバーバンド１２０、１２２のリミット長をｌ_r ^*とすると、図１６（Ｂ）、（Ｃ）、（Ｄ）は全て釣り合い状態となる。図１６（Ｂ）、（Ｃ）、（Ｄ）では、ラバーバンド１２０、１２２の長さは全てｌ_r ^*以上になっており、ラバーバンド１２０、１２２の張力が全て等しく上限値になっているからである。
【０１２４】
そこでラバーバンドのウェイト値Ｗ_rを、次式に示すように、ラバーバンドの長さｌ_riの総和の逆数に比例した値にする。
【０１２５】
【数１７】

但し、ラバーバンド長の総和が小さいときに、ウェイト値Ｗ_rが大きくなりすぎないように、Ｗ_rには上限値Ｗ_r ^*を設定しておく。
【０１２６】
Ｗ_rを式(19)のように可変制御することで、複数のノードと複数の制御点との間に働くラバーバンドの張力の総和が所与の値以下になるような条件の下で、スケルトンモデルの形状を変形できるようになる。また、各ラバーバンドの張力には固有の上限値が設けられていなく、式(17)のように、ラバーバンドの張力は、パスカーブが指定されたノードＮ_i（ｘ_i，ｙ_i，ｚ_i）と、制御点（ｘ_ci，ｙ_ci，ｚ_ci）との距離に応じて変化する。従って、図１６（Ｂ）、（Ｃ）、（Ｄ）のような釣り合い状態が一意的に定まらないという事態を回避できるようになる。
【０１２７】
４.４.３ ノードpuller
ノードpullerは、４.４.１、４.４.２節で説明したラバーバンドを利用して実現する。ノードpullerを作用させて収束計算を行うことで、ノードpullerによるスケルトンモデルの変形を実現できる。
【０１２８】
４.４.４ AV puller
AV pullerを作用させた際に、各アークのアーク方向ベクトルと中割りアーク方向ベクトルとの向きの差の２乗和が極小になるよう、スケルトンモデルを変形させる。式(13)の評価式Ｕ_eに、次式Ｕ_Aを加えて収束計算を行うことで、この変形を実現できる。
【０１２９】
【数１８】

ここでＷ_Aは、AV pullerの強さを表すウェイト値（重み係数）である。図１７に示すように、アークＡ_ijのアーク方向ベクトルａ_ijと中割りアーク方向ベクトルａ_pijとのなす角をθ_pijとする。また、θ_pijの変化量を次式のようにφ_pijとする。
【０１３０】
【数１９】

φ_pijを、ξ，η，ζの１次近似式で表すことにする。まず、次式が成り立つ。
【０１３１】
【数２０】

上式を、φ_pijの２次以上の項を無視して変形すると、次式が得られる。
【０１３２】
【数２１】

図１７に示すように、ａ_ijとａ_pijが作る平面内でａ_ijに垂直な単位ベクトルａ_qijを作る。
【０１３３】
【数２２】

式(26)を式(27)等を用いて変形し、ξ_i，ξ_j，η_i，η_j，ζ_i，ζ_j，ρ_ijによるＵ_Aijの偏微分を求めると、次式のようになる。
【０１３４】
【数２３】

以上の方法では、θ_pij＝０の場合に、ベクトルａ_qijが不定となり計算不能となる。そこで、θ_pij＜＜１の場合は、次式を用いる。
【０１３５】
【数２４】

式(30)を変形し、ξ_i，ξ_j，η_i，η_j，ζ_i，ζ_j，ρ_ijによるＵ_Aijの偏微分を求めると、下式のようになる。
【０１３６】
【数２５】

４.４.５ NV puller
NV pullerを作用させた際に、各アークのアーク法線ベクトルと中割りアーク法線ベクトルとの向きの差の２乗和が極小になるよう、スケルトンモデルを変形させる。式(13)の評価式Ｕ_eに次式Ｕ_Nを加えることで、これを実現できる。
【０１３７】
【数２６】

Ｗ_Nは、NV pullerの強さを表すウェイト値（重み係数）である。また、アークＡ_ijの法線ベクトルｎ_ij（ｕ_ij，ｖ_ij，ｗ_ij）に対する中割りアーク法線ベクトルをｎ_pij（ｕ_pij，ｖ_pij，ｗ_pij）とする。
【０１３８】
ξ_i，ξ_j，η_i，η_j，ζ_i，ζ_j，ρ_ijによるＵ_Nijの偏微分を求めると、次式のようになる。
【０１３９】
【数２７】

５．画像生成装置、情報記憶媒体
図１８（Ａ）、（Ｂ）、（Ｃ）に、本実施形態のスケルトンモデルの中間フレーム形状導出方法、形状変形方法を利用した画像生成装置、情報記憶媒体の種々の実施形態を示す。
【０１４０】
図１８（Ａ）は、画像生成装置の１つである形状データ作成ツールに本実施形態を適用した例である。スケルトンモデルのキーフレームの形状の作成のための指示、パスカーブの指定等は、例えばキーボード２００、ポインティングデバイスであるマウス２０２を用いて行われる。処理部２１０は、本実施形態の方法によりスケルトンモデルの形状変形を行い形状データを生成する形状データ生成部２１２と、この形状データ生成部２１２で生成された形状データに基づいてスケルトンモデルの画像を合成する画像生成部２１４とを含む。処理部２１０は、ハードウェア的には、ＣＰＵ、ＤＳＰ、メモリ、必要であれば画像生成用のＡＳＩＣ等により構成される。ＦＤ、ＣＤ、ＤＶＤ、ＩＣカード、メモリ等で構成される情報記憶媒体２１６には、本実施形態の方法を実現する形状データ作成プログラム、このプログラムの実行のために必要なデータ等の種々の情報が格納されている。処理部２１０は、キーボード２００、マウス２０２からの入力情報、情報記憶媒体２１６に格納される情報に基づいて処理を行い、これにより表示部２１８上にスケルトンモデル画像２１９等が表示される。この形状データ作成ツールによれば、表示されるスケルトンモデル画像２１９の形状を確認しながら、形状データの作成を行うことができ、設計作業の効率化を図れる。
【０１４１】
図１８（Ｂ）は、画像生成装置の１つであるゲーム装置に本実施形態を適用した例である。ゲームコントローラ２２０、２２２は、プレーヤが操作情報を入力するためのものである。処理部２３０は、プレーヤからの操作情報に基づいてゲーム画像を合成するための演算等を行うゲーム演算部２３２と、このゲーム演算部２３２からの演算結果に基づいて画像生成を行う画像生成部２３４とを含み、ハードウェア的には、ＣＰＵ、ＤＳＰ、メモリ、必要であれば画像生成用のＡＳＩＣ等により構成される。情報記憶媒体２３６には、本実施形態の方法により作成された形状データ或いはこの形状データに基づき生成された種々の情報、及びゲームプログラム等が格納されている。表示部２３８上には、上記形状データ等に基づいて動作するゲームキャラクタの画像２３９、２４０等が表示される。ゲーム装置が業務用のものであれば、形状データ、ゲームプログラムは、半導体メモリ、ハードディスク等から成る情報記憶媒体に格納され、ゲーム装置が家庭用のものであれば、形状データ、ゲームプログラムは、ＣＤ、ＤＶＤ、ゲームカセット等から成る情報記憶媒体に格納される。また複数の端末をホスト装置を介して通信回線で接続し、ゲームプログラム等を配給するタイプのゲーム装置においては、形状データ、ゲームプログラムはホスト装置の情報記憶媒体、例えば磁気ディスク、ＣＤ、ＤＶＤ、半導体メモリ等に格納される。
【０１４２】
一方、図１８（Ｃ）は、ゲーム演算部２４２が形状データ生成部２４３を含む場合のゲーム装置の例である。この場合、情報記憶媒体２４６には、形状データの代わりに、本実施形態の方法を実現する形状データ生成プログラムが格納され、形状データの生成はゲーム装置に内蔵される形状データ生成部２４３がリアルタイムに行う。例えばゲームコントローラ２２０、２２２等によりプレーヤが、スケルトンモデルに所望の動作を行わせる。これによりスケルトンモデルに付随して動くオブジェクトの画像２３９、２４０が表示部２３８に表示されることになる。
【０１４３】
なお本発明は上記実施形態で説明したものに限らず、種々の変形実施が可能である。
【０１４４】
例えば本実施形態では、ノードpullerによる変形の後にAV pullerによる変形を行う場合について説明したが、本発明では、AV pullerによる変形の後にノードpullerによる変形を行うようにしてもよい。例えば、指定ノードがパスカーブ上を通ることよりも、アークが指定方向に向くことを優先する場合には、AV pullerによる変形の後にノードpullerによる変形を行うことが望ましい。この場合には、４.３節で説明したアークの方向固定の手法により、アークの向く方向を固定することになる。
【０１４５】
また、ノードpuller、AV puller、NV pullerによる変形は、図１３（Ａ）〜図１３（Ｄ）で説明した手法（基本式や評価式を所与の情報に基づき変化させながら基本変数の解を求める手法）により実現することが特に望ましい。しかしながら、本発明はこれに限定されず、これらの変形を、別の手法により実現するようにしてもよい。
【０１４６】
また、２.４節で説明したラバーバンドの張力の適応可変の手法は、ノードpullerにおけるラバーバンドのみならず、スケルトンモデルの変形に使用する種々のラバーバンドに対して広く適用できる。例えば特開平10-208072に開示されるような、ユーザのマウス操作によるスケルトンモデルの変形の際に使用するラバーバンドに対しても、ラバーバンドの張力の適応可変の手法は適用できる。
【０１４７】
また、第１の変形ステップの反復計算での初期段階において、第２の変形ステップの第２の条件が加味された演算を行う手法の適用例は、ノードpullerによる変形の初期段階にAV pullerを作用させる適用例（図１２参照）に限定されるものではない。例えば、AV pullerによる変形の初期段階にノードpullerを作用させる適用例など、種々の適用例を考えることができる。
【０１４８】
【図面の簡単な説明】
【図１】図１（Ａ）、（Ｂ）、（Ｃ）は、キャラクタのモーション作成の手順について説明するための図である。
【図２】図２（Ａ）、（Ｂ）は、パスカーブ指定や中間フレームの形状導出について説明するための図である。
【図３】図３（Ａ）、（Ｂ）は、本実施形態の比較例について説明するための図である。
【図４】本実施形態の処理について説明するためのＰＡＤである。
【図５】中割りアーク方向ベクトルの導出について説明するための図である。
【図６】ノードpullerによる変形について説明するための図である。
【図７】 AV pullerによる変形について説明するための図である。
【図８】図８（Ａ）、（Ｂ）は、中割りアーク法線ベクトルの導出について説明するための図である。
【図９】図９（Ａ）、（Ｂ）は、ノードpullerとしてラバーバンドを用いる手法について説明するための図である。
【図１０】図１０（Ａ）、（Ｂ）、（Ｃ）、（Ｄ）は、ラバーバンドの張力の適応可変について説明するための図である。
【図１１】図１１（Ａ）、（Ｂ）、（Ｃ）は、ノードpullerを作用させて行う反復計算の初期段階において、AV pullerを作用させる手法について説明するための図である。
【図１２】ノードpullerを作用させて行う反復計算の初期段階において、AV pullerを作用させる手法について説明するためのＰＡＤである。
【図１３】図１３（Ａ）、（Ｂ）、（Ｃ）、（Ｄ）は、基本式や評価式を所与の情報に基づき変化させながら基本変数の解を求める手法について説明するための図である。
【図１４】図１４（Ａ）は、アーク法線ベクトルの変化量を１変数で表す手法について説明するための図であり、図１４（Ｂ）は、評価式の種々の例を示す図である。
【図１５】アーク、ノード、アーク法線ベクトル等の関係について説明するための図である。
【図１６】図１６（Ａ）、（Ｂ）、（Ｃ）、（Ｄ）は、ラバーバンドの張力の適応可変について説明するための図である。
【図１７】アーク方向ベクトル、中割りアーク方向ベクトル等の関係について説明するための図である。
【図１８】図１８（Ａ）、（Ｂ）、（Ｃ）は、画像生成装置、情報記憶媒体の種々の実施形態について示す図である。
【符号の説明】
１０ スケルトンモデル
１２ 関節点（ノード）
１４ 端点（ノード）
１６ 骨（アーク）
２０、２２ キーフレームの形状
２４ 中間フレームの形状
２６ スケルトンモデル
２８ パスカーブ
４０、４２ アーク方向ベクトル
４４ パスカーブ上の位置
４６、４８、５０ 中割りアーク方向ベクトル
５２ ノードpuller、AV pullerによる変形後のアーク法線ベクトル
５４ キーフレーム登録時のアーク法線ベクトル
５６ アーク法線ベクトル
５８ 中割りアーク法線ベクトル
６０ 制御点（パスカーブ上の位置）
６２ ラバーバンド
６４ パスカーブ
６６ 制御点（パスカーブ上の位置）
６８ ラバーバンド[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a skeleton model intermediate frame shape deriving method, a skeleton model shape deforming method, an image generating apparatus, and an information storage medium.
[0002]
[Background Art and Problems to be Solved by the Invention]
In the field of computer graphics and the like, the following procedure is often used when creating motion (animation) of characters such as people and animals.
[0003]
(D₁First, a skeleton model 10 as shown in FIG. In the following, the joint points 12 and end points 14 of the skeleton model 10 are referred to as nodes, and the bone 16 connecting the nodes is referred to as an arc.
[0004]
(D₂Next, as shown in FIG. 1B, the skeleton model 10 is deformed to create key frame shapes 20 and 22 of the skeleton model.
[0005]
(D_Three) Next, as shown in FIG. 1C, the key frame shapes 20 and 22 are interpolated to create the intermediate frame shape 24 of the skeleton model.
[0006]
Now, in a general work procedure, the above steps (D₂) Key frame shapes 20 and 22 are manually created by a user (operator in a broad sense) using an input device such as a mouse or a keyboard. On the other hand, the process (D_ThreeThe intermediate frame shape 24) is automatically generated by the program.
[0007]
Usually, the process (D_Three), The user fixes nodes or designates path curves (moving paths in a broad sense) for several nodes.
[0008]
Here, the node fixation is an instruction to keep the node at the same position in all intermediate frames between two key frames to be interpolated. Such node fixing is necessary, for example, when the arm is shaken while fixing the character's shoulder.
[0009]
The designation of the path curve is to instruct the node to move on the designated path curve between key frames. The designation of the path curve corresponds to designation of the position of the node (the node for which the path curve is designated) in each intermediate frame between the key frames as well as the designation of the path itself. Such a path curve designation is necessary, for example, when it is desired to move the tip of the character's hand or foot on the trajectory desired by the user.
[0010]
In the example shown in FIG. 2A, the skeleton model 26 has four nodes N.₁, N₂, N_Three, N_FourAnd 3 arcs A₁₂, A_{twenty three}, A₃₄It is composed of Each arc A₁₂, A_{twenty three}, A₃₄Includes an arc normal vector NV to indicate the direction of twist of each arc.₁₂, NV_{twenty three}, NV₃₄Is attached. Each of these arc normal vectors has a size of 1 and is perpendicular to each arc.
[0011]
In this example, two key frame shapes are prepared for the skeleton model 26. In addition, node N₁Is fixed and node N_FourA path curve 28 is designated. Even if such a designation is made, the frame (key frame) f₀, F_FourSmoothly interpolate the shape of the intermediate frame f as shown in FIG.₁, F₂, F_ThreeIt is desirable to generate the shape of the skeleton model at. That is, the node N is moved on the designated path curve 28._FourHowever, it is desired that the shape of the skeleton model in the intermediate frame also changes smoothly.
[0012]
The present invention has been made in view of the technical problems as described above, and an object thereof is to provide an intermediate frame of a skeleton model that is smoothly interpolated even when a movement path of a node is designated. An object of the present invention is to provide an intermediate frame shape derivation method of a skeleton model capable of obtaining a shape, a shape deformation method of a skeleton model, an image generation apparatus, and an information storage medium.
[0013]
[Means for Solving the Problems]
In order to solve the above-described problems, the present invention provides an intermediate frame shape derivation method for deriving the shape of an intermediate frame of a skeleton model from the shape of a key frame of the skeleton model. A first deformation step for deforming the shape of the skeleton model to be pulled to a given position on the movement path, and an orientation of the arc direction vector of the skeleton model based on the arc direction vector at the key frame. A second deformation step for deforming the shape of the skeleton model so as to approach the direction of the intermediate arc direction vector, and the direction of the arc normal vector of the skeleton model is obtained based on the arc normal vector at the key frame Shape the skeleton model so that it approaches the direction of the mid-arc normal vector. Characterized in that it comprises a third modification step of the form.
[0014]
In the present invention, in the first deformation step, the skeleton model is deformed so that the node whose movement path is specified is pulled to a position on the movement path, and in the second deformation step, the direction of the arc direction vector is divided. The skeleton model is deformed so as to approach the direction of the arc direction vector. Further, the skeleton model is deformed by the third deformation step so that the direction of the arc normal vector approaches the direction of the intermediate arc normal vector. Therefore, according to the present invention, the direction of the arc direction vector or the arc normal vector is set to the direction of the middle arc direction vector or the middle arc normal vector while bringing the node for which the movement route is designated closer to the position on the movement route. It becomes possible to approach. As a result, it is possible to achieve both the designation of the movement path of the node and the smooth interpolation of the intermediate frame shape of the skeleton model.
[0015]
The order of the first, second, and third deformation steps is arbitrary. Also, the position of the node, the direction of the arc direction vector, and the direction of the arc normal vector may be at least close to the position on the moving path, the direction of the intermediate arc direction vector, and the direction of the intermediate arc normal vector, There is no need to match exactly. Further, the intermediate arc direction vector and the intermediate arc normal vector only need to be obtained using at least the arc direction vector and the arc normal vector in the key frame, respectively.
[0016]
Further, the present invention represents the skeleton model by a basic variable including the coordinates of the nodes of the skeleton model, and includes an expression defining that the arc length of the skeleton model becomes a given value, and the basic variable is an unknown. At least one of the basic expression and an evaluation expression for uniquely identifying a solution satisfying the basic expression is changed based on given information, and the direction of the arc direction vector of the skeleton model is substantially satisfied with the basic expression. Find the solution of the basic variable so that the value of the evaluation formula including the difference from the direction of the intermediate arc direction vector is almost minimal, almost maximal, and almost stationary, and the shape of the skeleton model based on the obtained solution It is characterized by deforming. In this way, by adding a condition that makes the evaluation expression including the difference between the direction of the arc direction vector and the direction of the middle arc direction vector almost minimal, a solution satisfying the basic expression is uniquely identified, and the skeleton The shape of the model is determined. Therefore, the deformation of the skeleton model that makes the direction of the arc direction vector close to the direction of the intermediate arc direction vector can be easily realized.
[0017]
Further, the present invention represents the skeleton model by a basic variable including the coordinates of the nodes of the skeleton model, and includes an expression defining that the arc length of the skeleton model becomes a given value, and the basic variable is an unknown. At least one of the basic expression and the evaluation expression for uniquely identifying a solution satisfying the basic expression is changed based on given information, and the direction of the arc normal vector of the skeleton model is satisfied substantially by satisfying the basic expression. The basic variable solution is calculated so that the value of the evaluation expression including the difference between the direction of the normal vector and the intermediate arc normal vector is almost minimal, almost maximal, or almost stationary, and the skeleton model is based on the obtained solution. It is characterized by deforming the shape of. In this way, a solution that satisfies the basic formula is uniquely identified by adding a condition that makes the evaluation formula including the difference between the direction of the arc normal vector and the direction of the intermediate arc normal vector almost minimal. The shape of the skeleton model is determined. Therefore, the deformation of the skeleton model that makes the direction of the arc normal vector close to the direction of the intermediate arc normal vector can be easily realized.
[0018]
The present invention also provides a control point for controlling the position of the node of the skeleton model in which the movement path is designated. In the first deformation step, the node and the control in the skeleton model in which the movement path is designated are provided. The shape of the skeleton model is deformed by applying a tension that changes according to the distance between the node and the control point between the nodes. In this way, it is possible to avoid the failure of the calculation even when the node cannot pass on the designated movement route.
[0019]
The present invention also provides at least one control point for controlling the positions of a plurality of nodes of a skeleton model in which a movement path is specified, and the plurality of the movement paths specified in the first deformation step. A tension that varies depending on the distance between the plurality of nodes and the at least one control point is applied between the node and the at least one control point, and the sum of the tensions is less than a given value. The shape of the skeleton model is deformed under such conditions. In this way, it is possible to prevent a situation in which the total sum of tensions becomes excessive due to the plurality of nodes being pulled by at least one control point, and the skeleton model is violated. Furthermore, according to the present invention, each tension has a strength corresponding to the distance between the node and the control point. Accordingly, it is possible to prevent a situation where a plurality of balanced states occur in the shape of the skeleton model.
[0020]
According to the present invention, the second deformation step is performed after the first deformation step, and the orientation of the arc direction vector of the skeleton model is set to the middle in the initial stage of the first iterative calculation of the first deformation step. The calculation is performed so as to approach the direction of the split arc direction vector. In this way, the skeleton model can be deformed into a shape suitable for deformation in the second deformation step in the initial stage of the first iterative calculation of the first deformation step. As a result, it is possible to prevent a situation in which the deformation of the skeleton model into an appropriate shape is disabled in the second deformation step.
[0021]
In the present invention, the first deformation step is performed after the second deformation step, and at the initial stage of the second iterative calculation of the second deformation step, the node of the skeleton model in which the movement path is designated It is characterized by performing an operation of pulling a point to a given position on the movement route. By doing so, it is possible to deform the skeleton model into a shape suitable for deformation in the first deformation step in the initial stage of the second iterative calculation of the second deformation step. As a result, it is possible to prevent a situation in which the deformation of the skeleton model into an appropriate shape is disabled in the first deformation step.
[0022]
The present invention is also a method for deforming a shape of a skeleton model, wherein at least one control point is prepared to control positions of a plurality of nodes of the skeleton model, and the plurality of nodes of the skeleton model and the at least one of the at least one A tension that varies depending on the distance between the plurality of nodes and the at least one control point is applied between the control points and a skeleton is obtained under a condition that the sum of the tensions is less than or equal to a given value. It is characterized by changing the shape of the model.
[0023]
According to the present invention, it is possible to prevent a situation in which the skeleton model is violated due to a plurality of nodes being pulled by at least one control point, and to prevent a situation in which a plurality of balanced states are generated in the shape of the skeleton model. it can.
[0024]
The present invention is also a method for deforming a shape of a skeleton model, wherein a first deformation step of deforming the shape of the skeleton model by a first iterative calculation according to a given first condition, a given second And a second deformation step for deforming the shape of the skeleton model by a second iterative calculation according to the above condition, and performing the second deformation step after the first deformation step and the first deformation In an initial stage of the first iterative calculation of a step, an operation is performed in consideration of the second condition of the second deformation step.
[0025]
According to the present invention, in the initial stage of the first iterative calculation of the first deformation step, the skeleton model can be deformed into a shape suitable for the deformation in the second deformation step. As a result, it is possible to prevent a situation in which the deformation of the skeleton model into an appropriate shape is disabled in the second deformation step.
[0026]
Further, the image generation apparatus according to the present invention includes means for outputting the shape of the skeleton model obtained by any one of the above methods, and operation means for giving an instruction for the operator to create the shape of the skeleton model. It is characterized by. As a result, a shape data creation tool or the like using the method of the present invention can be realized.
[0027]
The image generation apparatus according to the present invention includes means for outputting an image of a moving object accompanying the skeleton model obtained by any one of the methods described above. As a result, it is possible to realize a game device or the like using the shape data obtained by the method of the present invention.
[0028]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
[0029]
1. Explanation of comparative example
First, a comparative example of this embodiment will be described.
[0030]
Intermediate frame f as shown in FIG.₁, F₂, F_ThreeAs a comparative example for obtaining the shape of the skeleton model, a method using joint angle interpolation and a method using inverse kinematics can be considered.
[0031]
1.1 Joint angle interpolation
In Comparative Example 1, the shape of the intermediate frame is obtained by interpolating the joint angles of the skeleton model.
[0032]
Taking FIG. 3A as an example, the key frame f₀Arc A at₁₂Joint angle θ_TenAnd key frame f_FourArc A at₁₂Joint angle θ₁₄And the intermediate frame f₂Joint angle at₁₂Seeking. More specifically, θ₁₂= (Θ_Ten+ Θ₁₄) / 2. Similarly, θ₂₀And θ_{twenty four}By interpolating_{twenty two}And θ₃₀And θ₃₄By interpolating₃₂Seeking.
[0033]
However, in this comparative example 1, the node N_FourHowever, it does not move on the designated path curve 28. That is, node N_FourPasses through the position 32 instead of the position 30 on the path curve 28. Therefore, the shape of the intermediate frame can be changed smoothly, but the node N_FourIt is impossible to meet the user's desire to move the path on the path curve 28.
[0034]
1.2 Inverse Kinematics
In this comparative example 2, the shape of the intermediate frame is obtained using inverse kinematics with the fixed node as the root and the node with the specified path curve as the effector. Taking FIG. 3B as an example, the fixed node N₁Becomes the root and the node N where the path curve 28 is specified_FourBecomes an effector. And node N_FourThe shape of the skeleton model at the intermediate frame is obtained by inverse kinematics while pinching and moving along the path curve 28.
[0035]
However, in Comparative Example 2, the frame f obtained by inverse kinematics_FourThe shape 34 in FIG. 5 becomes different from the shape 36 in the original key frame. Therefore, node N_FourCan be moved on the path curve 28, but cannot satisfy the user's desire to change the key frame shape to a desired shape.
[0036]
In order to solve the problems of Comparative Examples 1 and 2 as described above, in this embodiment, the intermediate frame shape of the skeleton model is derived by the following method.
[0037]
2. Overview of this embodiment
2.1 Preconditions
First, it is assumed that the user creates a character motion (animation) in the following procedure. That is, first, the user creates several poses of the character and registers them as key frames. Next, a path curve (moving path in a broad sense) between key frames is designated for some nodes. By specifying the path curve, the position of the node in each intermediate frame between the key frames is specified. Note that the position of the node in the intermediate frame may be explicitly specified by the user, or may be calculated by a program based on the path curve specified by the user or the moving speed of the node specified by the user. Good.
[0038]
Now, when a user creates a motion of a character, there is a case where the position of a node is desired to be fixed from one key frame to the next key frame. Such node fixing can be understood as a case where the path curve is a straight line and the start point and end point of the path curve coincide with each other.
[0039]
Therefore, in this embodiment, the node is fixed by specifying a path curve. In other words, when the user wants to fix a node, the user designates a straight path curve whose start point and end point coincide with the node. In this way, in addition to specifying the path curve, there is no need to provide a separate user interface for specifying fixed nodes. As a result, it is possible to prevent a situation in which the calculation fails due to the inconsistent node fixing designation by the user.
[0040]
The present embodiment aims to generate an intermediate frame that satisfies the following two requirements and smoothly interpolates between key frames.
[0041]
First, make sure the motion of the completed skeleton model passes through the keyframe pose. However, this does not apply when the skeleton model interferes with the polygon object.
[0042]
Secondly, a node for which a path curve is specified always moves as specified unless the shape is impossible. Here, “impossible in terms of shape” means a state in which a node cannot move on a specified path curve due to constraints such as arc length, movable range of joint angles, interference with polygon objects, and the like. .
[0043]
2.2 Method for deriving intermediate frame shape by 3-step puller
In this embodiment, the shape of the intermediate frame of the skeleton model is derived by a three-step puller. This derivation method will be described in detail using a PAD (Program Analysis Diagram) in FIG.
[0044]
In the following description, it is assumed that the two key frames to be interpolated are the kth frame and the k + n frame. Also, the shape of the skeleton model at these key frames is interpolated to derive the shape at the (k + 1) th to (k + n-1) th frames which are intermediate frames.
[0045]
2.2.1 Derivation of mid-arc direction vector
First, a middle arc direction vector is derived for each arc of the skeleton model (step U1 in FIG. 4). More specifically, the direction of the arc direction vector of the kth frame and the direction of the arc direction vector of the k + n frame are equally divided, and the k + 1 to k + n-1 frames are used. Find the middle arc direction vector.
[0046]
A unit vector from one end of the arc to the other end is referred to as an arc direction vector. The middle arc direction vector is obtained by equally dividing the direction of the arc direction vector in the key frame.
[0047]
Arc A in FIG.₁₂For example, the key frame f₀Direction of the arc direction vector 40 and the key frame f_FourBy dividing the direction of the arc direction vector 42 at 4 into four equal parts, a middle arc direction vector is derived. Arc A_{twenty three}, A₃₄The intermediate arc direction vector for is similarly derived.
[0048]
The derived mid-arc direction vector is used in Step 2 when deriving the shape of the intermediate frame, as will be described later.
[0049]
2.2.2 Deformation by node puller and AV puller
After deriving the intermediate arc direction vector, the shape of the skeleton model from the (k + 1) th frame to the (k + n) th frame is sequentially derived by the following procedure. That is, the shape of the skeleton model of the i-1 frame (the shape one frame before) is read (step U2 in FIG. 4), the next two steps (Step1, Step2) are modified (step U3, U4), and the i frame (Step U5).
[0050]
Step 1: Unfix the node for which the path curve is not specified, pull the node for which the path curve is specified to a given position on the path curve, and deform the skeleton model until the calculation converges (step U3 in FIG. 4). The pull applied to the node in Step 1 is called a node puller.
[0051]
For example, in FIG.₀The node puller acts on the shape of the frame f₁The process of deriving the shape of is shown. In FIG. 6, node N₂, N_ThreeIs unfixed and node N₁, N_FourThe node puller is made to act on. Where node N_FourIs a node for which a path curve is specified. Node N_FourIs pulled to a position 44 on the path curve by this node puller. On the other hand, node N₁Is a fixed node. Fixed node N₁As described above, it is assumed that a straight path curve having the same start point and end point is designated. That is, node N₁The length of the node puller acting on is 0 in the initial state.
[0052]
Step2: Fix the node where the path curve is specified at the position at the end of Step1, and leave the node where the path curve is not specified unfixed. Then, a twist is applied so that the direction of the arc direction vector is as close as possible to the direction of each intermediate arc direction vector, and the skeleton model is deformed until the calculation converges (step U4 in FIG. 4). This twist acting on the arc is referred to as AV puller (arc vector puller).
[0053]
For example, in FIG.₁, N_FourIs fixed, nodes N2 and N3 are not fixed, and AV puller is operated. As a result, Arc A₁₂, A_{twenty three}, A₃₄The skeleton model is deformed so that the direction of (arc direction vector) approaches the direction of the middle arc direction vector 46, 48, 50, respectively.
[0054]
The deformation of the skeleton model by the node puller and AV puller can be realized, for example, by inverse kinematics according to the technique of Japanese Patent Application Laid-Open No. 10-208072 filed by the present applicant.
[0055]
Also, the direction of each arc direction vector and the direction of each middle arc direction vector generally do not completely coincide. For example, in FIG.₁, N_FourThis is because it is often impossible geometrically to make the direction of each arc direction vector and the direction of each arc direction vector perfectly match under such conditions. . However, if the deformation by the node puller and AV puller is performed using inverse kinematics as disclosed in JP-A-10-208072, the shape of the intermediate frame can be smoothly changed.
[0056]
The above-described transformation processing (steps U2 to U5 in FIG. 4) by the nodes puller and AV puller is repeated until i = k + 1 to i = k + n, and the k + 1th frame is changed from the shape of the kth frame. Shape, shape of k + 1 frame to shape of k + 2 frame, shape of k + 2 frame to shape of k + 3 frame, shape of k + 3 frame to shape of k + 4 frame In this way, the shape of the skeleton model is sequentially derived. When the shape of the skeleton model of the (K + n) th frame is derived, the process of correcting the direction of each arc normal vector is performed.
[0057]
That is, the direction of the arc normal vector in the (k + n) th frame finally obtained by the deformation by the nodes puller and AV puller is different from the direction when registered as the key frame.
[0058]
Taking FIG. 8A as an example, the frame f obtained by the deformation by the nodes puller and AV puller._FourThe direction of the arc normal vector 52 of (k + n frame) is different from the direction of the arc normal vector 54 when registered as a key frame. Therefore, it is necessary to correct the direction of the normal vector 52 of the arc.
[0059]
2.2.3 Derivation of mid-arc normal vector
First, an intermediate arc normal vector is derived for each arc of the skeleton model (step U6 in FIG. 4).
[0060]
More specifically, the arc normal vector of the k + n frame finally obtained by the deformation by the node puller and AV puller is compared with the arc normal vector of the k + n frame at the time of key frame registration. Rotation angle φ around the arc direction vector_NVAsk for. Taking FIG. 8A as an example, the rotation angle φ around the arc direction vector from the arc normal vector 52 to 54._NVAsk for.
[0061]
Next, this φ_NVIs divided evenly by the number of frames n. Then, the arc normal vector of each frame, twisted around the arc direction vector of the arc, is defined as a middle-arc normal vector. That is, in the k + i frame, the arc normal vector is φ_NV-The twisted i / n is the middle arc normal vector.
[0062]
Taking FIG. 8B as an example, the frame f₁Then, let the arc normal vector 56 be φ_NVAn intermediate arc normal vector 58 is twisted about the arc direction vector by / 4. On the other hand, the frame f₂Then φ_NV/ 2, frame f_ThreeThen 3φ_NVAn arc normal vector twisted by / 4 becomes a middle arc normal vector.
[0063]
The arc normal vector is orthogonal to the arc direction vector, and the intermediate arc normal vector is obtained by rotating the arc normal vector by a given angle around the arc direction vector. Therefore, the intermediate arc normal vector is also orthogonal to the arc direction vector and satisfies the requirement as an arc normal vector.
[0064]
2.2.4 Deformation by NV puller
After deriving the intermediate arc normal vector, the shape of the skeleton model from the (k + 1) th frame to the (k + n-1) th frame is sequentially corrected in the following procedure. That is, the shape of the skeleton model of the i frame is read (step U7 in FIG. 4), the next step 3 is transformed (step U8), and the shape is stored as the shape of the i frame (step U9).
[0065]
Step3: Fix all nodes. Then, a twist is applied so that the direction of the arc normal vector is as close as possible to the direction of each middle arc normal vector of the frame, and the skeleton is deformed until the calculation converges (step U8 in FIG. 4). This torsion acting on the arc normal vector is called NV puller (normal vector puller). The deformation processing by the NV puller (steps U7 to U9 in FIG. 4) is repeated from i = k + 1 to i = k + n-1, from the k + 1 frame to the k + n-1 frame. The direction of the arc normal vector of the skeleton model is sequentially corrected.
[0066]
Taking FIG. 8B as an example, the frame f₁Then Arc A₁₂An NV puller is applied to make the direction of the arc normal vector 56 close to the direction of the intermediate arc normal vector 58. Frame f₂, F_Three, F_FourThe same applies to. For example, frame f_FourThen, in FIG. 8A, an NV puller acts to make the direction of the arc normal vector 52 as close as possible to the direction of the intermediate arc normal vector 54. As a result, it is possible to eliminate the situation in which the direction of the arc normal vector 52 is different from the direction of the arc normal vector (intermediate arc normal vector) 54 at the time of key frame registration.
[0067]
As described above, the three requirements of node puller, AV puller, and NV puller are sequentially applied to derive the shape of the intermediate frame, so that the above two requirements of 2.1 (the motion of the completed skeleton model is The key frame pose must be passed, and the node with the specified path curve must move as specified unless the shape is impossible. Become.
[0068]
2.3 Node puller by rubber band
In the present embodiment, the rubber band technique disclosed in Japanese Patent Laid-Open No. 10-208072 is used as the node puller of Step 1 described above.
[0069]
Taking FIG. 9A as an example, node N with a specified path curve._FourIs pulled to a position (control point) 60 on the path curve by a node puller, that is, a rubber band 62. Here, the rubber band 62 has a root and a tip, the root of the rubber band 62 moves with the control point 60, and the tip of the rubber band 62 is a node N._FourWill remain fixed. The rubber band 62 has the property of trying to shrink, and the node N_FourBetween the control point 60 and, for example, the node N_FourTherefore, a tension (force for minimizing the distance) that changes in accordance with the distance between the control point 60 and the control point 60 acts. Due to this tension, as shown in FIG._FourIs pulled toward the control point 60, and the skeleton model is deformed.
[0070]
The following advantages can be obtained by using a rubber band as the node puller. For example, when the user designates a path curve 64 as shown in FIG.₂Node N_FourCannot be moved to a position 66 on the path curve 64. In such a case, if the rubber band is not used, the calculation is broken. However, using the rubber band 68, the frame f₂Node N_FourIs pulled to the position 66 which is the control point, the above-described calculation failure can be avoided.
[0071]
2.4 Variable adjustment of rubber band tension
In this embodiment, it is possible to specify a path curve for a plurality of nodes. For example, as shown in FIG._Four, N_FiveIf a path curve is specified for these two nodes N_Four, N_FiveTwo control points 70 and 72 are prepared for controlling the position of. And node N_Four, N_FiveAnd rubber bands 74 and 76 act between the control points 70 and 72.
[0072]
Thus, in this embodiment, a plurality of rubber bands may act on a plurality of nodes.
[0073]
When the rubber band tension is increased, the skeleton model is likely to be ramped, but this rampage can be solved to some extent by setting an upper limit on the rubber band tension. However, when a plurality of rubber bands act on a plurality of nodes as described above (when a plurality of rubber bands act on a skeleton model), the following problem occurs only by setting an upper limit on the tension of the rubber band. End up.
[0074]
For example, as shown in FIG._Four, N_FiveAre pulled in the same direction, even if the tension of the individual rubber bands 74 and 76 is small, the total sum of the tensions of all the rubber bands becomes large. For this reason, even if an upper limit is set for the tension of each rubber band 74, 76, the skeleton model will be rampant.
[0075]
In addition, as shown in FIG._,N_ThreePass curves 78 and 80 are specified for the intermediate frame f₂Suppose that the rubber bands 82 and 84 are stretched and balanced. In this case, all the states shown in FIGS. 10B, 10C, and 10D are balanced by simply setting an upper limit on the tension of the rubber bands 82 and 84. The rubber band has a length of, for example, l_r ^*This is because the tension becomes the upper limit at the time of (1) and the tensions of the rubber bands 82 and 84 reach the upper limit and are equal in all cases of FIGS. 10 (B), (C), and (D). That is, for the user, the balanced state of FIG. 10B is most desirable, but there is a possibility that the balanced state is obtained as shown in FIGS. 10C and 10D.
[0076]
Therefore, in this embodiment, when a plurality of tensions (rubber bands) act between a plurality of nodes and a plurality (or one) of control points as described above, the distance between the nodes and the control points is as follows. The skeleton model is deformed under the condition that the tension according to is applied and the total sum of the tensions is less than a given value.
[0077]
According to this embodiment, a plurality of nodes N as shown in FIG._Four, N_FiveHowever, even if tension is applied by a plurality of rubber bands 74 and 76, the total sum of these tensions is less than a given value. Therefore, it is possible to avoid a situation in which the skeleton model is rampant. Further, each tension does not have a specific upper limit value, and its strength changes according to the distance between the node and the control point. Therefore, a situation where a balanced state as shown in FIGS. 10C and 10D can be avoided. This is because the tension of 84 is stronger than that of the rubber band 82 in FIG. 10C, and the tension of 82 is stronger than that of the rubber band 84 in FIG.
[0078]
2.5 Addition of AV puller in Step1
As shown in FIG. 11A, the frame (key frame) f₀, F_Four, The node N_FourSuppose that a path curve as shown in 86 is designated. In this case, the frame f₁The shape of the skeleton model should be the shape 87 shown in FIG.
[0079]
However, in FIG. 11C, the frame f₀When only the node puller of Step 1 described above is applied to the shape of the skeleton model, it is undefined whether the shape of the skeleton model is deformed to the shape 88 or 90 in FIG. In this case, there is no problem if the shape 88 is deformed. However, if the shape 90 is deformed, the arc A will be applied even if the AV puller is applied in the subsequent Step 2.₁₂AV puller and arc A₃₄AV puller acting on the balance is balanced with each other. For this reason, the shape 90 is not further deformed and cannot reach the original shape 87 of FIG.
[0080]
Therefore, in the present embodiment, step U3 in FIG. 4 is modified as shown in the PAD in FIG. 12, and only the node puller is used in the first loop of the iterative calculation in Step 1 (in the broader sense, the initial stage of the iterative calculation). In addition, the skeleton model is deformed by simultaneously operating the AV puller (step V1). That is, in the first loop of the iterative calculation, not only an operation for pulling a node with a specified path curve to a given position on the path curve, but also an operation for bringing the direction of the arc normal vector closer to the direction of the intermediate arc direction vector. Do. On the other hand, after the second loop, only the node puller is applied to deform the skeleton model until the calculation converges (step V2).
[0081]
By doing so, the frame f₁It is possible to change the shape of the skeleton model to the original shape 87 of FIG.
[0082]
In FIG. 12, both the node puller and the AV puller are operated only in the first loop. However, for example, both the node puller and the AV puller are operated in the second and third loops. Also good. It is also possible to operate only the node puller in the first loop and to operate both the node puller and AV puller in the second loop.
[0083]
3. Skeleton model shape deformation method
When the skeleton model is deformed by the node puller, AV puller, or NV puller, for example, the shape deformation method of the skeleton model disclosed in JP-A-10-208072 can be used. Hereinafter, a method for deforming the shape of the skeleton model will be briefly described.
[0084]
3.1 Basic principle
In the shape deforming method of the present embodiment, as shown in FIG. 13A, the coordinates (x, y, z) of the nodes 102, 103, 104, the arcs 106, 107, 108 are used as basic variables representing the skeleton model 118. Use the components (u, v, w) of the arc normal vectors 110, 111, 112 perpendicular to. Thus, by using node coordinates and arc normal vectors as basic variables, it becomes possible to treat all nodes and arcs as equivalent. It is also possible to substitute the arc normal vector with another variable.
[0085]
Next, as shown in FIG. 13B, as a basic expression with the above-mentioned basic variables as unknowns, an expression that specifies that the length of the arc is a given value, and the length of the arc normal vector is given. And an expression that prescribes that the arc normal vector is perpendicular to the arc. For example, the basic expressions g = 0 and h = 0 can be replaced by other expressions.
[0086]
Here, the basic equation shown in FIG. 13B is nonlinear. Therefore, in this embodiment, a solution is obtained by an iterative calculation method such as Newton's method. By using the Newton method or the like in this way, the basic expression can be expressed by a linear expression of the change amount of the basic variable. Thus, the simultaneous equations to be solved are as shown in FIG.
[0087]
However, in the equation of FIG. 13C, the number of variables is larger than the number of equations. Therefore, in this embodiment, an evaluation formula for uniquely identifying a solution that satisfies the basic formula is prepared. Then, a condition that the value of the evaluation formula is made to be almost minimum, almost maximum or almost stopped is added, and a solution of the basic variable is obtained by applying the Lagrange multiplier method. By using the Lagrange multiplier method, the equation to be solved is as shown in FIG. 13D, and the number of variables matches the number of equations, so that the solution can be uniquely determined.
[0088]
In the present embodiment, the skeleton model is deformed based on given information such as the coordinates of a given position on the path curve, the middle arc direction vector, and the middle arc normal vector. At this time, the basic formula and the evaluation formula change based on the given information. Specifically, based on the given information, the known number included in the basic formula and the evaluation formula, and the shape of the formula itself change, thereby deforming the shape of the skeleton model.
[0089]
3.2 First order approximation of change in arc normal vector
In the present embodiment, as shown in FIG. 14A, the change amount of the arc normal vector n (u, v, w) is represented by a given variable ρ, and the solution of the basic variable is obtained. Seeking. More specifically, the change amount of the arc normal vector n is approximated by a linear expression of the variable ρ. The arc normal vector n is represented by three variables u, v, and w. However, as shown in FIG. 14A, n is perpendicular to the arc 150 and has a constant size. The degree is 1. Therefore, the amount of change of n can also be expressed by one variable ρ, thereby reducing the number of basic variables to be solved and speeding up the processing.
[0090]
3.3 Evaluation formula
Also, in this embodiment, in order to obtain a preferred skeleton model deformation, the amount of change in arc-to-arc angle, the distance between a node and a given control point, the amount of change in the direction of an arc having a fixed node at the end, The amount of change in coordinates and the amount of change in velocity of node coordinates are included in the evaluation formula. More specifically, as shown in FIG. 14B, various conditions are added to the evaluation formula. For example, by including the change amount of the arc-to-arc angle in the evaluation formula and minimizing the sum of squares of the change amount of the arc-to-arc angle, it is possible to prevent a situation such that only one set of arcs protrude and bend, The bending between the arcs can be balanced overall. In addition, a rubber band can be realized by including the distance between the node and a given control point in the evaluation formula. In addition, the amount of change in the direction of an arc having a fixed node at the end and the amount of change in node coordinates are included in the evaluation formula, and the arc rotation damper, node damper, etc. around the fixed node can be set to make the solution undefined. Can be prevented. Further, by including the node coordinate change amount and the node coordinate speed change amount in the evaluation formula and setting the node damper and the node inertia, it is possible to prevent the arc from being unstable due to unstable calculation convergence.
[0091]
4). Detailed algorithm
Next, an example of a detailed algorithm of the present embodiment will be described. In addition, the meaning of the sum code used in the following description is as follows. In the following, the angle between the arcs is referred to as an angle, and the two arcs constituting the angle and the three nodes that are the end points thereof are referred to as angle components.
[0092]
[Expression 1]

The relationship between the order of the subscripts and the sign is as follows.
[0093]
[Expression 2]

4.1 Basic formula
In FIG. 15, node N_iThe coordinates of (x_i, Y_i, Z_i). The arc is provided with an arc normal vector to represent rotation in a three-dimensional space. Arc A_ij(Node N_i, Node N_jNormal vector of arc)_ij(U_ij, V_ij, W_ij). In the present embodiment, the shape of the skeleton model is represented using these basic variables. The following basic formula holds for each arc.
[0094]
[Equation 3]

Equation (1) is the arc A_ijLength of L_ijIt means that. Equation (2) means that the size of the normal vector is 1. Equation (3) means that the arc normal vector and the arc are perpendicular.
[0095]
4.2 Solving the basic equation
Equations (1), (2), and (3) are nonlinear equations, and the number of equations is less than the number of variables. Therefore, the Newton method and the Lagrange multiplier method are combined to solve.
[0096]
If there is no need to instruct, the variable suffix is omitted.
[0097]
4.2.1 Application of Newton's method
The amount of change of each variable per loop is defined as follows.
[0098]
[Expression 4]

When the Newton method is applied to the above basic equation (1), the following equation is obtained.
[0099]
[Equation 5]

To summarize this, the following formula is obtained.
[0100]
[Formula 6]

l_ijIs the current value of the arc length and is expressed by the following equation. When the calculation is converged, l_ij= L_ijIt becomes.
[0101]
[Expression 7]

Λ is a scale factor. The value of λ is the arc length L as in the following equation:_ijThe average value of is used. N_arcIs the number of arcs constituting the skeleton.
[0102]
[Equation 8]

For the equations (2), (3) and the variables u, v, w, in order to reduce the unknowns of the equations to be solved, the Newton method is not used, but the first-order approximation using the one variable ρ described below is used.
[0103]
4.2.2 First order approximation of arc normal vector variation
Arc normal vector n_ijIs Arc A_ijComponent u since it is perpendicular to_ij, V_ij, W_ijAlthough there are three variables, the degree of freedom of change is 1 as shown in FIG. Therefore, in order to reduce the number of unknown equations to be solved, linear approximation with one variable is performed.
[0104]
As shown in FIG. 15, the starting node N of the arc_iTo end node N_jA unit vector heading to the arc direction vector a_ijIt is defined as In addition, as shown in FIG._ijVector s on_ijmake.
[0105]
[Equation 9]

Differentiating and organizing equations (2) and (3), n_ij(U_ij, V_ij, W_ij) Of change Δn_ij(Δu_ij, Δv_ij, Δw_ij) Is a newly introduced unknown variable ρ_ijIt can be approximated as a linear expression of
[0106]
[Expression 10]

n_ijN 'is the value to be taken in the next event cycle_ijAnd n '_ijIs originally Arc A_ijIt should be perpendicular to the size of 1 and have an error in the order of the square of the amount of change. Therefore, as shown in the following equation, the direction is first corrected, and the size is further corrected to 1, n ′_ijAnd However, a '_ijIs a_ijIs the value taken in the next event cycle.
[0107]
[Expression 11]

4.2.3 Application of Lagrange's multiplier method
In Equation (6), since the number of equations is smaller than the number of variables and the variable ρ is not included, it is not possible to uniquely determine the deformation of the skeleton model by itself. Therefore, an evaluation expression including ρ is prepared, and a solution is obtained by applying the Lagrange multiplier method under the condition that the expression is minimized. The evaluation formula is the formula U₁, U₂, U_Three, ... Sum of U_eConfigure as. Undetermined multiplier α_ijAnd U is defined as follows:
[0108]
[Expression 12]

By solving the equation (6) and the following equation (14) simultaneously, solutions ξ, η, ζ, and ρ are obtained.
[0109]
[Formula 13]

Based on the obtained solution, new values x ′, y ′, z ′ of x, y, z are obtained by the following equations, and the coordinates of the node are determined.
[0110]
[Expression 14]

Then, new values n ′ (u ′, v ′, w ′) of n (u, v, w) are obtained from the equations (11), (12), and the arc normal vector is determined.
[0111]
4.3 Fixed arc direction
4.3.1 Meaning of fixed arc direction
When the direction of the arc is fixed, the arc is subject to the following constraints.
[0112]
That is, when the nodes at both ends are not fixed, only translation is possible (the direction of the arc normal vector cannot be changed). On the other hand, when at least one of the nodes at both ends is fixed, neither movement nor rotation is possible (completely fixed state).
[0113]
4.3.2 Trans group
When a plurality of adjacent arcs are fixed in direction, and these arcs move, these arcs move together in parallel. Such a group of one or more arcs (or two or more nodes) is called a trans group.
[0114]
If one of the nodes in the trans group is a representative node, the movement amount of the nodes other than the representative node in the trans group is equal to the movement amount of the representative node.
[0115]
For arcs with a fixed direction, equations (1) and (6) are not required, and the variable ρ disappears. For nodes other than the representative node in the trans group, the variables ξ, η, and ζ disappear from Equation (14). Thus, the calculation load can be reduced by reducing the number of variables.
[0116]
4.4 Creating an evaluation formula
As described above, in order to apply the Lagrange multiplier method, it is necessary to prepare an evaluation formula to be minimized. As the evaluation formula, as described with reference to FIG. 14B, various evaluation formulas including a change amount of the arc-to-arc angle, a change amount of the node coordinate, a speed change amount of the node coordinate, and the like can be considered. Details of these evaluation formulas are disclosed in JP-A-10-208072.
[0117]
4.4.1 Rubber band setting
A rubber band is a virtual arc with the property of shrinking. Here, one end of the rubber band (x_i, Y_i, Z_i) And the other end (x_ci, Y_ci, Z_ci). As disclosed in Japanese Patent Laid-Open No. 10-208072, using this rubber band, the user can transform the skeleton model into a desired shape. In this case, one end of the rubber band (x_i, Y_i, Z_i) Is the node N picked by the user with the mouse etc._iAnd the other end (x_ci, Y_ci, Z_ci) Move according to the movement of the user's mouse.
[0118]
The rubber band can also be used for the node puller as described above. In this case, one end (x_i, Y_i, Z_i) Is the node N with the specified path curve_iAnd the other end (x_ci, Y_ci, Z_ci) Becomes a control point (a given position on the path curve).
[0119]
Evaluation formula U of formula (13)_eAnd U₂By adding, the shrinkage of the rubber band can be expressed. W_rIs a weight value (weighting coefficient) representing the strength of the contractibility (tension) of the rubber band.
[0120]
[Expression 15]

U_2iThe partial derivative of is as follows.
[0121]
[Expression 16]

4.4.2 Variable adjustment of rubber band weight value
When the rubber band tension is increased, rampage tends to occur. Therefore, rubber band weight value W_rIs made variable according to the state of the skeleton model. At this time, it is not sufficient to simply set an upper limit on the weight value, and it is necessary to consider the following cases.
[0122]
First, when a plurality of nodes are picked and pulled in the same direction, even if the tension of each rubber band is small, the total sum of tensions of all rubber bands becomes large (see FIG. 10A). ).
[0123]
Second, when a plurality of nodes are pulled in different directions, simply setting an upper limit on the rubber band tension causes the following problems. That is, when the shape of the skeleton model converges with the rubber band extended, the balance state may not be uniquely determined. For example, assume that one arc is pulled left and right as shown in FIG. Here, the limit length of the rubber bands 120 and 122 is set to l_r ^*Then, FIGS. 16B, 16C, and 16D are all in a balanced state. In FIGS. 16B, 16C, and 16D, the lengths of the rubber bands 120 and 122 are all l._r ^*This is because the tensions of the rubber bands 120 and 122 are all equal to the upper limit value.
[0124]
Therefore, rubber band weight value W_rIs the rubber band length l as shown in the following equation:_riThe value is proportional to the reciprocal of the sum of.
[0125]
[Expression 17]

However, when the total rubber band length is small, the weight value W_rW should not be too large_rHas an upper limit W_r ^*Is set in advance.
[0126]
W_rIs controlled variably as shown in Equation (19), under the condition that the sum of the tensions of the rubber bands acting between multiple nodes and multiple control points is less than a given value. The shape of can be deformed. Also, there is no specific upper limit for the tension of each rubber band, and the tension of the rubber band is expressed by the node N where the path curve is specified as shown in equation (17)._i(X_i, Y_i, Z_i) And the control point (x_ci, Y_ci, Z_ci) And changes according to the distance. Accordingly, it is possible to avoid a situation in which the balanced state as shown in FIGS. 16B, 16C, and 16D is not uniquely determined.
[0127]
4.4.3 Node puller
The node puller is realized using the rubber band described in Section 4.4.1 and 4.4.2. By performing the convergence calculation by applying the node puller, the deformation of the skeleton model by the node puller can be realized.
[0128]
4.4.4 AV puller
When the AV puller is applied, the skeleton model is deformed so that the sum of squares of the difference between the arc direction vectors of the arcs and the middle arc direction vector is minimized. Evaluation formula U of formula (13)_eAnd U_AThis transformation can be realized by performing convergence calculation by adding.
[0129]
[Expression 18]

Where W_AIs a weight value (weighting coefficient) representing the strength of the AV puller. As shown in FIG._ijArc direction vector a_ijAnd middle arc direction vector a_pijThe angle between_pijAnd And θ_pijThe amount of change in_pijAnd
[0130]
[Equation 19]

φ_pijIs expressed by a first-order approximation of ξ, η, ζ. First, the following equation holds.
[0131]
[Expression 20]

The above formula_pijIf the second and higher order terms are ignored and transformed, the following equation is obtained.
[0132]
[Expression 21]

As shown in FIG._ijAnd a_pijA in the plane_ijA unit vector a perpendicular to_qijmake.
[0133]
[Expression 22]

Equation (26) is transformed using Equation (27) etc._i, Ξ_j, Η_i, Η_j, Ζ_i, Ζ_j, Ρ_ijBy U_AijWhen the partial derivative of is obtained, the following equation is obtained.
[0134]
[Expression 23]

In the above method, θ_pijIf = 0, vector a_qijBecomes indefinite and cannot be calculated. Where θ_pijIn the case of << 1, the following formula is used.
[0135]
[Expression 24]

Equation (30) is transformed and ξ_i, Ξ_j, Η_i, Η_j, Ζ_i, Ζ_j, Ρ_ijBy U_AijWhen the partial derivative of is obtained, the following equation is obtained.
[0136]
[Expression 25]

4.4.5 NV puller
When the NV puller is applied, the skeleton model is deformed so that the sum of squares of the difference in direction between the arc normal vector and the middle arc normal vector of each arc is minimized. Evaluation formula U of formula (13)_eThe following formula U_NThis can be realized by adding.
[0137]
[Equation 26]

W_NIs a weight value (weight coefficient) representing the strength of the NV puller. Arc A_ijNormal vector n_ij(U_ij, V_ij, W_ij) For the mid-arc normal vector_pij(U_pij, V_pij, W_pij).
[0138]
ξ_i, Ξ_j, Η_i, Η_j, Ζ_i, Ζ_j, Ρ_ijBy U_NijWhen the partial derivative of is obtained, the following equation is obtained.
[0139]
[Expression 27]

5. Image generating apparatus and information storage medium
18A, 18B, and 18C show various embodiments of an image generation apparatus and an information storage medium using the skeleton model intermediate frame shape derivation method and shape deformation method of the present embodiment.
[0140]
FIG. 18A shows an example in which the present embodiment is applied to a shape data creation tool that is one of image generation apparatuses. An instruction for creating the key frame shape of the skeleton model, designation of a path curve, and the like are performed using, for example, the keyboard 200 and the mouse 202 which is a pointing device. The processing unit 210 deforms the shape of the skeleton model by the method of the present embodiment to generate shape data, and the image of the skeleton model based on the shape data generated by the shape data generation unit 212. And an image generation unit 214 to be combined. The processing unit 210 is configured by a CPU, a DSP, a memory, and an ASIC for image generation if necessary, in terms of hardware. An information storage medium 216 composed of an FD, a CD, a DVD, an IC card, a memory, and the like has various information such as a shape data creation program for realizing the method of the present embodiment and data necessary for executing the program. Is stored. The processing unit 210 performs processing based on information input from the keyboard 200 and the mouse 202 and information stored in the information storage medium 216, thereby displaying a skeleton model image 219 or the like on the display unit 218. According to this shape data creation tool, shape data can be created while confirming the shape of the displayed skeleton model image 219, and the efficiency of design work can be improved.
[0141]
FIG. 18B shows an example in which the present embodiment is applied to a game device which is one of image generation devices. The game controllers 220 and 222 are for the player to input operation information. The processing unit 230 performs a game calculation unit 232 that performs a calculation for synthesizing a game image based on operation information from the player, and an image generation unit 234 that generates an image based on a calculation result from the game calculation unit 232. In terms of hardware, it includes a CPU, a DSP, a memory, and an ASIC for image generation if necessary. The information storage medium 236 stores shape data created by the method of the present embodiment or various information generated based on the shape data, a game program, and the like. On the display unit 238, game character images 239, 240 and the like that are operated based on the shape data and the like are displayed. If the game device is for business use, the shape data and the game program are stored in an information storage medium such as a semiconductor memory and a hard disk. If the game device is for home use, the shape data and the game program are It is stored in an information storage medium consisting of a CD, DVD, game cassette or the like. In a game device of a type in which a plurality of terminals are connected via a communication line via a host device and a game program or the like is distributed, the shape data and the game program are stored in an information storage medium of the host device such as a magnetic disk, CD, DVD, It is stored in a semiconductor memory or the like.
[0142]
On the other hand, FIG. 18C is an example of a game device when the game calculation unit 242 includes a shape data generation unit 243. In this case, the information storage medium 246 stores a shape data generation program that implements the method of the present embodiment instead of the shape data, and the shape data generation unit 243 built in the game device generates the shape data in real time. To do. For example, the player causes the skeleton model to perform a desired operation using the game controllers 220 and 222 and the like. As a result, the images 239 and 240 of the moving object accompanying the skeleton model are displayed on the display unit 238.
[0143]
The present invention is not limited to that described in the above embodiment, and various modifications can be made.
[0144]
For example, in the present embodiment, the case where the deformation by the AV puller is performed after the deformation by the node puller has been described. However, in the present invention, the deformation by the node puller may be performed after the deformation by the AV puller. For example, when priority is given to the direction of the arc in the specified direction rather than the specified node passing on the path curve, it is desirable to perform the deformation by the node puller after the deformation by the AV puller. In this case, the direction of the arc is fixed by the method of fixing the direction of the arc described in Section 4.3.
[0145]
In addition, the deformation by the nodes puller, AV puller, and NV puller is performed by changing the basic variables and the solutions described in FIGS. 13 (A) to 13 (D) based on given information. It is particularly desirable to achieve this by a desired method. However, the present invention is not limited to this, and these modifications may be realized by another method.
[0146]
The method of adaptively changing the rubber band tension described in Section 2.4 can be widely applied not only to the rubber band in the node puller but also to various rubber bands used for deformation of the skeleton model. For example, a technique for adaptively changing the rubber band tension can be applied to a rubber band used when a skeleton model is deformed by a user's mouse operation as disclosed in Japanese Patent Laid-Open No. 10-208072.
[0147]
In addition, an application example of a technique for performing an operation in consideration of the second condition of the second deformation step in the initial stage of the iterative calculation of the first deformation step is that AV puller is used in the initial stage of deformation by the node puller. It is not limited to the application example (refer FIG. 12) made to act. For example, various application examples such as an application example in which a node puller is operated in the initial stage of deformation by AV puller can be considered.
[0148]
[Brief description of the drawings]
FIGS. 1A, 1B, and 1C are diagrams for explaining a procedure for creating a motion of a character.
FIGS. 2A and 2B are diagrams for explaining path curve designation and intermediate frame shape derivation. FIG.
FIGS. 3A and 3B are diagrams for explaining a comparative example of the present embodiment.
FIG. 4 is a PAD for explaining processing of the present embodiment.
FIG. 5 is a diagram for explaining derivation of a middle arc direction vector.
FIG. 6 is a diagram for explaining deformation by a node puller.
FIG. 7 is a diagram for explaining deformation by an AV puller.
FIGS. 8A and 8B are diagrams for explaining the derivation of the mid-arc normal vector. FIGS.
FIGS. 9A and 9B are diagrams for explaining a method using a rubber band as a node puller. FIG.
FIGS. 10A, 10B, 10C, and 10D are diagrams for explaining an adaptive variable of the rubber band tension. FIG.
FIGS. 11A, 11B, and 11C are diagrams for explaining a method of operating an AV puller in an initial stage of iterative calculation performed by operating a node puller.
FIG. 12 is a PAD for explaining a method of operating an AV puller in an initial stage of iterative calculation performed by operating a node puller.
FIGS. 13A, 13B, 13C, and 13D are diagrams for explaining a method for obtaining a solution of a basic variable while changing a basic expression or an evaluation expression based on given information. FIG.
FIG. 14A is a diagram for explaining a technique for expressing the change amount of the arc normal vector by one variable, and FIG. 14B is a diagram showing various examples of the evaluation formulas. is there.
FIG. 15 is a diagram for explaining the relationship among arcs, nodes, arc normal vectors, and the like.
16 (A), (B), (C), and (D) are diagrams for explaining an adaptive variable of the rubber band tension. FIG.
FIG. 17 is a diagram for explaining a relationship between an arc direction vector, an intermediate arc direction vector, and the like.
FIGS. 18A, 18B, and 18C are diagrams illustrating various embodiments of an image generation apparatus and an information storage medium.
[Explanation of symbols]
10 Skeleton model
12 Joint points (nodes)
14 End point (node)
16 Bone (Arc)
20, 22 Key frame shape
24 Intermediate frame shape
26 Skeleton model
28 Path curve
40, 42 arc direction vector
44 Position on the path curve
46, 48, 50 Middle arc direction vector
52 Arc normal vector after deformation by node puller and AV puller
54 Arc normal vector for keyframe registration
56 arc normal vector
58 Medium Arc Normal Vector
60 control points (positions on the path curve)
62 Rubber Band
64 path curve
66 Control points (positions on the path curve)
68 Rubber Band

Claims (10)

An image generating device for generating a shape of an intermediate frame of a skeleton model by deforming a shape of a key frame of the skeleton model,
Transform the shape of the skeleton model so that the node of the skeleton model with the specified movement path is pulled to a given position on the movement path;
Deform the shape of the skeleton model so that the direction of the arc direction vector of the skeleton model approaches the direction of the intermediate arc direction vector obtained based on the arc direction vector at the key frame,
Includes a shape data generator that deforms the shape of the skeleton model so that the orientation of the arc normal vector of the skeleton model approaches the direction of the intermediate arc normal vector obtained based on the arc normal vector at the key frame An image generation apparatus characterized by the above. In claim 1,
The shape data generator
A skeleton model is represented by a basic variable that contains the coordinates of the nodes of the skeleton model,
A basic expression including an expression defining that the arc length of the skeleton model has a given value and having the basic variable as an unknown, and at least an evaluation expression for uniquely identifying a solution satisfying the basic expression Change one based on given information,
The basic variables are set so that the value of the evaluation formula that satisfies the basic formula and that includes the difference between the direction of the arc direction vector of the skeleton model and the direction of the intermediate arc direction vector is almost minimal, almost maximal, and almost stationary. Seeking a solution
Image generation apparatus characterized by causing deformation of the shape of the skeleton model based on the obtained solutions. In claim 1 or 2,
The shape data generator
A skeleton model is represented by a basic variable that contains the coordinates of the nodes of the skeleton model,
A basic expression including an expression defining that the arc length of the skeleton model has a given value and having the basic variable as an unknown, and at least an evaluation expression for uniquely identifying a solution satisfying the basic expression Change one based on given information,
Basic so that the value of the evaluation formula including the difference between the direction of the arc normal vector of the skeleton model and the direction of the intermediate arc normal vector is almost minimal, almost maximal, and almost stationary. Find the solution of the variable
Image generation apparatus characterized by causing deformation of the shape of the skeleton model based on the obtained solutions. In any one of Claims 1 thru | or 3,
The shape data generator
And a node of the moving path is specified skeleton model, between the control point for controlling the position of the node of the moving path is specified skeleton model, according to the distance between said node and said control point change An image generating apparatus that deforms the shape of a skeleton model by applying a tension to be applied . In any one of Claims 1 thru | or 4,
The shape data generator
A plurality of nodes of the moving path is specified skeleton model, between at least one control point for controlling the position of said plurality of nodes of the moving path is specified skeleton model, said plurality of nodes and the Generating an image characterized by applying a tension that changes according to the distance to at least one control point and deforming the shape of the skeleton model under a condition that the total sum of the tensions is less than or equal to a given value apparatus. In any one of Claims 1 thru | or 5,
The shape data generator
Node moving route is specified skeleton model, as tensioned hit in a given position on the movement path, after deforming the shape of the skeleton model, the direction of the arc direction vector of the skeleton model, keyframes While deforming the shape of the skeleton model so as to approach the direction of the intermediate arc direction vector obtained based on the arc direction vector at
In the initial stage of the first iteration when transforming the shape of the skeleton model so that the node of the skeleton model with the specified movement path is pulled to a given position on the movement path, the arc of the skeleton model An image generating apparatus characterized by performing a calculation to bring the direction of a direction vector closer to the direction of a middle arc direction vector . In any one of Claims 1 thru | or 5,
The shape data generator
After the shape of the skeleton model is deformed so that the direction of the arc direction vector of the skeleton model approaches the direction of the intermediate arc direction vector obtained based on the arc direction vector at the key frame, the skeleton whose movement path is specified Transforming the shape of the skeleton model so that the model node is pulled to a given position on the path of travel ;
Initial stage of second iterative calculation when deforming the shape of the skeleton model so that the direction of the arc direction vector of the skeleton model approaches the direction of the intermediate arc direction vector obtained based on the arc direction vector at the key frame The image generating apparatus according to claim 1, wherein a calculation is performed to pull a skeleton model node to which a movement path is designated to a given position on the movement path . In any one of Claims 1 thru | or 7,
An image generation apparatus, further comprising: an image generation unit configured to generate an image of a skeleton model based on a shape of an intermediate frame of the skeleton model. An information storage medium capable of reading information by a computer and generating a shape of an intermediate frame of a skeleton model by deforming a shape of a key frame of the skeleton model,
Node moving route is specified skeleton model, as pulled by the given position on the movement path, to deform the shape of the skeleton model,
Deform the shape of the skeleton model so that the direction of the arc direction vector of the skeleton model approaches the direction of the intermediate arc direction vector obtained based on the arc direction vector at the key frame ,
As a shape data generator that deforms the shape of the skeleton model so that the direction of the arc normal vector of the skeleton model approaches the direction of the intermediate arc normal vector obtained based on the arc normal vector at the key frame, An information storage medium storing a program for functioning a computer. The image generation apparatus includes a shape data generation unit, deforms the shape of the key frame of the skeleton model, and derives the shape of the intermediate frame of the skeleton model,
The shape data generator
Node moving route is specified skeleton model, as pulled by the given position on the movement path, to deform the shape of the skeleton model,
Deform the shape of the skeleton model so that the direction of the arc direction vector of the skeleton model approaches the direction of the intermediate arc direction vector obtained based on the arc direction vector at the key frame ,
Skeleton model characterized by deforming the shape of the skeleton model so that the direction of the arc normal vector of the skeleton model approaches the direction of the intermediate arc normal vector obtained based on the arc normal vector at the key frame Intermediate frame shape derivation method.

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