JP4726347B2 - Image display device, image display method, information storage medium, and image display program - Google Patents

Description

【００５５】
また、図６において、原点ｏと点Ｐ_dを結ぶ直線とｚ軸とのなす角度をθとすると、この角度θは、次式により表される。
【００５６】
【数２】

【００５７】
本実施形態で使用したレンズ３は、図５に示す点Ｆ（Ｘ，Ｙ）を投影面Ｓに投影する場合に、原点Ｏから点Ｆまでの距離Ｌが、図６に示す角度θに比例する特性を有している。したがって、θ＝０の時にＬ＝０、θ＝π／２の時にＬ＝Ｒになり、その間の任意の角度θに対応する距離Ｌは次式で表すことができる。
【００５８】
Ｌ＝θ／(π／２)×Ｒ
また、図５において、円形フレームバッファ５０上の原点Ｏと点Ｆ（Ｘ，Ｙ）とを結ぶ直線とＸ軸とのなす角度をΦとする。図６において、点Ｐ_d（ｘ_d，ｙ_d，ｚ_d） のｘｙ平面への写像点Ｐ_d′（ｘ_d，ｙ_d，０） と原点ｏを結ぶ直線とｘ軸とのなす角度をφとする。この角度Φと角度φは等しい。ここで、cosφ、sinφは、以下の式で表すことができる。
【００５９】
【数３】

【００６０】
点Ｆ（Ｘ，Ｙ）は、投影面Ｓ上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の各軸の座標値を用いて次式のように表すことができる。
【００６１】
【数４】

【００６２】
したがって、ゲーム空間内に配置された三次元オブジェクトを構成する各ポリゴンの頂点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）がわかっているときに、対応する円形フレームバッファ５０の格納位置を計算するために、座標変換処理部４２は、まず、頂点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）の座標値を上述した（１）〜（３）式に代入することにより、投影面Ｓ上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標を計算する。その後、座標変換処理部４２は、この計算によって得られた点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標値を上述した（４）式および（５）式に代入して、円形フレームバッファ５０上の点Ｆ（Ｘ，Ｙ）を計算する。また、図３および図４に示した中間点Ｐ′あるいはＰ″についても同様の手順により、円形フレームバッファ５０の格納位置が計算される。
【００６３】
このようにして三次元オブジェクトの各ポリゴンの頂点と中間点のそれぞれに対応する円形フレームバッファ５０の格納位置が計算される。特に、このようにして行われる座標変換処理は、三次元オブジェクトのゲーム空間内における位置や視点位置および投影位置を用いて正確に行われているため、視点位置から見たときに理論上歪みのない正確なゲーム画像を球面スクリーン４上に投影するために必要な円形フレームバッファ５０の格納位置を得ることができる。
【００６４】
図７は、円形フレームバッファ５０に格納されたポリゴンの頂点と中間点との対応関係を示す図である。例えば、三角形形状のポリゴンが用いられているものとし、３つの頂点のそれぞれに対応する円形フレームバッファ５０上の頂点をＦ_a、Ｆ_b、Ｆ_cとする。また、隣接する２つの頂点に挟まれた３つの中間点のそれぞれに対応する円形フレームバッファ５０上の中間点をＦ₁、Ｆ₂、Ｆ₃とする。図７に示すように、隣接する２つの頂点とこれらに挟まれた中間点に着目した場合に、これら３点は一直線上には配置されない。
【００６５】
（２−２）投影位置のみを球面スクリーン４の球心からずらした場合
ところで、上述した説明では、視点位置Ｐ_eと投影位置Ｐ_rを球面スクリーン４の球心に一致させた場合を考えたが、実際には、このような位置関係を実現することは難しい。実用的な幾何学的配置を考えた場合に、球面スクリーン４を用いることによる臨場感の高いゲーム画像をプレーヤに見せようとすると、プレーヤの視点位置を球面スクリーン４の球心近傍に設定することが望ましい。したがって、この場合には投影位置Ｐ_rを球面スクリーン４の球心からずらして設定する必要がある。
【００６６】
図８は、投影位置を球面スクリーン４の球心位置からずらした場合の座標変換処理の概要を示す図である。同図に示す座標軸は、上述した図６に示したものと同じである。投影位置Ｐ_r（ｘ_r，ｙ_r，ｚ_r）は、球面スクリーン４の球心以外の所定位置（例えば、プレーヤの頭上等）に設定されている。また、円形フレームバッファ５０については、その原点が投影位置Ｐ_rに対応付けられるため、上述した（２−１）の場合における座標軸の表示（図５参照）と区別するために、原点をＯ′とし、水平方向に沿った軸をＸ′軸、垂直方向に沿った軸をＹ′軸と表すことにする。
【００６７】
上述した（２−１）で説明したように、球面スクリーン４の球心に対応する原点ｏの位置に視点位置Ｐ_eを一致させた場合には、ゲーム空間内の点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）は、投影面Ｓ上における点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）として見えることになる。すなわち、任意の投影位置Ｐ_rから球面スクリーン４上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）に投影してやれば、その点は、視点位置Ｐ_eからはゲーム空間内の点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）として認識されることになる。
【００６８】
したがって、任意の投影位置Ｐ_rに対応して、上述した（２−１）に示した手順と同様な座標変換処理を点Ｐ_dに対して行えば、投影位置Ｐ_rから点Ｐ_dに投影する場合に必要な円形フレームバッファ５０上の点Ｆ′（Ｘ′，Ｙ′）を求めることができる。ただし、投影位置Ｐ_rを原点ｏからずらした場合のｘ′軸、ｙ′軸、ｚ′軸は、元のｘ軸、ｙ軸、ｚ軸を平行移動したものであり、軸回りの回転はないものとする。また、ｘ_r ²＋ｙ_r ²＋ｚ_r ²＜ｒ² を満たす範囲（原点ｏから半径ｒ以下）で投影位置Ｐ_rが設定されているものとする。
【００６９】
図８において、投影位置Ｐ_rと点Ｐ_dを結ぶ直線とｚ′軸とのなす角度をθ′とすると、角度θ′は、次式により表される。
【００７０】
【数５】

【００７１】
また、円形フレームバッファ５０上の原点Ｏ′と点Ｆ′（Ｘ′，Ｙ′）を結ぶ直線とＸ′軸とのなす角度をΦ′とし、図８において、点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）のｘ′ｙ′平面への写像点Ｐ_d″（ｘ_d−ｘ_r，ｙ_d−ｙ_r，０） と点Ｐ_rを結ぶ直線とｘ′軸とのなす角度をφ′とすると、これらの角度Φ′およびφ′は等しくなる。ここで、cosφ′、sinφ′は、以下の式で表すことができる。
【００７２】
【数６】

【００７３】
また、投影面Ｓ上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標値は、上述した（１）〜（３）式に基づいて求められる。
点Ｆ′（Ｘ′，Ｙ′）は、投影面Ｓ上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）および投影位置Ｐ_r（ｘ_r，ｙ_r，ｚ_r）の各座標値を用いて次式のように表すことができる。
【００７４】
【数７】

【００７５】
したがって、ゲーム空間内に配置された三次元オブジェクトを構成する各ポリゴンの頂点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）がわかっているときに、対応する円形フレームバッファ５０上の格納位置を計算するために、座標変換処理部４２は、まず、頂点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）の座標値を上述した（１）〜（３）式に代入することにより、投影面Ｓ上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標を計算する。その後、座標変換処理部４２は、この計算によって得られた点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標値を上述した（７）式および（８）式に代入して、円形フレームバッファ５０上の点Ｆ′（Ｘ′，Ｙ′）の座標を計算する。また、図３および図４に示した中間点Ｐ′あるいはＰ″についても同様の手順により、円形フレームバッファ５０の格納位置が計算される。
【００７６】
このようにして三次元オブジェクトの各ポリゴンの頂点や中間点のそれぞれに対応する円形フレームバッファ５０上の格納位置が計算される。特に、このようにして行われる座標変換処理は、三次元オブジェクトのゲーム空間内における位置や視点位置および投影位置を用いて正確に行われているため、投影位置を任意の位置へ移動した場合においても、視点位置から見たときに理論上歪みのない正確なゲーム画像を球面スクリーン４上に投影するために必要な円形フレームバッファ５０の格納位置を得ることができる。
【００７７】
なお、上述した図８では、説明の都合上、投影位置Ｐ_rはｚ_r≧０の領域に描かれていたが、実際には、レンズ３の投影角が１８０度であるため、球面スクリーン４の全体にゲーム画像を表示するために、投影位置Ｐ_rは、ｚ_r≦０の範囲で設定することが望ましい。
【００７８】
また、本実施形態のレンズ３として用いている魚眼レンズは、一般的には、焦点深度が深いため、フォーカスが合っている範囲が広いという特徴がある。このため、投影位置をずらした場合においても、球面スクリーン４に表示されるゲーム画像は、全体がほぼフォーカスが合っている状態になる。
【００７９】
（２−３）視点位置、投影位置の両方を球面スクリーン４の球心からずらした場合
ところで、上述した（２−２）における説明では、投影位置Ｐ_rが球面スクリーン４の球心位置からずれた位置に設定される場合について説明していたが、実際には、プレーヤの視点位置Ｐ_eも、球面スクリーン４の球心位置からずらしたい場合がある。以下では、視点位置および投影位置の両方を球面スクリーン４の球心位置からずらして設定した場合について説明する。
【００８０】
図９は、視点位置および投影位置を球面スクリーン４の球心位置からずらした場合の座標変換処理の概要を示す図である。同図に示す座標軸は、上述した図６等に示したものと同じである。視点位置Ｐ_e、投影位置Ｐ_rの両者が球面スクリーン４の球心以外の所定位置に設定されている。また、円形フレームバッファ５０については、その原点が投影位置Ｐ_rに対応付けられるため、上述した（２−１）の場合における座標軸の表示（図５参照）と区別するために、上述した（２−２）の場合と同様に、原点をＯ′とし、水平方向に沿った軸をＸ′軸、垂直方向に沿った軸をＹ′軸と表すことにする。
【００８１】
図９において、ゲーム空間内の点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）と視点位置Ｐ_e（ｘ_e，ｙ_e，ｚ_e）を結ぶ直線は、以下の式で表される。
【００８２】
【数８】

【００８３】
また、投影面Ｓに対応する半球は、以下に示す球の方程式で表される（ただし、ｚ≧０）。
ｘ² ＋ｙ² ＋ｚ² ＝ｒ² …（10）
視点位置Ｐ_eからゲーム空間内の点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）を見たときに、この点Ｐ_p に対応する投影面Ｓ上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標は、上述した（９）式に示す直線と（10）式に示す半球との交点の座標を計算することにより求めることができる。
【００８４】
具体的には、（９）式を変形することにより、以下の各式が導かれる。
【００８５】
【数９】

【００８６】
（11）式および（12）式を（10）式に代入すると、次式が得られる。
((ｘ_p−ｘ_e)²＋(ｙ_p−ｙ_e)²＋(ｚ_p−ｚ_e)²)×ｘ²
−２×((ｙ_p−ｙ_e)×(ｘ_e×ｙ_p−ｙ_e×ｘ_p)＋(ｚ_p−ｚ_e)
×(ｘ_e×ｚ_p−ｚ_e×ｘ_p))×ｘ
＋((ｘ_e×ｙ_p−ｙ_e×ｘ_p)²＋(ｘ_e×ｚ_p−ｚ_e×ｘ_p)²
−ｒ²×(ｘ_p−ｘ_e)²) ＝０ …（13）
ここで、
ａ＝(ｘ_p−ｘ_e)²＋(ｙ_p−ｙ_e)²＋(ｚ_p−ｚ_e)²
ｂ＝(ｙ_p−ｙ_e)×(ｘ_e×ｙ_p−ｙ_e×ｘ_p)＋(ｚ_p−ｚ_e)×(ｘ_e×ｚ_p−ｚ_e×ｘ_p)
ｃ＝(ｘ_e×ｙ_p−ｙ_e×ｘ_p)²＋(ｘ_e×ｚ_p−ｚ_e×ｘ_p)²−ｒ²×(ｘ_p−ｘ_e)²
とおくと、上述した（13）式の解は、次式のように表される。
【００８７】
【数１０】

【００８８】
したがって、ゲーム空間内の点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）と視点位置Ｐ_e（ｘ_e，ｙ_e，ｚ_e）の各座標値を用いて（14）式を計算することにより、投影面Ｓ上の点Ｐ_dのｘ座標値（ｘ_d）が求められる。また、（14）式を上述した（11）式および（12）式に代入することにより、点Ｐ_dのｙ座標値（ｙ_d）、ｚ座標値（ｚ_d）が求められる。
【００８９】
実際に（14）式を用いてｘ座標値を計算すると、２つの解ｘ₁、ｘ₂が得られる。これらの２つの解のうち、一方の解ｘ₁を（11）式および（12）式にそれぞれ代入することにより、対応するｙ座標値（ｙ₁）およびｚ座標値（ｚ₁）が得られる。この結果、点Ｐ_dの座標値は（ｘ₁，ｙ₁，ｚ₁）となる。また、他方の解ｘ₂を（11）式および（12）式にそれぞれ代入することにより、対応するｙ座標値（ｙ₂）およびｚ座標値（ｚ₂）が得られる。この結果、点Ｐ_dの座標値は（ｘ₂，ｙ₂，ｚ₂）となる。これら２つの座標値のうちで、必要な解としては、点Ｐ_eから各座標値（ｘ₁，ｙ₁，ｚ₁）および（ｘ₂，ｙ₂，ｚ₂）の点へ向かう２本のベクトルのうちで、視点位置Ｐ_eから点Ｐ_p へ向かうベクトルと同じ向きを有するベクトルに対応する座標値が選択される。
【００９０】
このようにして、点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標値を求めることができる。その後、この座標値を上述した（７）式および（８）式に代入することにより、投影位置Ｐ_rから投影面Ｓ上の点Ｐ_dに画像を投影する際に必要な円形フレームバッファ５０上の点Ｆ′（Ｘ′，Ｙ′）の座標を求めることができる。
【００９１】
したがって、ゲーム空間内に配置された三次元オブジェクトを構成する各ポリゴンの頂点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）がわかっているときに、対応する円形フレームバッファ５０上の格納位置を計算するために、座標変換処理部４２は、まず、頂点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）の座標値と視点位置Ｐ_e（ｘ_e，ｙ_e，ｚ_e）の座標値を用いて上述した（14）式等を計算することにより、投影面Ｓ上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標を計算する。その後、座標変換処理部４２は、この計算によって得られた点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標値を上述した（７）式および（８）式に代入して、円形フレームバッファ５０上の点Ｆ′（Ｘ′，Ｙ′）の座標を計算する。また、図３および図４に示した中間点Ｐ′あるいはＰ″についても同様の手順により、円形フレームバッファ５０の格納位置が計算される。
【００９２】
このようにして三次元オブジェクトの各ポリゴンの頂点や中間点のそれぞれに対応する円形フレームバッファ５０上の格納位置が計算される。特に、このようにして行われる座標変換処理は、三次元オブジェクトのゲーム空間内における位置や視点位置および投影位置を用いて正確に行われているため、視点位置や投影位置を任意の位置へ移動した場合においても、視点位置から見たときに理論上歪みのない正確なゲーム画像を球面スクリーン４上に投影するために必要な円形フレームバッファ５０の格納位置を得ることができる。
【００９３】
なお、上述した図９においても、説明の都合上、投影位置Ｐ_rはｚ_r≧０の領域に描かれていたが、上述した（２−２）の場合と同様の理由により、実際の投影位置Ｐ_rは、ｚ_r≦０の範囲で設定することが望ましい。
（３）輪郭線算出処理
図１０は、輪郭線算出部４３によってポリゴンの輪郭線算出処理の概要を示す図である。図１０において、ポリゴンに含まれる２つの頂点の円形フレームバッファ５０上の写像をＦ_a（Ｘ_a，Ｙ_a）、Ｆ_b（Ｘ_b，Ｙ_b）とし、これらに挟まれた中間点をＦ₁（Ｘ₁，Ｙ₁）とする。また、これら３点Ｆ_a、Ｆ₁、Ｆ_bを通る円の中心をＥ（Ｘ₀，Ｙ₀）、この円の半径をＲ１とする。
【００９４】
円の中心をＥ（Ｘ₀，Ｙ₀）とする円の方程式は、
（Ｘ−Ｘ₀）² ＋（Ｙ−Ｙ₀）² ＝Ｒ１² …（15）
となる。この円の方程式に、３点Ｆ_a、Ｆ₁、Ｆ_bの座標値を代入することにより、以下の連立方程式が得られる。
【００９５】
（Ｘ_a−Ｘ₀）² ＋（Ｙ_a−Ｙ₀）² ＝Ｒ₁ ²
（Ｘ_b−Ｘ₀）² ＋（Ｙ_b−Ｙ₀）² ＝Ｒ₁ ²
（Ｘ₁−Ｘ₀）² ＋（Ｙ₁−Ｙ₀）² ＝Ｒ₁ ²
この連立方程式を解くことにより、
Ｙ₀＝（ｉ×ｊ−ｇ×ｈ）／（２×（Ｙ_a×ｇ−Ｙ₁×ｇ−Ｙ₁×ｉ＋Ｙ_b×ｉ））
Ｘ₀＝（ｈ＋２×Ｙ_a×Ｙ₀−２×Ｙ₁×Ｙ₀）／ｉ
Ｒ₁＝√（（Ｘ_a−Ｘ₀）² ＋（Ｙ_a−Ｙ₀）² ）
が得られる。ここで、
ｇ＝−２×Ｘ₁＋２×Ｘ_b
ｈ＝−Ｘ_a ² ＋Ｘ₁ ² −Ｙ_a ² ＋Ｙ₁ ²
ｉ＝−２×Ｘ_a＋２×Ｘ₁
ｊ＝−Ｘ₁ ² ＋Ｘ_b ² −Ｙ₁ ² ＋Ｙ_b ²
とする。
【００９６】
このようにして、輪郭線算出部４３は、円の方程式を決定することにより、３点Ｆ_a、Ｆ₁、Ｆ_bを通る輪郭線の形状（円弧形状）を決定する。
（４）テクスチャマッピング処理
図１１は、テクスチャマッピング処理の概要を示す図である。図１１に示すように、本実施形態では、ポリゴンの３つの頂点のそれぞれに対応した頂点Ｆ_a、Ｆ_b、Ｆ_cのそれぞれをつなぐ各輪郭線は、円弧によって近似されており、これらの内部が、１つのポリゴンに対応して画像情報を書き込む描画領域となる。
【００９７】
テクスチャマッピング処理部４４は、この描画領域の上端（Ｙ_max）から下端（Ｙ_min）まで順番にＸ方向のスキャンを行い、円弧形状で近似された輪郭線に挟まれた領域に含まれる各画素の画像情報を生成する。
この画像情報の生成は、一般的なテクスチャマッピングの手法を用いて行われる。すなわち、別に用意されたテクスチャデータ（ポリゴンに対応させるテクスチャの画像情報）の中から、ポリゴン内の描画位置に対応するものを取得することにより行われる。
【００９８】
ところで、従来のテクスチャマッピング処理では、フレームバッファ上のポリゴン形状も多角形形状を有していたため、ポリゴン内の任意の描画位置に対応するテクスチャ座標を求める際に、単純な直線補間演算を行うだけでよかった。しかし、本実施形態では、円形フレームバッファ５０上のポリゴン形状は、輪郭線が円弧形状で近似されているため、任意の描画位置に対応するテクスチャ座標を単純な直線補間演算によって求めることができない。
【００９９】
図１２は、テクスチャマッピング処理部４４によって円形フレームバッファ５０上の任意の描画位置に対応するテクスチャ座標を求める処理手順の概要を示す図である。
まず、テクスチャマッピング処理部４４は、画像情報を生成しようとする円形フレームバッファ５０上の描画点Ｆ′の座標を決定した後に、ゲーム空間に配置されたポリゴン内の対応位置Ｐ_p′ を計算する。次に、テクスチャマッピング処理部４４は、このポリゴン内の対応位置Ｐ_p′ に基づいてテクスチャ座標Ｔを計算する。ゲーム空間内のポリゴンは、３つの頂点を直線で囲んだ三角形形状を有しているため、このポリゴン内の特定位置Ｐ_p′ に対応するテクスチャ座標Ｔは、単純な直線補間演算により求めることができる。
【０１００】
このように、本実施形態のゲームシステムでは、複数のポリゴンによって構成された三次元オブジェクトの画像情報を円形フレームバッファ５０に書き込む際に、多角形で表されたポリゴンの輪郭線形状を円弧で近似している。したがって、ゲーム空間内の三次元オブジェクトの形状を正確に再現することができ、球面スクリーン４に投影される画像の歪みを低減することができる。
【０１０１】
なお、本発明は上記実施形態に限定されるものではなく、本発明の要旨の範囲内において種々の変形実施が可能である。例えば、上述した実施形態では、（２−１）視点位置、投影位置の両者を球面スクリーン４の球心位置に一致させる場合、（２−２）投影位置のみをずらして設定する場合、（２−３）視点位置、投影位置の両者をずらして設定する場合のそれぞれについて、座標変換処理の方法を説明したが、これらを応用することにより、視点位置のみを球面スクリーン４の球心からずらして設定した場合においても、歪みの少ないゲーム画像を表示するための画像情報を生成することができる。
【０１０２】
具体的には、上述した（２−３）に示した視点位置、投影位置の両者をずらして設定する場合において説明したように、ゲーム空間内に配置された各三次元オブジェクトを構成する各ポリゴンの頂点座標を点Ｐ_p（ｘ_p，ｙ_p，ｚ_p）として、これらの座標値と視点位置Ｐ_e（ｘ_e，ｙ_e，ｚ_e）の座標値を用いて、上述した（14）式等を計算することにより、投影面Ｓ上の点Ｐ_d（ｘ_d，ｙ_d，ｚ_d）の座標値を求める。その後、これらの座標値に基づいて、上述した（４）式および（５）式を計算することにより、円形フレームバッファ５０上の格納位置を求めればよい。
【０１０３】
また、投影位置Ｐ_rを球面スクリーン４の球心位置からずらして設定する場合（上述した（２−２）および（２−３）の場合など）には、投影位置Ｐ_rから球面スクリーン４上の位置Ｐ_dまでの距離を考慮して、円形フレームバッファ５０に格納する画像情報に対して明るさ補正を行うようにしてもよい。
【０１０４】
図１３は、明るさ補正を行う変形例について説明する図であり、球面スクリーン４の断面を簡略化した様子が示されている。投影位置Ｐ_rが球面スクリーン４の球心位置Ｑからずれている場合には、投影位置Ｐ_rから球面スクリーン４上の任意の位置までの距離は等距離ではなくなる。例えば、図１３に示すように、投影位置Ｐ_rから球面スクリーン４上のある点Ｐ_d1までの距離Ｄ1 と別の点Ｐ_d2までの距離Ｄ2 とは大きく異なることになる。投影位置Ｐ_rから照射された光（ゲーム画像を構成する各画素に対応する光）の強度、すなわち明るさは、距離の２乗に反比例するため、球面スクリーン４上に表示されるゲーム画像の明るさには偏りが生じることとなる。
【０１０５】
したがって、例えば、投影位置Ｐ_rから球面スクリーン４上の位置までの距離の２乗に反比例する所定の係数を設定し、これを円形フレームバッファ５０に格納される画像情報に対して乗算すれば、画像情報の明るさの補正を行うことができる。これにより、ゲーム画像の明るさの偏りを軽減し、より質の高いゲーム画像を投影することができるようになる。
【０１０６】
また、より簡便な方法としては、例えば、投影位置Ｐ_rから球面スクリーン４上の位置までの距離に反比例する所定の係数を設定し、これを円形フレームバッファ５０に格納される画像情報に対して乗算するようにしてもよい。この場合には、ゲーム画像の明るさの偏りをある程度軽減することができるとともに、明るさ補正に要する計算量を低減することができる。また、投影角度も投影位置から球面スクリーン４上に投影された位置までの距離と所定の相関を有するため、距離の代わりに投影角度を用いて明るさ補正を行うようにしてもよい。なお、上述したような明るさ補正処理は、画像処理部４０内のシェーディング処理部４５によって行うことができる。
【０１０７】
また、上述した実施形態では、曲面スクリーンの一種である球面スクリーンに画像を投影する場合を説明したが、ゲーム空間内に配置された三次元オブジェクトを視点位置から見たときに、曲面スクリーン上に投影された位置が計算によって得られる場合には、球面以外の曲面スクリーンに画像を表示する場合に本発明を適用することができる。例えば、楕円を回転させた回転体を半分に切断した投影面を有する曲面スクリーンに画像を投影するようにしてもよい。このような曲面スクリーンを用いた場合であっても、ゲーム空間内に配置された三次元オブジェクトの位置情報に基づいてこの曲面スクリーン上に投影された位置を算出し、さらに、この算出位置に画像を投影するために必要な円形フレームバッファ５０上の格納位置を計算することにより、ほぼ歪みのない画像表示を行うことができる。
【０１０８】
また、上述した実施形態では、ポリゴンの輪郭線を円の方程式を用いて近似するようにしたが、それ以外の曲線を用いて近似するようにしてもよい。例えば、スプライン曲線やその他の関数を用いて近似する場合が考えられる。これらの場合には、例えば、Ｎ個の点を特定することにより近似関数の各係数を決定することができるものとすると、２つの頂点を除く（Ｎ−２）個の中間点をゲーム空間内で計算すればよい。これらの中間点に対応する円形フレームバッファ５０の格納位置を求めることにより、上述した実施形態と同様の手順で近似関数を求めることができる。
【０１０９】
また、上述した実施形態では、本発明をゲームシステムに適用した場合の例について説明してきたが、三次元オブジェクトを用いた三次元画像を曲面スクリーンに投影する各種の装置に本発明を適用することができる。例えば、三次元オブジェクトを用いてプレゼンテーションを行う装置や、フライトシミュレータ等の各種のシミュレータ装置などに本発明を適用することができる。
【０１１０】
【発明の効果】
上述したように、本発明によれば、フレームバッファ上のポリゴンの輪郭線を直線形状ではなく曲線形状で近似することにより、曲面スクリーンに投影された三次元オブジェクトを構成する各ポリゴンの輪郭線を、歪みの少ないほぼ直線形状にすることができる。
【図面の簡単な説明】
【図１】一実施形態のゲームシステムの構成を示す図である。
【図２】ゲームシステムの動作手順の概要を示す流れ図である。
【図３】中間点算出処理の概要を示す図である。
【図４】中間点算出処理の概要を示す図である。
【図５】円形フレームバッファの描画範囲を示す図である。
【図６】座標変換処理の概要を示す図である。
【図７】円形フレームバッファ上のポリゴンの頂点と中間点との対応関係を示す図である。
【図８】投影位置のみを球面スクリーンの球心からずらした場合の座標変換処理の概要を示す図である。
【図９】視点位置および投影位置を球面スクリーンの球心からずらした場合の座標変換処理の概要を示す図である。
【図１０】ポリゴンの輪郭線算出処理の概要を示す図である。
【図１１】テクスチャマッピング処理の概要を示す図である。
【図１２】円形フレームバッファ上の任意の描画位置に対応するテクスチャ座標を求める処理手順の概要を示す図である。
【図１３】明るさ補正を行う変形例について説明する図である。
【符号の説明】
１ ゲーム装置
２ プロジェクタ
３ レンズ
４ 球面スクリーン
１０ 入力装置
２０ ゲーム演算部
２２ 入力判定部
２４ イベント処理部
２６ ゲーム空間演算部
３０ 情報記憶媒体
４０ 画像処理部
４１ 中間点算出部
４２ 座標変換処理部
４３ 輪郭線算出部
４４ テクスチャマッピング処理部
４５ シェーディング処理部
５０ 円形フレームバッファ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an image display device, an image display method, an information storage medium, and an image display program that project an image onto a curved screen through a wide-angle lens.
[0002]
[Prior art]
Conventionally, an image display apparatus that projects an image on a non-planar screen is known. For example, Japanese Patent Application Laid-Open Nos. 9-81785 and 3-82493 disclose various image display devices that project an image on a non-planar screen and correct distortion of the projected image. When an image created for projection on a flat screen is projected on a non-planar screen as it is, a distorted image is displayed. For this reason, in the above-described image display device, in consideration of distortion at the time of display, by generating an image distorted in the opposite direction in advance so as to obtain normal display contents as a result of distortion, Display distortion is corrected.
[0003]
[Problems to be solved by the invention]
By the way, in the conventional image display apparatus described above, when the image is distorted into a convex shape by projecting onto a non-planar screen, an image distorted into a concave shape is generated in advance, and as a result, the distortion on the non-planar screen is generated. Is corrected. However, with this method, distortion cannot be corrected sufficiently when a three-dimensional object arranged in a three-dimensional space is displayed on a non-planar screen. For example, if the projected position of the image is different from the viewpoint position, the degree of distortion applied to the generated image differs depending on the perspective of the three-dimensional object. Therefore, simply distorting the generated image results in a projected image. The distortion cannot be removed.
[0004]
In particular, although it is considered that the distortion correction of the two-dimensional image and the distortion correction of the three-dimensional image are essentially different, the image display device disclosed in the above-mentioned publication simply discloses a technique for correcting the distortion of the two-dimensional image. However, there is a problem that the distortion of each polygon shape that occurs when a three-dimensional object composed of a plurality of objects is projected onto the screen cannot be removed sufficiently only by using these methods. .
[0005]
The present invention was created in view of the above points, and an object of the present invention is to reduce distortion of each polygon shape when displaying an image of a three-dimensional object composed of polygons on a curved screen. An object is to provide an image display device, an image display method, an information storage medium, and an image display program.
[0006]
[Means for Solving the Problems]
  In order to solve the above-described problem, an image display device of the present invention includes a frame buffer, a projection device, and a projection device for projecting an image of a three-dimensional object arranged in a virtual three-dimensional space onto a curved screen through a wide-angle lens. Outline calculating means, image information storing meansCoordinate calculation meansIt has. In the frame buffer, the position to be projected on the curved screen corresponds to the storage position of the image information. The projection device irradiates an image corresponding to the image information stored in the frame buffer toward the wide-angle lens. The contour calculation means approximates the shape of the polygon outline on the frame buffer corresponding to the polygon outline constituting the three-dimensional object with a curve. The image information storage means stores the image information of the corresponding three-dimensional object in the storage position of the frame buffer surrounded by the outline approximated by the outline calculation means.The coordinate calculation means calculates the storage position of the frame buffer in correspondence with the position on the curved screen when the three-dimensional object is viewed from a predetermined viewpoint position. The coordinate calculation means calculates the storage position based on the position information of the three-dimensional object in the virtual three-dimensional space and the projection position corresponding to the viewpoint position and the position of the wide-angle lens. Further, the viewpoint position and the projection position are made different.When a 3D object is composed of polygons and the drawing process is performed on the frame buffer with the outline of each polygon as a straight line, the image on the curved screen is distorted. Will be distorted and become non-linear. In the present invention, by approximating the polygon outline on the frame buffer with a curved shape instead of a linear shape, the outline of each polygon constituting the three-dimensional object projected on the curved screen is substantially linear with little distortion. Can be.
[0007]
  Moreover, the image display device of the present invention includes:Midpoint calculation meansIt is desirable to have more. The midpoint calculation means connects two adjacent vertices that are included in the polygon.On a straight lineThe coordinates of the intermediate point in the virtual three-dimensional space located at is calculated.Also mentioned aboveThe coordinate calculation means calculates the storage position of the frame buffer corresponding to each of the two vertices and intermediate points in the virtual three-dimensional space. Then, the above-described contour line calculation means determines the shape of a curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point. In this way, by performing curve approximation, the outline of each polygon constituting the actually projected three-dimensional object is brought close to a shape passing through a plurality of points arranged on the straight line, that is, a straight line with less distortion. be able to.
[0008]
Further, when it is necessary to designate N points in order to determine the shape of the curve described above, it is desirable that the midpoint calculation means calculates at least (N−2) midpoint coordinates. In this way, since two vertices and (N−2) intermediate points are specified, an accurate curve shape with respect to the polygon outline can be obtained.
[0009]
In particular, the curve described above is a circular arc, and it is desirable to calculate the coordinates of one intermediate point by the intermediate point calculating means. When curve approximation is performed using arcs, it is only necessary to add one intermediate point, so the amount of calculation necessary to perform curve approximation and the amount of calculation necessary to calculate the intermediate point are reduced. be able to.
[0010]
In addition, the above-described intermediate point calculation means calculates the angle formed by two line segments connecting the projection position corresponding to the position of the wide-angle lens and each of the two vertices to 2 etc. by the line segment connecting the projection position and the intermediate point. It is desirable to set an intermediate point so that it can be divided. By using such an intermediate point, the position of the intermediate point on the frame buffer corresponding to the intermediate point used for curve approximation is located at approximately the same distance from each vertex on the frame buffer corresponding to each vertex. The accuracy of curve approximation can be increased.
[0011]
Moreover, it is desirable that the wide-angle lens described above is a fish-eye lens. By using a fisheye lens, a projection angle of approximately 180 ° can be realized. Therefore, by displaying an image projected in this way on a curved screen, it is possible to project a realistic image without distortion. it can.
[0012]
  Also,As mentioned above,The coordinate calculation means associates the storage position of the frame buffer with the position on the curved screen when the three-dimensional object is viewed from a predetermined viewpoint position.I'm calculating.When viewing a 3D object from the viewpoint position, the position on the curved screen that corresponds to the actual position is calculated, and the storage position of the frame buffer required to project the image at this position is calculated. An accurate image without distortion can be projected.
[0013]
  Also,As mentioned above,The coordinate calculation means calculates the position information of the three-dimensional object in the virtual three-dimensional space and the viewpoint position.andProjection position corresponding to the position of the wide-angle lensWhenBased on the frame buffer storage locationI'm calculating.The three-dimensional shape and the display position of the three-dimensional object are determined by the relative state of the three-dimensional object in the virtual three-dimensional space with positional information, the viewpoint position, and the projection position. For this reason, an image with almost no distortion can be projected by calculating the storage position of the frame buffer based on the position information.
[0014]
  Also,As mentioned above,Viewpoint position and projection positionIt is different.Actually, the image on the curved screen cannot be seen from the projection position. Therefore, by performing distortion correction on the assumption that the viewpoint position and the projection position are different, it is possible to project an image without distortion under conditions that are realistic.
[0015]
In addition, when the projection position is set to be shifted from the center position of the curved screen, the above-described image information storage means considers the distance between the projection position and the position to be projected on the curved screen, and stores it in the frame buffer. It is desirable to perform brightness correction on the stored image information. If the projection position is deviated from the center position, even if an image with uniform brightness is projected, the brightness of the projected image is biased. Therefore, by performing the brightness correction in consideration of the distance, it is possible to obtain an image with almost uniform brightness without the brightness bias.
[0016]
Further, the image information storage means described above performs texture mapping processing for specifying image information included in the texture data corresponding to the polygon and storing it in the frame buffer, and the texture coordinates corresponding to the storage position on the frame buffer are obtained. In order to obtain the coordinates, it is desirable to obtain the coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position and determine the texture coordinates corresponding to the coordinates. If the outline of the polygon in the frame buffer becomes a curved shape, the correspondence between the arbitrary position inside the polygon and the texture coordinates cannot be obtained, but the corresponding position in the polygon having the polygon shape in the virtual three-dimensional space By calculating, it becomes easy to take this correspondence, and necessary image information can be read out.
[0017]
In addition, it is desirable to further include object calculation means for calculating the coordinates of the vertices of the polygons in the virtual three-dimensional space at predetermined intervals, and to repeat the storage processing of the image information in the frame buffer at the predetermined intervals. When a three-dimensional object moves in a virtual three-dimensional space or the viewpoint that is the basis for perspective projection transformation moves, the coordinates of the three-dimensional object are calculated at predetermined intervals, and an image without distortion is generated each time. Therefore, it is possible to project a distortion-free moving image on a curved screen in a game or presentation using a three-dimensional object.
[0018]
  In addition, the image display method of the present invention uses the positional information in the virtual three-dimensional space of each vertex included in the polygon constituting the three-dimensional object.By calculation by game space calculation meansBased on the acquired first step and the acquired position information, the shape of the polygon outline on the frame buffer corresponding to the polygon outline is determined.By contour calculation meansThe second step of approximating with a curve and the image information at the storage position of the frame buffer surrounded by the approximated outlineBy image information storage meansThe third step of storing and reading out the image information stored in the frame buffer and passing it through the wide-angle lens onto the curved screenBy projection deviceAnd a fourth step of projecting.In addition, the coordinate calculation means calculates the storage position of the frame buffer in correspondence with the position on the curved screen when the three-dimensional object is viewed from a predetermined viewpoint position. The storage position is calculated based on the position information in the three-dimensional space and the projection position corresponding to the viewpoint position and the position of the wide-angle lens, and the viewpoint position and the projection position are made different.
[0019]
The information storage medium of the present invention includes a program for executing these first step to fourth step.
In addition, the image display program of the present invention performs these first to fourth steps on a computer to project an image of a three-dimensional object arranged in a virtual three-dimensional space onto a curved screen through a wide-angle lens. It is for execution.
[0020]
By executing the image display method of the present invention, or by executing the program stored in the information storage medium of the present invention or the image display program of the present invention, the outline of the polygon on the frame buffer is not linear. Since it is approximated by a curved shape, the outline of each polygon constituting the three-dimensional object projected on the curved screen can be made into a substantially straight shape with little distortion.
[0021]
  Also, two adjacent vertices that are included in the polygon are connected.On a straight lineThe coordinates of the intermediate point in the virtual three-dimensional space located atBy way of midpoint calculation meansThe fifth step of calculating, and the storage position of the frame buffer corresponding to each of the two vertices and intermediate points in the virtual three-dimensional spaceBy coordinate calculation meansA sixth step to calculate is inserted before the second step described above, and in the second step, the shape of the curve passing through each point on the frame buffer corresponding to each of the two vertices and intermediate points is It is desirable to decide. In this way, by performing curve approximation, the outline of each polygon constituting the actually projected three-dimensional object is brought close to a shape passing through a plurality of points arranged on the straight line, that is, a straight line with less distortion. be able to.
[0022]
Further, the curve used for the approximation process in the second step described above is an arc, and it is desirable that this approximation process is performed using the coordinates of one intermediate point. When curve approximation is performed using arcs, it is only necessary to add one intermediate point, so the amount of calculation necessary to perform curve approximation and the amount of calculation necessary to calculate the intermediate point are reduced. be able to.
[0023]
  Also,As described above, the coordinate calculation means isCorresponding to the position on the curved screen when viewing the 3D object from the specified viewpoint position, the storage position of the frame buffer isI'm calculating.When viewing a 3D object from the viewpoint position, the position on the curved screen that corresponds to the actual position is calculated, and the storage position of the frame buffer required to project the image at this position is calculated. An accurate image without distortion can be projected.
[0024]
  Also,As described above, the coordinate calculation means isBased on the position information of the 3D object in the virtual 3D space and the projection position corresponding to the viewpoint position or the position of the wide-angle lens, the storage position of the frame buffer is determined.I'm calculating.The three-dimensional shape and the display position of the three-dimensional object are determined by the relative state of the three-dimensional object in the virtual three-dimensional space with positional information, the viewpoint position, and the projection position. For this reason, an image with almost no distortion can be projected by calculating the storage position of the frame buffer based on the position information.
[0025]
  In addition, when the projection position is set to be shifted from the center position of the curved screen, the brightness correction is performed on the image information stored in the frame buffer in consideration of the distance between the projection position and the position to be projected on the curved screen. TheBy image information storage meansIt is desirable to insert the seventh step to be performed before the fourth step. By performing the brightness correction in consideration of the distance, it is possible to obtain an image with almost uniform brightness by eliminating the unevenness of brightness.
[0026]
Further, in the fourth step described above, the texture mapping process is performed in which the image information included in the texture data corresponding to the polygon is specified and stored in the frame buffer, and the texture coordinates corresponding to the storage position on the frame buffer are determined. In order to obtain the coordinates, it is desirable to obtain the coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position and determine the texture coordinates corresponding to the coordinates. If the outline of the polygon in the frame buffer becomes a curved shape, the correspondence between the arbitrary position inside the polygon and the texture coordinates cannot be obtained, but the corresponding position in the polygon having the polygon shape in the virtual three-dimensional space By calculating, it becomes easy to take this correspondence, and necessary image information can be read out.
[0027]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, a game system according to an embodiment to which the present invention is applied will be described with reference to the drawings.
FIG. 1 is a diagram showing a configuration of the game system of the present embodiment. The game system shown in the figure includes a game apparatus 1, a projector 2, a lens 3, and a spherical screen 4.
[0028]
The game apparatus 1 performs various game calculations in response to operations by the player and generates image information for displaying a game image corresponding to the progress of the game. The projector 2 irradiates the spherical screen 4 with a game image based on the image information generated by the game apparatus 1. The lens 3 projects the game image emitted from the projector 2 onto the spherical screen 4. In this embodiment, a wide-angle lens, more specifically, a fish-eye lens with a projection angle of approximately 180 ° is used as the lens 3. The spherical screen 4 is a kind of curved screen and has a hemispherical projection surface, and a game image irradiated from the projector 2 and passed through the lens 3 is projected inside.
[0029]
Next, a detailed configuration of the game apparatus 1 will be described. The game device 1 shown in FIG. 1 includes an input device 10, a game calculation unit 20, an information storage medium 30, an image processing unit 40, and a circular frame buffer 50.
The input device 10 is for a player to input various instructions to the game apparatus 1 and includes various operation keys, operation levers, and the like corresponding to the type of game performed in the game apparatus 1. Yes. For example, the input device 10 provided for playing a drive game includes a handle, an accelerator, a brake, a shift lever, and the like.
[0030]
The game calculation unit 20 performs predetermined game calculations necessary for the progress of the game. The game calculation unit 20 includes an input determination unit 22, an event processing unit 24, and a game space calculation unit 26. The game calculation unit 20 is realized by executing a predetermined game program using a semiconductor memory such as a CPU, ROM, or RAM.
[0031]
The input determination unit 22 determines an operation state of a handle, an accelerator, a brake, or the like provided in the input device 10 and outputs a signal corresponding to the operation state to the event processing unit 24. The event processing unit 24 performs processes necessary for the progress of the game, such as occurrence of various events and branch determination corresponding to the progress of the game. The game space calculation unit 26 calculates position information of various three-dimensional objects existing in the game space that is a virtual three-dimensional space. Each of the three-dimensional objects in this embodiment is composed of a plurality of polygons, and the game space calculation unit 26 calculates the vertex coordinates of each polygon constituting the three-dimensional object.
[0032]
The information storage medium 30 is for storing a program and data for operating the game apparatus 1 having a function as a computer. Specifically, the information storage medium 30 stores a game program executed by the game calculation unit 20, data necessary for displaying a game image (texture data for texture mapping, etc.), and an image display program. The information storage medium 30 is realized by a CD-ROM, DVD-ROM, hard disk device, semiconductor memory, or the like.
[0033]
The image processing unit 40 receives the vertex coordinates of each polygon calculated by the game space calculation unit 26 in the game calculation unit 20, and displays an image on the circular frame buffer 50 in order to display an image on the spherical screen 4. Process to store information. The image processing unit 40 includes an intermediate point calculation unit 41, a coordinate conversion processing unit 42, an outline calculation unit 43, a texture mapping processing unit 44, and a shading processing unit 45. Normally, the image processing unit 40 is realized by using a dedicated graphic LSI, DSP, or the like. However, the CPU that realizes the game calculation unit 20 has high performance and has a sufficient processing capacity. In this case, the CPU may cause the image processing unit 40 to perform processing.
[0034]
The intermediate point calculation unit 41 receives the vertex coordinates of each polygon calculated by the game space calculation unit 26, and calculates the coordinates of the intermediate point on a straight line connecting two adjacent vertices.
The coordinate conversion processing unit 42 calculates which position on the spherical screen 4 the three-dimensional object actually corresponds to when viewing the three-dimensional object from the viewpoint position, and projects an image on the spherical screen 4. The storage position on the circular frame buffer 50 necessary for the calculation is calculated. Specifically, the coordinate conversion processing unit 42 receives the vertex coordinates of the polygon calculated by the game space calculation unit 26 and the coordinates of the intermediate point calculated by the intermediate point calculation unit 41. The coordinate conversion processing unit 42 calculates coordinates on the spherical screen 4 corresponding to each of these vertices and intermediate points, and further calculates the storage position of the circular frame buffer 50 using this calculation result.
[0035]
The contour calculation unit 43, based on the calculation result of the coordinate conversion processing unit 42, the shape of the polygonal contour on the circular frame buffer 50 corresponding to the contour of each polygon (each side of the polygon having a polygonal shape). Is calculated. In general, each polygon existing in the game space has a polygonal shape (for example, a triangular shape) in which each side is a straight line. However, since the shape of each side is distorted when projected onto the curved screen 4, the shape of each side on the circular frame buffer 50 is not a straight line but a curved line. Therefore, as in general 3D image processing, after calculating the storage position on the frame buffer for each vertex of the polygon, the shape of each side of the polygon is actually obtained by simply performing the texture mapping process. Will deviate from the shape. For this reason, in the present embodiment, each side of each polygon displayed on the spherical screen 4 from a predetermined viewpoint position is approximated by approximating the contour shape of each polygon on the circular frame buffer 50 with a curve. The device has been devised so as to be almost straight when looking at the shape. Specifically, the contour calculation unit 43 calculates the 3 based on the coordinates of the two adjacent vertices in each polygon and the midpoint existing on the straight line having the two vertices at both ends in the game space. The arc shape passing through the point is calculated. Hereinafter, each polygon shape in the game space will be described as a triangle.
[0036]
After the contour shape of each polygon on the circular frame buffer 50 is calculated by the contour line calculation unit 43, the texture mapping processing unit 44 pastes texture data inside the polygon defined by these contour lines ( Texture mapping process). Further, the shading processing unit 45 performs a shading correction process on the result of the texture mapping process. In this way, image information of each pixel included in a region (corresponding region on the circular frame buffer 50) surrounded by a plurality of (for example, three) vertex coordinates constituting each polygon is obtained. For example, color information represented by RGB data is used as image information.
[0037]
The circular frame buffer 50 stores the image information obtained by the image processing unit 40. Each storage position of the circular frame buffer 50 corresponds to each position to be projected on the spherical screen 4, and is specified by this image information by storing the image information at a predetermined position of the circular frame buffer 50. A color image is projected onto a corresponding position on the spherical screen 4.
[0038]
The projector 2 described above is a projection device, the intermediate point calculation unit 41 is an intermediate point calculation unit, the coordinate conversion processing unit 42 is a coordinate calculation unit, the contour calculation unit 43 is an outline calculation unit, a texture mapping processing unit 44, The shading processing unit 45 corresponds to the image information storage unit, and the game space calculation unit 26 corresponds to the object calculation unit.
[0039]
The game system of the present embodiment has such a configuration, and the operation thereof will be described next.
FIG. 2 is a flowchart showing an outline of the operation procedure of the game system of the present embodiment, and shows the flow of the entire game. Note that the series of processing shown in FIG. 2 is repeatedly performed at a period (for example, 1/60 second) corresponding to a predetermined display interval.
[0040]
When the input device 10 is operated and a game start instruction is given by the player, the game calculation unit 20 starts a predetermined game calculation based on the game program read from the information storage medium 30. Specifically, the input determination unit 22 in the game calculation unit 20 performs a predetermined input determination process for outputting a signal corresponding to the content of the operation performed by the player based on the signal output from the input device 10. Perform (step 100).
[0041]
Next, in response to the signal output from the input determination unit 22, the event processing unit 24 performs processing (event generation processing) for generating various events necessary for the game progress (step 101). In addition, the game space calculation unit 26 performs coordinate calculation of various three-dimensional objects existing in the game space in response to the event generation process performed by the event processing unit 24 (step 102). By this coordinate calculation, the vertex coordinates of a plurality of polygons constituting the three-dimensional object are calculated.
[0042]
When the coordinate calculation of each three-dimensional object is performed by the game space calculation unit 26 in this way and the position information of the three-dimensional object is acquired, the intermediate point calculation unit 41 in the image processing unit 40 is within each polygon. The coordinates of the intermediate point corresponding to the two adjacent vertices are calculated (step 103). In addition, the coordinate conversion processing unit 42 performs a predetermined coordinate conversion process for converting the vertex coordinates and intermediate point coordinates of the polygon into coordinates on the circular frame buffer 50 (step 104). In addition, the contour calculation unit 43 calculates the contour shape of each polygon on the circular frame buffer 50 based on the calculation result of the coordinate conversion processing unit 42 (step 105).
[0043]
Next, the texture mapping processing unit 44 and the shading processing unit 45 obtain image information (color information) to be stored in the circular frame buffer 50, and write this image information in the corresponding position of the circular frame buffer 50 (step 106). Specifically, a predetermined texture mapping process is performed by the texture mapping processing unit 44, and then a predetermined shading process is performed by the shading processing unit 45, whereby an area on the circular frame buffer 50 corresponding to each polygon is obtained. Image information is written.
[0044]
The image information written in the circular frame buffer 50 is read out in a predetermined scanning order and sent to the projector 2. The projector 2 forms an image based on this image information, and projects it on the spherical screen 4 through the lens 3 (step 107).
[0045]
In this way, a new game image is generated at a predetermined repetition period and projected onto the spherical screen 4. In the above description of the operation, the drawing process is performed by performing the series of processes shown in FIG. 2 at a cycle corresponding to the display interval. However, the display interval and the repetition interval of the drawing process do not necessarily match. Good. In addition, when the drawing process is in time for the display timing, the drawing process is performed in synchronization with each display timing, and when the drawing process is not in time, the same screen display is performed. May not match.
[0046]
Next, details of the intermediate point calculation process in step 103, the coordinate conversion process in step 104, the contour calculation process in step 105, and the texture mapping process in step 106 will be described.
(1) Intermediate point calculation processing
3 and 4 are diagrams showing an outline of the midpoint calculation process performed in the midpoint calculation unit 41. FIG. In these figures, the point P₀, P₁Indicates two vertices included in one polygon arranged in the game space.
[0047]
In the case of performing the simplest calculation, as shown in FIG.₀, P₁The coordinates of the intermediate point P ′ in the game space are calculated. In this case, the coordinates of the intermediate point P ′ are simply two vertices P₀, P₁It is obtained by calculating the arithmetic mean of each coordinate value.
[0048]
In addition, the position on the circular frame buffer 50 corresponding to the above-described intermediate point P ′ is the vertex P.₀, P₁Are not equidistant from each vertex on the circular frame buffer 50 corresponding to. Therefore, as shown in FIG._r(For example, coincident with the ball center) and two vertices P₀, P₁It is desirable to calculate the coordinates of an intermediate point P ″ that bisects the projection angle formed by the two vertexes P ″ by using such an intermediate point P ″.₀, P₁Since the distance from each of the vertices on the circular frame buffer 50 corresponding to to the intermediate point on the circular frame buffer 50 corresponding to the intermediate point P ″ can be set to be approximately equal, an interpolation process is performed in step 105. It is possible to reduce an error when obtaining the contour line.
[0049]
Specifically, vertex P₀, P₁The distance from the center point P ″ to the intermediate point P ″ is L1 and L2, respectively.₀, P₁L3 and L4 satisfy the relationship of L1: L2 = L3: L4 because of the property of the bisector of the triangle. Sphere and two vertices P₀, P₁The coordinates of the intermediate point P ″ can be obtained by performing a simple calculation.
[0050]
(2) Coordinate conversion process
FIG. 5 is a diagram showing a drawing range of the circular frame buffer 50. The projector 2 according to the present embodiment has a rectangular image whose image projection range is horizontally long (for example, the aspect ratio is 3: 4), and a portion of the image is drawn corresponding to an image projected onto the spherical screen 4. Used as a region. This figure corresponds to a case where a projection plane S of FIG. 6 described later is viewed from the positive direction of the z axis (upper side in FIG. 6) toward the origin.
In FIG. 5, the rectangular area 200 corresponds to the projection range of the projector 2. Further, the circular area 210 corresponds to the range actually projected onto the spherical screen 4 through the lens 3. Therefore, in the present embodiment, image information is written only for the range included in the circular area 210 in the coordinates of the circular frame buffer 50.
[0051]
As shown in FIG. 5, the horizontal axis is the X axis and the vertical direction is the Y axis. The center (circular center) of the circular area 210 is the origin O, and the radius of the circular area 210 is R. The image information stored at an arbitrary point F (X, Y) in the circular frame buffer 50 is the point P on the spherical screen 4._dProjected on.
[0052]
(2-1) When both the viewpoint position and the projection position are set to the spherical center position of the spherical screen 4
FIG. 6 is a diagram showing an outline of the coordinate conversion process. As shown in the figure, the hemispherical projection surface corresponding to the spherical screen 4 is set as S, and the spherical center of the projection surface S is set as the origin o. Further, the z axis is defined from the origin o toward the center of the projection surface S, and the x axis and the y axis are defined perpendicular to the z axis. Furthermore, in this example, the viewpoint position P of the player_eAnd projection position (position of lens 3) P_rIs coincident with the origin o.
[0053]
Arbitrary point P in the game space which is a three-dimensional space_p(X_p, Y_p, Z_p) To a point F (X, Y) on the circular frame buffer 50. In FIG. 6, a point P in the game space_p(X_p, Y_p, Z_p) From the origin o, this point P_p And the intersection of the projection plane S and the straight line connecting the origin o_d(X_d, Y_d, Z_d). If the radius of the hemisphere corresponding to the projection plane S is r, x_d, Y_d, Z_dAre represented by the following equations, respectively.
[0054]
[Expression 1]

[0055]
In FIG. 6, the origin o and the point P_dAssuming that the angle between the straight line connecting the z axis and the z axis is θ, this angle θ is expressed by the following equation.
[0056]
[Expression 2]

[0057]
In the lens 3 used in the present embodiment, when the point F (X, Y) shown in FIG. 5 is projected onto the projection surface S, the distance L from the origin O to the point F is proportional to the angle θ shown in FIG. It has the characteristic to do. Therefore, L = 0 when θ = 0, and L = R when θ = π / 2, and the distance L corresponding to an arbitrary angle θ between them can be expressed by the following equation.
[0058]
L = θ / (π / 2) × R
In FIG. 5, the angle formed by the straight line connecting the origin O and the point F (X, Y) on the circular frame buffer 50 and the X axis is Φ. In FIG. 6, the point P_d(X_d, Y_d, Z_d) Mapping point P to xy plane_d′ (X_d, Y_d, 0) and the angle between the straight line connecting the origin o and the x-axis is φ. The angle Φ is equal to the angle φ. Here, cosφ and sinφ can be expressed by the following equations.
[0059]
[Equation 3]

[0060]
The point F (X, Y) is a point P on the projection plane S._d(X_d, Y_d, Z_d) Can be expressed as follows using the coordinate values of each axis.
[0061]
[Expression 4]

[0062]
Therefore, the vertex P of each polygon constituting the three-dimensional object arranged in the game space_p(X_p, Y_p, Z_p) Is known, in order to calculate the storage position of the corresponding circular frame buffer 50, the coordinate conversion processing unit 42 first calculates the vertex P_p(X_p, Y_p, Z_p) To the point P on the projection plane S by substituting the coordinate value of () into the above-described equations (1) to (3)._d(X_d, Y_d, Z_d). Thereafter, the coordinate transformation processing unit 42 obtains the point P obtained by this calculation._d(X_d, Y_d, Z_d) Is substituted into the above-described equations (4) and (5), and a point F (X, Y) on the circular frame buffer 50 is calculated. Further, the storage position of the circular frame buffer 50 is calculated for the intermediate point P ′ or P ″ shown in FIGS. 3 and 4 by the same procedure.
[0063]
In this way, the storage position of the circular frame buffer 50 corresponding to each vertex and intermediate point of each polygon of the three-dimensional object is calculated. In particular, the coordinate transformation process performed in this way is performed accurately using the position, viewpoint position, and projection position of the three-dimensional object in the game space. It is possible to obtain the storage position of the circular frame buffer 50 necessary for projecting a non-accurate game image on the spherical screen 4.
[0064]
FIG. 7 is a diagram showing a correspondence relationship between the vertexes of the polygons stored in the circular frame buffer 50 and the intermediate points. For example, assuming that a triangular polygon is used, the vertexes on the circular frame buffer 50 corresponding to each of the three vertices are represented by F._a, F_b, F_cAnd Further, the intermediate points on the circular frame buffer 50 corresponding to the three intermediate points sandwiched between two adjacent vertices are denoted by F.₁, F₂, F_ThreeAnd As shown in FIG. 7, when attention is paid to two adjacent vertices and an intermediate point sandwiched between them, these three points are not arranged on a straight line.
[0065]
(2-2) When only the projection position is shifted from the spherical center of the spherical screen 4
In the above description, the viewpoint position P_eAnd projection position P_rHas been considered to coincide with the spherical center of the spherical screen 4, but in reality, it is difficult to realize such a positional relationship. When a practical geometric arrangement is considered, if the player tries to show a highly realistic game image using the spherical screen 4, the player's viewpoint position is set near the spherical center of the spherical screen 4. Is desirable. Therefore, in this case, the projection position P_rNeeds to be shifted from the spherical center of the spherical screen 4.
[0066]
FIG. 8 is a diagram showing an outline of the coordinate conversion processing when the projection position is shifted from the spherical center position of the spherical screen 4. The coordinate axes shown in the figure are the same as those shown in FIG. Projection position P_r(X_r, Y_r, Z_r) Is set at a predetermined position other than the spherical center of the spherical screen 4 (for example, above the player's head). The origin of the circular frame buffer 50 is the projection position P._rIn order to distinguish from the display of coordinate axes in the case of (2-1) described above (see FIG. 5), the origin is O ′, the horizontal axis is the X ′ axis, and the vertical direction is the vertical direction. The axis along the axis is represented as Y ′ axis.
[0067]
As described in (2-1) above, the viewpoint position P is set at the position of the origin o corresponding to the spherical center of the spherical screen 4._eAre matched, the point P in the game space_p(X_p, Y_p, Z_p) Is a point P on the projection plane S_d(X_d, Y_d, Z_d). That is, an arbitrary projection position P_rTo point P on the spherical screen 4_d(X_d, Y_d, Z_d) Is projected onto the viewpoint position P._eFrom point P in the game space_p(X_p, Y_p, Z_p) Will be recognized.
[0068]
Therefore, an arbitrary projection position P_rCorresponding to the point P, a coordinate conversion process similar to the procedure described in (2-1) above is performed_dTo the projection position P_rTo point P_dThe point F ′ (X ′, Y ′) on the circular frame buffer 50 required for projection onto the frame can be obtained. However, the projection position P_rWhen x is shifted from the origin o, the x ′, y ′, and z ′ axes are translations of the original x, y, and z axes, and there is no rotation around the axes. X_r ²+ Y_r ²+ Z_r ²<R²Projection position P within a range satisfying (radius r from origin o)_rIs set.
[0069]
In FIG. 8, the projection position P_rAnd point P_dIf the angle between the straight line connecting the z ′ axis and the z ′ axis is θ ′, the angle θ ′ is expressed by the following equation.
[0070]
[Equation 5]

[0071]
In addition, an angle formed by a straight line connecting the origin O ′ and the point F ′ (X ′, Y ′) on the circular frame buffer 50 and the X ′ axis is Φ ′, and in FIG._d(X_d, Y_d, Z_d) To the x′y ′ plane_d″ (X_d-X_r, Y_d-Y_r, 0) and point P_rIf the angle between the straight line connecting x and the x ′ axis is φ ′, these angles Φ ′ and φ ′ are equal. Here, cos φ ′ and sin φ ′ can be expressed by the following equations.
[0072]
[Formula 6]

[0073]
Further, the point P on the projection plane S_d(X_d, Y_d, Z_d) Is obtained based on the above-described equations (1) to (3).
A point F ′ (X ′, Y ′) is a point P on the projection plane S._d(X_d, Y_d, Z_d) And projection position P_r(X_r, Y_r, Z_r) Can be expressed as follows using each coordinate value.
[0074]
[Expression 7]

[0075]
Therefore, the vertex P of each polygon constituting the three-dimensional object arranged in the game space_p(X_p, Y_p, Z_p) Is known, in order to calculate the storage position on the corresponding circular frame buffer 50, the coordinate conversion processing unit 42 first starts the vertex P_p(X_p, Y_p, Z_p) To the point P on the projection plane S by substituting the coordinate value of () into the above-described equations (1) to (3)._d(X_d, Y_d, Z_d). Thereafter, the coordinate transformation processing unit 42 obtains the point P obtained by this calculation._d(X_d, Y_d, Z_d) Is substituted into the above-described equations (7) and (8), and the coordinates of the point F ′ (X ′, Y ′) on the circular frame buffer 50 are calculated. Further, the storage position of the circular frame buffer 50 is calculated for the intermediate point P ′ or P ″ shown in FIGS. 3 and 4 by the same procedure.
[0076]
In this way, the storage position on the circular frame buffer 50 corresponding to each vertex and intermediate point of each polygon of the three-dimensional object is calculated. In particular, the coordinate conversion processing performed in this way is accurately performed using the position, viewpoint position, and projection position of the three-dimensional object in the game space, and therefore when the projection position is moved to an arbitrary position. However, it is possible to obtain the storage position of the circular frame buffer 50 necessary for projecting an accurate game image, which is theoretically free of distortion when viewed from the viewpoint position, onto the spherical screen 4.
[0077]
In FIG. 8 described above, the projection position P is shown for convenience of explanation._rIs z_rAlthough drawn in the region of ≧ 0, in reality, since the projection angle of the lens 3 is 180 degrees, in order to display the game image on the entire spherical screen 4, the projection position P_rIs z_rIt is desirable to set in the range of ≦ 0.
[0078]
In addition, the fisheye lens used as the lens 3 of the present embodiment is generally characterized by a wide range of focus because the depth of focus is deep. For this reason, even when the projection position is shifted, the entire game image displayed on the spherical screen 4 is almost in focus.
[0079]
(2-3) When both the viewpoint position and the projection position are shifted from the spherical center of the spherical screen 4
By the way, in the description in (2-2) above, the projection position P_rIs set at a position deviated from the spherical center position of the spherical screen 4, but in reality, the viewpoint position P of the player is_eHowever, there is a case where it is desired to shift from the spherical center position of the spherical screen 4. Hereinafter, a case where both the viewpoint position and the projection position are set so as to be shifted from the spherical center position of the spherical screen 4 will be described.
[0080]
FIG. 9 is a diagram showing an outline of the coordinate conversion process when the viewpoint position and the projection position are shifted from the spherical center position of the spherical screen 4. The coordinate axes shown in the figure are the same as those shown in FIG. Viewpoint position P_e, Projection position P_rBoth are set at predetermined positions other than the spherical center of the spherical screen 4. The origin of the circular frame buffer 50 is the projection position P._rTherefore, in order to distinguish from the display of the coordinate axes in the case of (2-1) described above (see FIG. 5), the origin is set to O ′ and the horizontal as in the case of (2-2) described above. The axis along the direction is represented as the X ′ axis, and the axis along the vertical direction is represented as the Y ′ axis.
[0081]
In FIG. 9, a point P in the game space_p(X_p, Y_p, Z_p) And viewpoint position P_e(X_e, Y_e, Z_e) Is represented by the following formula.
[0082]
[Equation 8]

[0083]
Further, the hemisphere corresponding to the projection plane S is represented by the following sphere equation (where z ≧ 0).
x²+ Y²+ Z²= R²                                      …(Ten)
Viewpoint position P_eTo point P in the game space_p(X_p, Y_p, Z_p), This point P_p Point P on the projection plane S corresponding to_d(X_d, Y_d, Z_d) Can be obtained by calculating the coordinates of the intersection point of the straight line shown in equation (9) and the hemisphere shown in equation (10).
[0084]
Specifically, the following equations are derived by modifying equation (9).
[0085]
[Equation 9]

[0086]
Substituting equations (11) and (12) into equation (10) yields the following equation:
((x_p-X_e)²+ (Y_p-Y_e)²+ (Z_p-Z_e)²) × x²
-2 × ((y_p-Y_e) × (x_eXy_p-Y_eX_p) + (Z_p-Z_e)
× (x_eXz_p-Z_eX_p)) × x
+ ((X_eXy_p-Y_eX_p)²+ (X_eXz_p-Z_eX_p)²
-R²× (x_p-X_e)²) = 0 (13)
here,
a = (x_p-X_e)²+ (Y_p-Y_e)²+ (Z_p-Z_e)²
b = (y_p-Y_e) × (x_eXy_p-Y_eX_p) + (Z_p-Z_e) × (x_eXz_p-Z_eX_p)
c = (x_eXy_p-Y_eX_p)²+ (X_eXz_p-Z_eX_p)²-R²× (x_p-X_e)²
In other words, the solution of the above equation (13) is expressed as the following equation.
[0087]
[Expression 10]

[0088]
Therefore, the point P in the game space_p(X_p, Y_p, Z_p) And viewpoint position P_e(X_e, Y_e, Z_e) To calculate the point (14) on the projection plane S by calculating the equation (14)._dX coordinate value (x_d) Is required. Further, by substituting the equation (14) into the above equations (11) and (12), the point P_dY coordinate value (y_d), Z-coordinate value (z_d) Is required.
[0089]
When the x coordinate value is actually calculated using equation (14), two solutions x₁, X₂Is obtained. One of these two solutions x₁By substituting (11) and (12) respectively for the corresponding y coordinate value (y₁) And z-coordinate values (z₁) Is obtained. As a result, point P_dThe coordinate value of is (x₁, Y₁, Z₁) The other solution x₂By substituting (11) and (12) respectively for the corresponding y coordinate value (y₂) And z-coordinate values (z₂) Is obtained. As a result, point P_dThe coordinate value of is (x₂, Y₂, Z₂) Of these two coordinate values, the necessary solution is the point P_eTo each coordinate value (x₁, Y₁, Z₁) And (x₂, Y₂, Z₂), The viewpoint position P_eTo point P_p Coordinate values corresponding to vectors having the same orientation as the vector going to are selected.
[0090]
In this way, the point P_d(X_d, Y_d, Z_d) Can be obtained. Thereafter, by substituting this coordinate value into the above-described equations (7) and (8), the projection position P_rTo point P on the projection plane S_dThe coordinates of the point F ′ (X ′, Y ′) on the circular frame buffer 50 necessary for projecting an image on the frame can be obtained.
[0091]
Therefore, the vertex P of each polygon constituting the three-dimensional object arranged in the game space_p(X_p, Y_p, Z_p) Is known, in order to calculate the storage position on the corresponding circular frame buffer 50, the coordinate conversion processing unit 42 first starts the vertex P_p(X_p, Y_p, Z_p) Coordinate value and viewpoint position P_e(X_e, Y_e, Z_e) To calculate the above-described equation (14) and the like to obtain a point P on the projection plane S._d(X_d, Y_d, Z_d). Thereafter, the coordinate transformation processing unit 42 obtains the point P obtained by this calculation._d(X_d, Y_d, Z_d) Is substituted into the above-described equations (7) and (8), and the coordinates of the point F ′ (X ′, Y ′) on the circular frame buffer 50 are calculated. Further, the storage position of the circular frame buffer 50 is calculated for the intermediate point P ′ or P ″ shown in FIGS. 3 and 4 by the same procedure.
[0092]
In this way, the storage position on the circular frame buffer 50 corresponding to each vertex and intermediate point of each polygon of the three-dimensional object is calculated. In particular, the coordinate conversion processing performed in this way is accurately performed using the position, viewpoint position, and projection position of the three-dimensional object in the game space, and thus the viewpoint position and projection position are moved to an arbitrary position. Even in this case, it is possible to obtain the storage position of the circular frame buffer 50 necessary for projecting an accurate game image that is theoretically free of distortion when viewed from the viewpoint position onto the spherical screen 4.
[0093]
In FIG. 9 described above, the projection position P is also shown for convenience of explanation._rIs z_rAlthough it was drawn in the region of ≧ 0, for the same reason as in the case of (2-2) described above, the actual projection position P_rIs z_rIt is desirable to set in the range of ≦ 0.
(3) Outline calculation processing
FIG. 10 is a diagram showing an outline of polygon contour calculation processing by the contour calculator 43. In FIG. 10, the mapping on the circular frame buffer 50 of the two vertices included in the polygon is F._a(X_a, Y_a), F_b(X_b, Y_b), And the intermediate point between them is F₁(X₁, Y₁). These three points F_a, F₁, F_bThe center of the circle passing through E (X₀, Y₀), Let the radius of this circle be R1.
[0094]
E (X₀, Y₀)
(XX₀)²+ (Y-Y₀)²= R1²                      (15)
It becomes. In this circle equation, 3 points F_a, F₁, F_bThe following simultaneous equations can be obtained by substituting the coordinate values of.
[0095]
(X_a-X₀)²+ (Y_a-Y₀)²= R₁ ²
(X_b-X₀)²+ (Y_b-Y₀)²= R₁ ²
(X₁-X₀)²+ (Y₁-Y₀)²= R₁ ²
By solving these simultaneous equations,
Y₀= (I * j-g * h) / (2 * (Y_aXg-Y₁Xg-Y₁Xi + Y_bXi))
X₀= (H + 2 × Y_a× Y₀-2 x Y₁× Y₀) / I
R₁= √ ((X_a-X₀)²+ (Y_a-Y₀)²)
Is obtained. here,
g = -2 × X₁+ 2 × X_b
h = −X_a ²+ X₁ ²-Y_a ²+ Y₁ ²
i = -2 × X_a+ 2 × X₁
j = -X₁ ²+ X_b ²-Y₁ ²+ Y_b ²
And
[0096]
In this manner, the contour calculation unit 43 determines the three points F by determining the equation of the circle._a, F₁, F_bThe shape of the contour line passing through (arc shape) is determined.
(4) Texture mapping processing
FIG. 11 is a diagram showing an outline of the texture mapping process. As shown in FIG. 11, in the present embodiment, the vertex F corresponding to each of the three vertices of the polygon._a, F_b, F_cEach contour line connecting each of the two is approximated by a circular arc, and the inside thereof becomes a drawing area in which image information is written corresponding to one polygon.
[0097]
The texture mapping processing unit 44 uses the upper end (Y_max) To bottom (Y_min) In order, and image information of each pixel included in a region sandwiched between contour lines approximated by an arc shape is generated.
The generation of the image information is performed using a general texture mapping technique. That is, it is performed by obtaining the data corresponding to the drawing position in the polygon from the separately prepared texture data (texture image information corresponding to the polygon).
[0098]
By the way, in the conventional texture mapping processing, the polygon shape on the frame buffer also has a polygon shape, so when obtaining texture coordinates corresponding to an arbitrary drawing position in the polygon, only a simple linear interpolation operation is performed. It was good. However, in the present embodiment, the polygonal shape on the circular frame buffer 50 is such that the contour line is approximated by an arc shape, and thus texture coordinates corresponding to an arbitrary drawing position cannot be obtained by a simple linear interpolation operation.
[0099]
FIG. 12 is a diagram showing an outline of a processing procedure for obtaining texture coordinates corresponding to an arbitrary drawing position on the circular frame buffer 50 by the texture mapping processing unit 44.
First, the texture mapping processing unit 44 determines the coordinates of the drawing point F ′ on the circular frame buffer 50 from which image information is to be generated, and then the corresponding position P in the polygon arranged in the game space._p′ Is calculated. Next, the texture mapping processing unit 44 uses the corresponding position P in the polygon._pBased on ′, the texture coordinate T is calculated. Since the polygon in the game space has a triangular shape with three vertices surrounded by a straight line, the specific position P in this polygon is_pThe texture coordinate T corresponding to ′ can be obtained by a simple linear interpolation operation.
[0100]
As described above, in the game system of this embodiment, when writing image information of a three-dimensional object composed of a plurality of polygons into the circular frame buffer 50, the polygonal outline shape represented by the polygon is approximated by an arc. is doing. Therefore, the shape of the three-dimensional object in the game space can be accurately reproduced, and distortion of the image projected on the spherical screen 4 can be reduced.
[0101]
In addition, this invention is not limited to the said embodiment, A various deformation | transformation implementation is possible within the range of the summary of this invention. For example, in the above-described embodiment, (2-1) when both the viewpoint position and the projection position are matched with the spherical center position of the spherical screen 4, (2-2) when only the projection position is shifted and set (2 -3) The coordinate conversion processing method has been described for each of the case where the viewpoint position and the projection position are set to be shifted. However, by applying these, only the viewpoint position is set to be shifted from the spherical center of the spherical screen 4. Even in this case, image information for displaying a game image with less distortion can be generated.
[0102]
Specifically, as described in the case where both the viewpoint position and the projection position shown in (2-3) above are set in a shifted manner, each polygon constituting each three-dimensional object arranged in the game space. The vertex coordinates of the point P_p(X_p, Y_p, Z_p) As these coordinate values and viewpoint position P_e(X_e, Y_e, Z_e) By using the coordinate values of (14) and the like to calculate the point P on the projection plane S._d(X_d, Y_d, Z_d) Is obtained. Thereafter, the storage position on the circular frame buffer 50 may be obtained by calculating the above-described equations (4) and (5) based on these coordinate values.
[0103]
In addition, the projection position P_rIs set to be shifted from the spherical center position of the spherical screen 4 (in the case of (2-2) and (2-3) described above), the projection position P_rTo position P on the spherical screen 4_dBrightness correction may be performed on the image information stored in the circular frame buffer 50.
[0104]
FIG. 13 is a diagram for explaining a modified example in which brightness correction is performed, and shows a state in which the cross section of the spherical screen 4 is simplified. Projection position P_rIs shifted from the spherical center position Q of the spherical screen 4, the projection position P_rTo an arbitrary position on the spherical screen 4 is not equidistant. For example, as shown in FIG._rTo a certain point P on the spherical screen 4_d1Distance D1 and another point P_d2This is greatly different from the distance D2. Projection position P_rSince the intensity of the light (light corresponding to each pixel constituting the game image), that is, the brightness is inversely proportional to the square of the distance, the brightness of the game image displayed on the spherical screen 4 is A bias will occur.
[0105]
Thus, for example, the projection position P_rBy setting a predetermined coefficient inversely proportional to the square of the distance from the position to the position on the spherical screen 4 and multiplying this by the image information stored in the circular frame buffer 50, the brightness of the image information is corrected. It can be carried out. Thereby, it is possible to reduce the unevenness of the brightness of the game image and project a higher quality game image.
[0106]
As a simpler method, for example, the projection position P_rA predetermined coefficient inversely proportional to the distance from the position to the position on the spherical screen 4 may be set, and this may be multiplied with the image information stored in the circular frame buffer 50. In this case, the unevenness of the brightness of the game image can be reduced to some extent, and the calculation amount required for the brightness correction can be reduced. Also, since the projection angle has a predetermined correlation with the distance from the projection position to the position projected on the spherical screen 4, brightness correction may be performed using the projection angle instead of the distance. The brightness correction process as described above can be performed by the shading processing unit 45 in the image processing unit 40.
[0107]
In the above-described embodiment, the case where an image is projected onto a spherical screen, which is a kind of curved screen, has been described. However, when a three-dimensional object placed in the game space is viewed from a viewpoint position, When the projected position is obtained by calculation, the present invention can be applied to the case where an image is displayed on a curved screen other than a spherical surface. For example, the image may be projected onto a curved screen having a projection surface obtained by cutting a rotating body obtained by rotating an ellipse in half. Even when such a curved screen is used, a position projected on the curved screen is calculated based on position information of a three-dimensional object arranged in the game space, and an image is further displayed at the calculated position. By calculating the storage position on the circular frame buffer 50 necessary for projecting the image, it is possible to display an image with almost no distortion.
[0108]
In the above-described embodiment, the polygon outline is approximated using a circle equation, but may be approximated using other curves. For example, the case where it approximates using a spline curve and another function can be considered. In these cases, for example, if each coefficient of the approximate function can be determined by specifying N points, (N−2) intermediate points excluding two vertices are set in the game space. Calculate with By obtaining the storage position of the circular frame buffer 50 corresponding to these intermediate points, the approximate function can be obtained by the same procedure as in the above-described embodiment.
[0109]
In the above-described embodiment, an example in which the present invention is applied to a game system has been described. However, the present invention is applied to various apparatuses that project a three-dimensional image using a three-dimensional object onto a curved screen. Can do. For example, the present invention can be applied to a device that makes a presentation using a three-dimensional object, various simulator devices such as a flight simulator, and the like.
[0110]
【The invention's effect】
As described above, according to the present invention, by approximating the polygon outline on the frame buffer with a curved shape instead of a linear shape, the outline of each polygon constituting the three-dimensional object projected on the curved screen is obtained. It is possible to make a substantially linear shape with little distortion.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating a configuration of a game system according to an embodiment.
FIG. 2 is a flowchart showing an outline of an operation procedure of the game system.
FIG. 3 is a diagram showing an outline of intermediate point calculation processing;
FIG. 4 is a diagram showing an outline of intermediate point calculation processing;
FIG. 5 is a diagram illustrating a drawing range of a circular frame buffer.
FIG. 6 is a diagram showing an outline of a coordinate conversion process.
FIG. 7 is a diagram illustrating a correspondence relationship between a vertex and a middle point of a polygon on a circular frame buffer.
FIG. 8 is a diagram showing an overview of coordinate conversion processing when only the projection position is shifted from the spherical center of a spherical screen.
FIG. 9 is a diagram showing an outline of coordinate conversion processing when the viewpoint position and the projection position are shifted from the spherical center of the spherical screen.
FIG. 10 is a diagram showing an outline of polygon outline calculation processing;
FIG. 11 is a diagram showing an outline of texture mapping processing;
FIG. 12 is a diagram showing an outline of a processing procedure for obtaining texture coordinates corresponding to an arbitrary drawing position on a circular frame buffer.
FIG. 13 is a diagram illustrating a modified example in which brightness correction is performed.
[Explanation of symbols]
1 Game device
2 Projector
3 Lens
4 Spherical screen
10 Input device
20 Game calculator
22 Input determination unit
24 Event processing section
26 Game Space Calculation Unit
30 Information storage media
40 Image processing unit
41 Midpoint calculation unit
42 Coordinate transformation processing unit
43 Outline calculation unit
44 Texture mapping processor
45 Shading processor
50 circular frame buffer

Claims (24)

An image display device that projects an image of a three-dimensional object arranged in a virtual three-dimensional space onto a curved screen through a wide-angle lens,
A frame buffer in which a position to be projected on the curved screen corresponds to a storage position of image information;
A projection device that irradiates an image corresponding to the image information stored in the frame buffer toward the wide-angle lens;
Contour calculating means for approximating the shape of the polygon outline on the frame buffer corresponding to the polygon outline constituting the three-dimensional object by a curve;
Image information storage means for storing image information of the corresponding three-dimensional object in the storage position of the frame buffer surrounded by the outline approximated by the outline calculation means;
Coordinate calculation means for calculating the storage position of the frame buffer in correspondence with the position on the curved screen when the three-dimensional object is viewed from a predetermined viewpoint position;
The coordinate calculation means calculates the storage position based on position information of the three-dimensional object in the virtual three-dimensional space and a projection position corresponding to the viewpoint position and the position of the wide-angle lens. And
An image display device, wherein the viewpoint position and the projection position are different. In claim 1,
An intermediate point calculating means for calculating coordinates of an intermediate point in the virtual three-dimensional space located on a straight line connecting two adjacent vertices included in the polygon;
The coordinate calculation means calculates a storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space,
The image display device, wherein the contour calculation means determines a shape of a curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point. In claim 2,
When it is necessary to designate N points for determining the shape of the curve, the intermediate point calculation means calculates at least (N-2) coordinates of the intermediate points. Image display device. In claim 2 or 3,
The curved line is an arc, and the intermediate point calculation means calculates the coordinates of one intermediate point. In any one of Claims 2-4,
The intermediate point calculating means calculates an angle formed by two line segments connecting the projection position corresponding to the position of the wide-angle lens and each of the two vertices by a line segment connecting the projection position and the intermediate point. An image display device, wherein the intermediate point is set so as to be equally divided. In any one of Claims 2-5,
The image display device according to claim 1, wherein the wide-angle lens is a fish-eye lens. In any one of Claims 1-6,
When the projection position is set to be shifted from the center position of the curved screen,
The image information storage means performs brightness correction on the image information stored in the frame buffer in consideration of a distance between the projection position and a position to be projected on the curved screen. apparatus. In any one of Claims 1-7,
The image information storage means performs texture mapping processing for specifying image information included in texture data corresponding to the polygon and storing the image information in the frame buffer, and sets the texture coordinates corresponding to the storage position on the frame buffer. In order to obtain, an image display apparatus characterized by obtaining coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position, and determining the texture coordinates corresponding to the coordinates. In any one of Claims 1-8,
An object calculating means for calculating coordinates of vertexes of the polygon in the virtual three-dimensional space at predetermined intervals;
An image display device characterized in that the storage processing of the image information in the frame buffer is repeated at the intervals. A first step of acquiring position information in a virtual three-dimensional space of each vertex included in a polygon constituting the three-dimensional object by calculation by a game space calculation means;
A second step of approximating the shape of the polygon outline on the frame buffer corresponding to the polygon outline on the basis of the position information acquired in the first step by a contour calculation means;
A third step of storing image information of the corresponding three-dimensional object by the image information storage means in the storage position of the frame buffer surrounded by the outline approximated in the second step;
A fourth step of reading out the image information stored in the frame buffer and projecting the image information onto a curved screen through a wide-angle lens;
And corresponding to the position on the curved screen when the three-dimensional object is viewed from a predetermined viewpoint position, the storage position of the frame buffer is calculated by the coordinate calculation means,
The coordinate calculation means calculates the storage position based on position information of the three-dimensional object in the virtual three-dimensional space, and a projection position corresponding to the viewpoint position and the position of the wide-angle lens,
An image display method, wherein the viewpoint position and the projection position are made different. In claim 10,
A fifth step of calculating by the intermediate point calculating means the coordinates of the intermediate point in the virtual three-dimensional space located on a straight line connecting two adjacent vertices included in the polygon;
A sixth step of calculating the storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space by the coordinate calculation means;
Before the second step,
In the second step, a shape of a curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point is determined. In claim 11,
2. The image display method according to claim 1, wherein the curve used for the approximation process in the second step is a circular arc, and the approximation process is performed using the coordinates of one intermediate point. In any one of Claims 10-12,
The image information stored in the frame buffer in consideration of the distance between the projection position and the position to be projected onto the curved screen when the projection position is set to be shifted from the center position of the curved screen. A seventh step of performing brightness correction on the image information storage means is inserted before the fourth step. In any one of Claims 10-13,
In the fourth step, texture mapping processing is performed in which the image information included in the texture data corresponding to the polygon is specified and stored in the frame buffer, and texture coordinates corresponding to the storage position on the frame buffer are performed. In order to obtain the image, a coordinate in the polygon in the virtual three-dimensional space corresponding to the storage position is obtained, and the texture coordinate corresponding to the coordinate is determined. A first step of acquiring position information in a virtual three-dimensional space of each vertex included in a polygon constituting the three-dimensional object by calculation by a game space calculation means;
A second step of approximating the shape of the polygon outline on the frame buffer corresponding to the polygon outline on the basis of the position information acquired in the first step by a contour calculation means;
A third step of storing image information of the corresponding three-dimensional object by the image information storage means in the storage position of the frame buffer surrounded by the outline approximated in the second step;
A fourth step of reading out the image information stored in the frame buffer and projecting the image information onto a curved screen through a wide-angle lens;
An information storage medium including a program for executing
Corresponding to the position on the curved screen when viewing the three-dimensional object from a predetermined viewpoint position, the storage position of the frame buffer is calculated by the coordinate calculation means,
The coordinate calculation means calculates the storage position based on position information of the three-dimensional object in the virtual three-dimensional space, and a projection position corresponding to the viewpoint position and the position of the wide-angle lens,
An information storage medium characterized in that the viewpoint position differs from the projection position. In claim 15,
A fifth step of calculating by the intermediate point calculating means the coordinates of the intermediate point in the virtual three-dimensional space located on a straight line connecting two adjacent vertices included in the polygon;
A sixth step of calculating the storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space by the coordinate calculation means;
Including a program that is inserted and executed before the second step,
In the second step, the shape of the curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point is determined. In claim 16,
The information storage medium characterized in that the curve used for the approximation process in the second step is an arc, and the approximation process is performed using the coordinates of one of the intermediate points. In claim 16 or 17,
The image information stored in the frame buffer in consideration of the distance between the projection position and the position to be projected onto the curved screen when the projection position is set to be shifted from the center position of the curved screen. An information storage medium comprising: a program for inserting and executing the seventh step of performing the brightness correction by the image information storage unit before the fourth step. In any one of Claims 15-18,
In the fourth step, texture mapping processing for specifying image information included in texture data corresponding to the polygon and storing the image information in the frame buffer is performed, and texture coordinates corresponding to the storage position on the frame buffer are determined. In order to obtain the information, a coordinate in the polygon in the virtual three-dimensional space corresponding to the storage position is obtained, and the texture coordinate corresponding to the coordinate is determined. To project an image of a 3D object placed in a virtual 3D space onto a curved screen through a wide-angle lens,
A first step of acquiring position information in the virtual three-dimensional space of each vertex included in the polygon constituting the three-dimensional object by calculation by a game space calculation means;
A second step of approximating the shape of the polygon outline on the frame buffer corresponding to the polygon outline on the basis of the position information acquired in the first step by a contour calculation means;
A third step of storing image information of the corresponding three-dimensional object by the image information storage means in the storage position of the frame buffer surrounded by the outline approximated in the second step;
A fourth step of reading out the image information stored in the frame buffer and projecting the image information onto a curved screen through the wide-angle lens;
An image display program for executing
Corresponding to the position on the curved screen when viewing the three-dimensional object from a predetermined viewpoint position, the storage position of the frame buffer is calculated by the coordinate calculation means,
The coordinate calculation means calculates the storage position based on position information of the three-dimensional object in the virtual three-dimensional space, and a projection position corresponding to the viewpoint position and the position of the wide-angle lens,
An image display program for making the viewpoint position different from the projection position. In claim 20,
A fifth step of calculating by the intermediate point calculating means the coordinates of the intermediate point in the virtual three-dimensional space located on a straight line connecting two adjacent vertices included in the polygon;
A sixth step of calculating the storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space by the coordinate calculation means;
Is executed before the second step,
In the second step, an image display program for determining a shape of a curve passing through each point on the frame buffer corresponding to each of the two vertexes and the intermediate point. In claim 21,
The curve used for the approximation process in the second step is an arc, and an image display program for performing the approximation process using the coordinates of one intermediate point. In any one of Claims 20-22,
The image information stored in the frame buffer in consideration of the distance between the projection position and the position to be projected onto the curved screen when the projection position is set to be shifted from the center position of the curved screen. An image display program for executing the seventh step of performing the brightness correction by the image information storage unit before the fourth step. In any one of Claims 20-23,
In the fourth step, texture mapping processing for specifying image information included in texture data corresponding to the polygon and storing the image information in the frame buffer is performed, and texture coordinates corresponding to the storage position on the frame buffer are determined. An image display program for obtaining coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position to determine the texture coordinates corresponding to the coordinates.

Images