JP3966433B2 - Gaseous object image synthesis circuit - Google Patents

Description

ここでＯｐ（透過値），Ｏｐｉ（ｉ番目の重ね書き透過値），ｋ（透過係数），Ａ（透過係数），Ｂ（指数），ｎ（オーバラップ数），Ｉｐ（合成輝度），Ｉｐｉ（ｉ番目の輝度），ｓ（合成減衰係数），ｊ（距離減衰係数），ｄｚｉ（ｉ番目のプリミティブ間の距離）を示す。プリミティブ間の合成は、まず輝度に関して、視点に近いプリミティブの輝度はそのままに、視点に遠い方のプリミティブに対しては、プリミティブ間の視点軸上の距離（通常Ｚ値）ｄｚｉを求めこれを関数１／（１＋ｊｄｚｉ）に代入した後、この値と遠いほうの輝度とを乗算したものと加算する。ｊは距離に関する減衰係数となる。即ち視点に近いプリミティブの輝度と、その点から離れるにしたがって減衰する他の一方の輝度とを加算し、これを全てのプリミティブのレンダリングが終了するまで繰り返し、この結果累積して得たものが最終的なプリミティブ間の合成輝度と定義する。またプリミティブの透過値はその合成に直接用いるのではなく、まずそれぞれを加算して画像メモリに記憶し（すなわち画像メモリに記憶されるものは（１）式のΣＯｐｉとなる）、面定義物体との合成時点でこれを（１）式に示すような関数で与えられる透過式の冪値として与えて合成透過値Ｏｐを決定しこれを用いるものとする。
通常（１）式のＢは指数で与えられる。このプロセスは前記透過式をそれぞれプリミティブ毎に計算した場合の負荷の増大を防ぐためである。よって、プリミティブ間で得られた画像メモリ内の透過値は変換前の値であり、正しい合成透過値ではない。一方、面定義物体との合成は次式の関係で定義される。

ここでａは（１−Ｏｐ）の関係からなる透明値であり、Ｓは面定義物体の輝度、Ｇはガス状物体プリミティブの輝度、ｋ，ｊは距離に関わる減衰係数、ｄｚはプリミテイブと面定義物体とのｚ（視点軸）方向の距離また−ｄは面定義物体からガス状物体までの背面距離ｄを示す。透過値Ｏｐは（１）式によって求められ透明値ａに変換される。この式からガス状物体が面定義物体の手前にある場合（ｄｚ≧０）には、ガス状物体が視点に近づくにしたがってガス状物体の輝度は増し、面定義物体の輝度は減少するものとしている。この距離に対する増減の割合は係数ｋによって調整できる。またガス状物体が面定義物体の背面に位置する場合（ｄｚ＜０）には、隠面消去を行って背面輝度を削除するのではなく、面定義物体からの距離によってガス状物体の輝度を減少させるものである。またガス状物体が面定義物体から背面に特定の距離ｄ以上離れている場合、ガス状物体の輝度はカットオフされるものとする。以上からガス状物体プリミティブ間の合成と、面定義物体の合成はそれぞれの視点方向の距離間と、透過値によって求められる。ガス状物体のスムーズな分布特性を得るために画像メモリでガス状物体間のプリミティブ合成が終了した段階でフィルタリングが行われる。
また（２）式で透明値は（１−Ｏｐ）として透過値で表現し直接Ｏｐを与えることもできる。
【０００３】
［実施例］
本発明のガス状物体の関係を図１に示し、合成回路例を図２に示す。図１においてガス状物体は３次元座標点で与えられる。図１では二つの物体Ｚ０とＺｉが同一視点軸上にあり、距離ｄＺｉを保っている。この場合視点Ｅに入る物体の輝度はＺ０の輝度（前記（１）式におけるＩｐ（ｎｅａｒｅｓｔ））と、Ｚｉ点の輝度ΣＩｐｉを（１＋ｄＺｉ）で除算したものとの和となる。また透過値はそれぞれの和として求める。この結果、これを実現する回路は本発明の図２に示すように、新たに求められたソースプリミティブの視点座標値Ｚｓ値と画像メモリ６から読みだされたディスティネーションプリミティブの視点座標値Ｚｄとが減算器１にて減算され、その差分値（距離）を求めると共に、この正負符号によってマルチプレクサ２ａおよび２ｂのソース輝度Ｉｓあるいはディスティネーション輝度Ｉｄ（ＩｓあるいはＩｄがそれぞれ（１）式のＩ（ｎｅａｒｅｓｔ）あるいはΣＯｐｉとなる）を選択する。プリミティブ間の距離ｄＺｉはメモリテーブル３に加えられ、ｓ／（１＋ｊｄＺｉ）を求める。メモリテーブルにはｄＺｉを入力変数（アドレス）としてｓ／（１＋ｊｄＺｉ）が記憶されている。このメモリテーブルは減衰係数ｊおよびｓが物体によって異なるため書き換えが必要となり、通常はＲＡＭで構成する。
ｓ／（１＋ｊｄＺｉ）はマルチプレクサ２ａの出力値と乗算器４にて乗算された後にマルチプレクサ２ｂの出力値と、加算器５ａにて加算され画像メモリ６に記憶される。一方、透過値はソースＯｐｓとディスティネーションＯｐｄそれぞれが加算器５ｂにて加算された後、画像メモリ６に記憶される。
ガス状物体生成プロセッサの画像メモリに記憶されたプリミティブは面定義物体描画プロセッサから出力される面定義物体と合成される。この合成に関わる本発明の物体間の関係図３に示す。図３ａは輝度Ｉｇ、視点軸点ｚ０をもつガス状物体が、輝度Ｉｓ、視点軸点ｚ１からなる面定義物体の手前にある場合、３ｂは後ろにある場合を示す。輝度の合成はすでに知られたアルハーブレンディングの線形混合式が用いられるが、本発明ではこのアルハー値（透明値）を前記（２）式の関係に基づき以下の方式で求める。図３ａの関係の場合、透明値はガス状物体がもつ透明値と１／（１＋ｋｄＺ）との積で与える。ここで透明値は前記（１）式の関係から求められた透過値Ｏｐから得たものである。
この結果、面定義物体とガス状物体との距離ｄＺが大きくなり、ガス状物体が視点に近くなるにしたがって、ガス状物体の輝度が強調される。一方、図３ｂの場合は、ガス状物体が面定義物体から離れるにしたがって、（２）式に基づき、面定義物体が強調される。これらの関係を回路図４に示す。
図４に於てガス状物体はそれぞれ輝度Ｉｇ、視点軸点Ｚ０および透過値Ａｇを持つ。また面定義物体は輝度Ｉｓと視点軸値Ｚ１をもつ。視点座標値Ｚ０とＺ１はそれぞれ減算器７ａにて減算されその差分値ｄＺを出力する。この値は減衰率ｋあるいはｊと、乗算器８ａにて乗算され、メモリーテーブル９に与えられ、１／（１＋ｋｄＺ）あるいは１／（１＋ｊｄＺ）を出力する。一方、差分値ｄＺは減衰率ｊと乗算器８ｂにて乗算された後、加算器１０ａにて（Ａｇ＋ｊｄＺ）が求められる。またマルチプレクサ１１は減算器７ａの符号でＡｇか（Ａｇ＋ｊｄＺ）かの選択を行う。以上から輝度は１１で選択された値とテーブル９の出力値が乗算器８ｃにて乗算され、この値が一方でＩｇと、他方でＩｓとそれぞれ乗算器８ｄおよび８ｅで乗算された後加算器１０ｂにて加算され、最終輝度Ｉｐを得る。８ｅでの出力は減算器７ｂに於て反転された後加算される。これらのプロセスは（２）式を実行するためのものである。こうして得られた合成輝度は直接あるいは別の画像メモリに記憶されたのち表示される。
【０００４】
［効果］
本発明のハードウエア化により、ガス状物体と面定義物体が３次元空間内で高速に合成でき、仮想現実システムの描画に不可欠なリアルタイム表示が可能と成る。
【図面の簡単な説明】
【図１】 本発明のガス状物体の関係図
【符号の説明】
Ｅ 視点
Ｚ０，Ｚ１ ガス状物体の視点軸上の座標値
ｄＺｉ ガス状物体間の距離
【図２】 本発明のガス状物体間の合成回路
【符号の説明】
１ 減算器
２ａ，２ｂ マルチプレクサ
３ メモリテーブル
４ 乗算器
５ａ，５ｂ 加算器
６ 画像メモリ
【図３】 本発明のガス状と面定義物体との関係
【符号の説明】
Ｅ 視点
Ｚ０ ガス状物体の視点軸座標値
Ｚ１ 面定義物体の視点軸座標値
Ｉｇ ガス状物体の輝度
Ｉｓ 面定義物体の輝度
ｄＺ ガス状および面定義物体間の距離
【図４】 本発明のガス状と面定義物体との合成回路
【符号の説明】
７ａ，７ｂ 減算器
８ａ，８ｂ，８ｃ，８ｄ，８ｅ 乗算器
９ メモリテーブル
１０ａ，１０ｂ 加算器
１１ マルチプレクサThe present invention relates to a hardware circuit for generating a natural phenomenon, for example, a gaseous shape such as fog or cloud in a three-dimensional space by computer graphics and dynamically visualizing the same, and volume rendering thereof.
[0001]
[Conventional technology]
Many shape models that display three-dimensional objects by computer graphics are mainly curved surfaces or solid models. Realistic images can be obtained by calculating reflections and shadows between light sources or objects on these surfaces. ing. Unlike objects such as this curved surface model, expressing natural phenomena such as fog and clouds requires calculation of shape complexity, dynamic changes, diffuse reflection, etc., and a large amount of calculation time is now required. is doing. Also, the process of synthesizing these gaseous objects with a curved surface model in a three-dimensional space is complicated, and enormous calculation costs are required. From this point of view, there are almost no hardware implementation examples of gaseous objects as volume rendering, and many are expressed by software. Even in some of the hardware methods, in the synthesis between gaseous objects, the Z value (viewpoint coordinate axis) of the gaseous object created by the rendering processor and the Z of the object already stored in the image memory are successively generated. If the Z value of the newly written gaseous object is closer to the viewpoint than the gaseous object in the image memory, the brightness of the new object is selected and the number of overlaps is counted as the density of that point. If the object is far away, the brightness of the object in the image memory is selected and the number of overlaps is counted. On the other hand, in the synthesis with a surface-defined object, if the gaseous object is closer to the viewpoint than the surface-defined object, the overlap value of the previously obtained gaseous object is left as it is, while if it is far away, a specific value such as zero is set. Set and then filter the number of these overlaps, assuming that there are primitives (minimum graphic elements of gaseous objects) with density corresponding to the number of overlaps in the surroundings. The surface definition object is synthesized using the transparency obtained by converting the value and the luminance of the primitive. In this method, the influence of the distance between primitives is not considered in the synthesis. The number of overlaps is used as the transmittance. In this method, when the overlap count overflows (for example, 256 times or more), there is a problem that the maximum value is fixed due to physical restrictions such as the size of the image memory. On the other hand, in the method of the present invention, unlike the conventional method, first, when the primitives overlap each other, the distance between the primitives is obtained, the combined luminance is determined by the function of the distance, and the transmission value is determined for each of the primitives. The sum of the transmission values of the primitives is stored. On the other hand, the composition with the surface definition object is also performed using the brightness and transmission value obtained as a result of the composition of the gaseous object, as well as the distance between each object, as with the gaseous object. Not in. This method, in which the luminance and transmissivity are attenuated and transmitted with distance, is a method more suited to the nature of the physical phenomenon.
As a result, according to the present invention, it is possible to provide a realistic video having a more expressive power than a display method based on filtering of the Z value or the number of overlaps.
[0002]
[Means for solving problems]
In the present invention, the synthesis of the gaseous object and the surface-defined object is divided into two processes. One is the synthesis process of gaseous objects and the subsequent synthesis of surface-defined objects. First, in the synthesis of gaseous objects, a random number is generated for the primitive, and the brightness value and the transmission value for determining the transmittance are defined as the coordinate values (here, the transmission value is defined as representing opacity, The transparency value represents transparency) and is set as its attribute. The primitives generated in this manner are sequentially stored in the image memory, but are random numbers, so that an unspecified number is overwritten on the same viewpoint axis (usually the Z axis). In this case, in the present invention, the following synthesizing process is performed.

Here, Op (transmission value), Opi (i-th overwritten transmission value), k (transmission coefficient), A (transmission coefficient), B (exponential), n (overlap number), Ip (combined luminance), Ipi (I-th luminance), s (combined attenuation coefficient), j (distance attenuation coefficient), and dzi (distance between i-th primitives). In the synthesis between primitives, first, with respect to the brightness, the brightness of the primitive close to the viewpoint is kept as it is, and for the primitive far from the viewpoint, the distance (usually Z value) dzi between the primitives is obtained as a function. After substituting for 1 / (1 + jdzi), the value multiplied by the far brightness is added. j is an attenuation coefficient related to distance. That is, add the luminance of the primitive close to the viewpoint and the other luminance that attenuates as you move away from the point, and repeat this until all the primitives have been rendered. It is defined as the combined luminance between the primitives. In addition, the transmission values of the primitives are not directly used for the synthesis, but are first added and stored in the image memory (that is, what is stored in the image memory is ΣOpi in equation (1)) This is given as a threshold value of the transmission formula given by the function shown in the equation (1) at the time of synthesis, and the synthesized transmission value Op is determined and used.
Usually, B in the equation (1) is given by an index. This process is to prevent an increase in load when the transmission formula is calculated for each primitive. Therefore, the transmission value in the image memory obtained between the primitives is a value before conversion, and is not a correct combined transmission value. On the other hand, the composition with the surface definition object is defined by the relationship of the following equation.

Here, a is a transparent value having a relationship of (1-Op), S is the luminance of the surface-defining object, G is the luminance of the gaseous object primitive, k and j are attenuation coefficients related to the distance, and dz is the primitive and the surface. The distance in the z (viewpoint axis) direction from the definition object or -d indicates the back surface distance d from the surface definition object to the gaseous object. The transmission value Op is obtained by the equation (1) and converted to the transparent value a. From this equation, when the gaseous object is in front of the surface definition object (dz ≧ 0), the luminance of the gaseous object increases and the luminance of the surface definition object decreases as the gaseous object approaches the viewpoint. Yes. The rate of increase / decrease with respect to this distance can be adjusted by the coefficient k. Also, when the gaseous object is located behind the surface definition object (dz <0), the luminance of the gaseous object is adjusted according to the distance from the surface definition object, instead of performing hidden surface removal and deleting the back surface luminance. It is to reduce. In addition, when the gaseous object is separated from the surface-defining object by a specific distance d or more, the luminance of the gaseous object is cut off. From the above, the composition between the gaseous object primitives and the composition of the surface definition object are obtained by the distance between the respective viewpoint directions and the transmission value. In order to obtain a smooth distribution characteristic of the gaseous object, filtering is performed at the stage where the primitive synthesis between the gaseous objects is completed in the image memory.
Further, in the equation (2), the transparency value can be expressed as a transmission value as (1-Op) and directly given Op.
[0003]
[Example]
FIG. 1 shows the relationship between the gaseous objects of the present invention, and FIG. 2 shows a synthesis circuit example. In FIG. 1, the gaseous object is given by three-dimensional coordinate points. In FIG. 1, two objects Z0 and Zi are on the same viewpoint axis, and the distance dZi is maintained. In this case, the luminance of the object entering the viewpoint E is the sum of the luminance of Z0 (Ip (nearest) in the equation (1)) and the luminance ΣIpi at the Zi point divided by (1 + dZi). Further, the transmission value is obtained as the sum of each. As a result, as shown in FIG. 2 of the present invention, the circuit that realizes this is the newly obtained viewpoint coordinate value Zs of the source primitive and the viewpoint coordinate value Zd of the destination primitive read from the image memory 6. Is subtracted by the subtracter 1, and the difference value (distance) is obtained, and the source luminance Is or the destination luminance Id (Is or Id) of the multiplexers 2a and 2b is respectively expressed by I (nearest ) Or ΣOpi). The distance dZi between the primitives is added to the memory table 3 to obtain s / (1 + jdZi). The memory table stores s / (1 + jdZi) with dZi as an input variable (address). This memory table needs to be rewritten because the attenuation coefficients j and s differ depending on the object, and is usually composed of a RAM.
s / (1 + jdZi) is multiplied by the output value of the multiplexer 2 a by the multiplier 4, then added to the output value of the multiplexer 2 b by the adder 5 a and stored in the image memory 6. On the other hand, the transmission value is stored in the image memory 6 after the source Ops and the destination Opd are added by the adder 5b.
The primitive stored in the image memory of the gaseous object generation processor is combined with the surface definition object output from the surface definition object drawing processor. FIG. 3 shows the relationship between the objects of the present invention related to this synthesis. FIG. 3A shows a case where the gaseous object having the luminance Ig and the viewpoint axis point z0 is in front of the surface defining object consisting of the luminance Is and the viewpoint axis point z1, and 3b is the case behind. The already known linear blending formula of al-herb lending is used for the synthesis of luminance. In the present invention, this alher value (transparency value) is obtained by the following method based on the relationship of the formula (2). In the case of the relationship of FIG. 3a, the transparency value is given by the product of the transparency value of the gaseous object and 1 / (1 + kdZ). Here, the transparency value is obtained from the transmission value Op obtained from the relationship of the equation (1).
As a result, the distance dZ between the surface definition object and the gaseous object increases, and the luminance of the gaseous object is enhanced as the gaseous object approaches the viewpoint. On the other hand, in the case of FIG. 3b, the surface-defining object is emphasized based on the equation (2) as the gaseous object moves away from the surface-defining object. These relationships are shown in the circuit diagram 4.
In FIG. 4, each gaseous object has luminance Ig, viewpoint axis point Z0, and transmission value Ag. Further, the surface definition object has the luminance Is and the viewpoint axis value Z1. The viewpoint coordinate values Z0 and Z1 are subtracted by the subtractor 7a, and the difference value dZ is output. This value is multiplied by the attenuation factor k or j by the multiplier 8a and given to the memory table 9 to output 1 / (1 + kdZ) or 1 / (1 + jdZ). On the other hand, after the difference value dZ is multiplied by the attenuation factor j and the multiplier 8b, (Ag + jdZ) is obtained by the adder 10a. The multiplexer 11 selects Ag or (Ag + jdZ) according to the sign of the subtractor 7a. From the above, the luminance is multiplied by the value selected in 11 and the output value of the table 9 by the multiplier 8c, and this value is multiplied by Ig on the one hand and Is on the other hand by the multipliers 8d and 8e, respectively, and then the adder The final luminance Ip is obtained by adding at 10b. The output at 8e is inverted by the subtractor 7b and then added. These processes are for executing equation (2). The synthesized luminance thus obtained is displayed directly or after being stored in another image memory.
[0004]
[effect]
By implementing the hardware of the present invention, a gaseous object and a surface-defined object can be synthesized at high speed in a three-dimensional space, and real-time display indispensable for drawing a virtual reality system becomes possible.
[Brief description of the drawings]
FIG. 1 Relationship diagram of gaseous objects of the present invention
E Viewpoints Z0, Z1 Coordinate values on the viewpoint axis of the gaseous object dZi Distance between the gaseous objects [FIG. 2] Synthesis circuit between gaseous objects of the present invention [Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Subtractor 2a, 2b Multiplexer 3 Memory table 4 Multiplier 5a, 5b Adder 6 Image memory [FIG. 3] Relationship between the gaseous state of this invention and a surface definition object
E Viewpoint Z0 Viewpoint axis coordinate value Z1 of gas-like object Viewpoint axis coordinate value Ig of surface-defined object Ig Luminance Is of gaseous object Is Luminance of surface-defined object dZ Distance between gaseous and surface-defined object FIG. Circuit of shape and surface definition object [Explanation of symbols]
7a, 7b Subtractors 8a, 8b, 8c, 8d, 8e Multiplier 9 Memory tables 10a, 10b Adder 11 Multiplexer

Claims (1)

Regarding a synthesis circuit in a three-dimensional space between gaseous objects and between a gaseous object and a surface-defined object in display processing of computer graphics, the gaseous object has three-dimensional coordinate values, luminance values, and transmission values, respectively. When the gaseous object newly generated in rendering is sequentially stored in the image memory, the distance on the viewpoint axis between the objects already stored in the image memory is obtained, and the viewpoint among the gaseous objects is determined. Multiplying the brightness of the object farther away from the object by the function of the distance and adding the brightness of the object closer to the viewpoint to the result, the subtraction circuit, division, memory table And a multiplier circuit, and the transmission value has an adder for adding the transmission values of the respective objects to determine the combined luminance and transmission values of these gaseous objects and store them in the image memory. In the combination of the first means to remember and the surface definition object and the gaseous object, the transmission value stored in the image memory is converted into a combined transmission value by a predetermined function, and between the gaseous and surface definition objects. A distance function that differs depending on the position of each object from the distance on the viewpoint axis is defined, and the brightness of each object is multiplied by this function and the value obtained from the combined transmission value to obtain a new gaseous object. An image synthesizing circuit having a second means having a circuit composed of a subtractor, a multiplier, a memory table, and an adder for determining a synthetic luminance with a surface definition object.

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