JP4632225B2 - Geometric pattern creation method and apparatus - Google Patents

Description

ここで、平行光線の光は白色光であるとし、Ｃ（ｘ，ｙ）の値が「１」は、ｘ−ｙ平面の位置（ｘ，ｙ）は白色であり、光が当たっていることを示し、「０」は黒色で光が当たっていないことを示すものとする。この点についても以下同じとする。
この場合、ｉ＝0,1,2,…として、
８ｉ≦ｘ＜４＋８ｉ …(7)
の範囲内には光が当たり、それ以外は光が当たらないことになるから、ｘ−ｙ平面上における光の当たり方、即ち平行光線のパターンは図４（ａ）に示すようにストライプ状となる。なお、図４（ａ）で斜線で示す部分は光が当たらない部分を示している。
【００３５】
（平行光線のパターンの例２）

この場合には、平行光線のパターンは図４（ｂ）に示すように市松状のものとなる。これは上記の例１から容易に理解することができる。なお、図４（ｂ）で斜線で示す部分は光が当たらない部分を示している。
【００３６】
このように、平行光線のパターンの定義は、ｘ−ｙ平面上の位置（ｘ，ｙ）の光の色を、その位置（ｘ，ｙ）の関数Ｃ（ｘ，ｙ）として定義することによって行うのであるが、この入力は、所望の関数Ｃ（ｘ，ｙ）を作って、その式を入力するようにすればよい。
【００３７】
また、予め関数Ｃ（ｘ，ｙ）の一般式をいくつか制御手段２に登録しておき、入力手段１によってその中から所望の関数を選択し、その関数中のパラメータの値を入力するようにしてもよい。例えば、平行光線のパターンとして、α、βをパラメータとして

という一般式を登録しておき、ストライプ状のパターンとしたい場合には、入力手段１によりこの関数を選択し、更にこの一般式中のパラメータα、βの値を入力するようにするのである。その他のパターンの関数の場合についても同様である。
【００３８】
なお、上記の例では、関数Ｃ（ｘ，ｙ）の値は、１（白色）または０（黒色）の値をとるものとしたが、赤（Ｒ）、緑（Ｇ）、青（Ｂ）の３色の値、あるいはシアン（Ｃ）、マゼンタ（Ｍ）、黄（Ｙ）、黒（Ｋ）の値をそれぞれ所望のように定めてもよい。例えば、

とすれば、図４（ａ）の白の部分は赤色となり、斜線部は緑色となる。
【００３９】
（４）３次元曲面形状：Ｚ（ｘ，ｙ）
これは、所望のパターンを有する平行光線が照射される３次元曲面の形状を定めるためのパラメータであり、この幾何学模様作成装置では、３次元直交座標系のｚ＝０の平面であるｘ−ｙ平面上からの高さＺを、そのｘ−ｙ平面上の位置（ｘ，ｙ）の関数Ｚ（ｘ，ｙ）として定義することによって、３次元曲面の形状を定義する。ここで、ｘ−ｙ平面上からの高さとは、ｚの正方向だけではなく、ｚの負方向をも含むものとする。
例えば、
Ｚ＝（ｘ，ｙ）＝5×｜sin（πｙ／20）｜ …(11)
とすると、この関数Ｚ（ｘ，ｙ）で表される３次元曲面は、概略図８に示すようになるが、各曲面形成単位体Ｂの表面形状は図１１（ｄ）に示すようにサインウェーブの半周期であり、その振幅は 5、その幅は座標値で20である。
【００４０】
このように、３次元曲面形状の定義は、ｘ−ｙ平面上の位置（ｘ，ｙ）からの高さを、その位置（ｘ，ｙ）の関数Ｚ（ｘ，ｙ）として定義することによって行うのであるが、この入力は、所望の関数Ｚ（ｘ，ｙ）を作って、その式を入力するようにしてもよく、また、また、予め関数Ｚ（ｘ，ｙ）の一般式をいくつか制御手段２に登録しておき、入力手段１によってその中から所望の関数を選択し、その関数中のパラメータの値を入力するようにしてもよい。例えば、３次元曲面形状として、α、βをパラメータとして
Ｚ＝（ｘ，ｙ）＝α×｜sin（πｙ／β）｜ …(12)
という一般式を登録しておき、所望であれば入力手段１によりこの関数を選択し、更にこの一般式中のパラメータα、βの値を入力するようにするのである。この場合、αは振幅を定めるパラメータであり、βは周期を定めるパラメータであることは明らかである。
【００４１】
［制御手段２］
制御手段２は、この幾何学模様作成装置の動作を統括して制御するものである。また、上述したように、制御手段２は、入力手段１及び表示手段３と共にＧＵＩを構成している。
【００４２】
［表示手段３］
表示手段３は、カラーＣＲＴやカラー液晶表示装置等の適宜な表示装置及びその表示制御手段で構成されるものであり、制御手段２により、入力手段１と共にＧＵＩを構成している。
【００４３】
［シミュレーション手段４］
これは、Ｚ（ｘ，ｙ）で表される形状の３次元曲面に対して、ｘ−ｙ平面において関数Ｃ（ｘ，ｙ）で表されるパターンとなるように、方向（φ、θ）から平行光線を照射したとき、視点をｚ＝∞において見たときに観察できる幾何学模様の画像データをシミュレーションによって求めるものである。ただし、このシミュレーションにおいては、陰影計算は行わない。即ち、一般に用いられるランバート（Lambert）の余弦則を基にした、法線方向に依存した陰影計算を行わず、当該位置に照射された光の強度をそのまま画素値として採用する。
【００４４】
このシミュレーションの処理を図５を参照して説明する。なお、図５では矢印Ｅで示す方向（φ、θ）から平行光線が照射されるものとし、平行光線のパターンを定める関数をＣ（ｘ，ｙ）、３次元曲面形状を定める関数をＺ（ｘ，ｙ）とする。
【００４５】
［ステップＳ１］
作成画像上の１画素に着目する。この作成画像上の着目画素の座標値を（ｘ，ｙ）とする。
【００４６】
［ステップＳ２］
３次元曲面上の位置であって、そのｘ座標値及びｙ座標値が、作成画像の着目画素のｘ座標値及びｙ座標値と同じ座標値を有する位置を求める。このような位置を求めるのは容易である。３次元曲面上の当該位置のｘ座標値とｙ座標値は、それぞれ着目画素のｘ座標値、ｙ座標値と同じであり、ｚ座標値は、この（ｘ，ｙ）の位置における高さに他ならないから、３次元曲面形状を定める関数Ｚ（ｘ，ｙ）により求めることができる。従って、３次元曲面上の当該位置の座標値は（ｘ，ｙ，Ｚ）である。図５では、当該位置をＰで示している。
【００４７】
［ステップＳ３］
ステップＳ２で求めた位置Ｐ（ｘ，ｙ，Ｚ）を通り、定められた照射方向（φ、θ）と平行な直線Ｌを求め、その直線がｚ＝０のｘ−ｙ平面と交わる位置Ｑを求める。このような直線Ｌを求めることは容易である。即ち、照射方向はφ、θであるから、φ及びθという角度を有する単位ベクトルを考えると、その単位ベクトルのｘ成分Ｉx、ｙ成分Ｉy、ｚ成分Ｉz は、それぞれ、
Ｉx ＝sinθ×cosφ …(13)
Ｉy ＝sinθ×sinφ …(14)
Ｉz ＝cosθ …(15)
であるから、このことから当該直線Ｌのｘ軸、ｙ軸及びｚ軸に対する傾きが分かり、そしてこの直線Ｌは点Ｐ（ｘ，ｙ，Ｚ）を通るから、これらのことから当該直線Ｌの方程式を求めることができ、この直線Ｌがｘ−ｙ平面と交わる位置Ｑを求めることができる。このような処理については周知であるので、詳細な説明は省略する。
ここでは、このようにして求められた位置Ｑの座標値を、図５に示すように、Ｑ（ｘ′，ｙ′，０）とする。
【００４８】
［ステップＳ４］
平行光線のパターンを定める関数Ｃ（ｘ，ｙ）に、ステップＳ３で求めた位置Ｑのｘ座標値ｘ′、ｙ座標値ｙ′を代入して、当該位置Ｑ（ｘ′，ｙ′，０）に対して定義される光Ｃ′（ｘ′，ｙ′）を求め、この求めた光Ｃ′の値を、ステップＳ１で着目した作成画像上の画素の画素値とする。
【００４９】
以上の処理を、作成画像の全ての画素について行うことによって、幾何学模様の画像データを作成する。
【００５０】
上記のシミュレーションの処理によって作成される幾何学模様の例を図６、図７に示す。図６、図７の各図において、横方向はｙ軸方向、縦方向はｘ軸方向である。図６、図７の各図の照射方向（φ、θ）、平行光線のパターンを定める関数Ｃ（ｘ，ｙ）及び３次元曲面形状を定める関数Ｚ（ｘ，ｙ）は次のようである。
【００５１】

［画像出力手段５］
画像出力手段５は、シミュレーション手段４で作成された幾何学模様の画像データを出力するものであり、プリンタ、あるいはフィルム出力装置、またはハードディスク装置等の外部記憶装置で構成することができる。勿論、画像出力手段５として、これらのものを全て備えてもよい。
【００５２】
以上、図１に示す幾何学模様作成装置の各部の概略について説明したが、この図１に示す幾何学模様作成装置は、コンピュータシステムにより構成することができる。即ち、入力手段１はキーボード、ポインティングデバイスで構成することができ、表示手段３はモニタ及び表示制御手段で構成でき、シミュレーション手段４についてはＣＰＵを含む制御装置に、上述の説明あるいは後述する説明の動作を行うソフトウェアを搭載することで構成することができる。
【００５３】
次に、図１に示す幾何学模様作成装置を用いて幾何学模様の画像を作成する場合の動作を説明する。
【００５４】
工程１：パラメータの入力及びシミュレーション実行の指示
まず、オペレータは入力手段１により所定のパラメータの値を入力する。ここでは少なくとも上記のパラメータを入力する。そして、オペレータは所定のパラメータを入力したら入力手段１によりシミュレーションの実行を指示する。
これにより、制御手段２は入力されたパラメータをシミュレーション手段４に渡すと共に、シミュレーションの実行を指示する。
【００５５】
工程２：シミュレーション
シミュレーション手段４は、制御手段２からパラメータを受けると、シミュレーションを実行する。このシミュレーションの処理は上述した通りである。これにより幾何学模様の画像データが作成される。そして、シミュレーション手段４は、シミュレーションを終了すると、その作成した幾何学模様の画像を表示手段３に表示する。
【００５６】
工程３：幾何学模様の画像データの出力あるいは修正
オペレータは、表示手段３に表示された幾何学模様の画像を観察して、それが満足できるものであれば画像出力手段５に出力する。上述したように、画像出力手段５としては、プリンタ、フィルム出力装置、外部記憶装置等を用いることができるので、作成された幾何学模様の画像データの出力としては、外部記憶装置に記憶したり、プリンタでプリントアウトしたり、フィルム出力装置でフィルム出力することができる。
【００５７】
しかし、作成された幾何学模様が不所望のものであったり、あるいは作成された幾何学模様から種々のバリエーションを作成したい場合には、平行光線の照射方向φ、θ、平行光線のパターンを定める関数Ｃ（ｘ，ｙ）、３次元曲面形状を定める関数Ｚ（ｘ，ｙ）の３つのパラメータのうちの所望パラメータを、所望のように変更して、再度シミュレーションを行えばよい。
【００５８】
以上のようであるので、この幾何学模様作成装置によれば、平行光線の照射方向φ、θ、平行光線のパターンを定める関数Ｃ（ｘ，ｙ）、及び３次元曲面形状を定める関数Ｚ（ｘ，ｙ）という３つのパラメータを所望のように設定して入力することによって、自動的に、所望の形状の３次元曲面に、所望のパターンを有する平行光線を、所望の方向から照射したときに観察できる幾何学模様を作成することができる。
【図面の簡単な説明】
【図１】本発明に係る幾何学模様作成装置の一実施形態を示す図である。
【図２】作成画像内の位置を、作成画像の左上隅を原点Ｏとし、横方向をｙ軸、縦方向をｘ軸とした直交座標系により表すことを説明するための図である。
【図３】３次元直交座標系と３次元極座標系との関係を説明するための図である。
【図４】平行光線のパターンの例を示す図である。
【図５】シミュレーション手段４が実行するシミュレーションの処理を説明するための図である。
【図６】シミュレーションの処理によって作成される幾何学模様の例を示す図である。
【図７】シミュレーションの処理によって作成される幾何学模様の例を示す図である。
【図８】本発明に係る幾何学模様作成装置で作成しようとする幾何学模様を説明するための図であって、基準面Ａ上に略半円筒状の曲面形成単位体Ｂを隙間無く配置した状態を示す図である。
【図９】３次元曲面に照射する平行光線のパターンを形成するスリットの例を示す図である。
【図１０】観察される幾何学模様の例を示す図である。
【図１１】３次元曲面の形状の変更を説明するための図である。
【図１２】３次元曲面の形状の変更を説明するための図である。
【図１３】スリットの開口の変更の例を示す図である。
【符号の説明】
１…入力手段、２…制御手段、３…表示手段、４…シミュレーション手段、５…画像出力手段。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a geometric pattern creation method and apparatus for creating, by simulation, a geometric pattern that can be observed when a three-dimensional curved surface is irradiated with parallel light rays having an appropriate pattern such as slit light.
[0002]
[Prior art and problems to be solved by the invention]
BACKGROUND OF THE INVENTION Geometric patterns are widely printed on the surface of various industrial products such as wallpaper, flooring and other building materials, decorative sheets used for various purposes, and miscellaneous goods and home appliances.
[0003]
Conventionally, the design of geometric patterns has been done by the designer by hand, or if it is a simple geometric pattern, it has been done by generating appropriate functions using commercially available paint software or drawing software. is there.
[0004]
There are various geometric patterns, but a three-dimensional curved surface having three-dimensional unevenness is considered, and it is considered that a parallel beam of a certain pattern is irradiated on the surface from a certain angle. Here, “a parallel light beam of a certain pattern” means a light beam that irradiates a certain part of the three-dimensional curved surface and does not irradiate a certain part, or a light beam that has a different color depending on the part. These are parallel light beams that are striped through slits, parallel light beams that are checkered, and the like. On the other hand, for example, in the case of irradiating sunlight rays as they are, the sunlight rays are considered to be uniform light over the entire surface even if they are parallel rays. Absent.
[0005]
In this way, when the surface of the three-dimensional curved surface is irradiated with a parallel beam of a certain pattern from a certain angle, the pattern of the irradiated light beam depends on the shape of the three-dimensional curved surface when viewed from directly above the three-dimensional curved surface. Looks distorted. Such a distorted ray pattern is not only very interesting as a geometric pattern, but such a geometric pattern is considered to be effective in design.
[0006]
For example:
Now, as shown in FIG. 8, let us consider a case in which a plurality of substantially semi-cylindrical objects B are arranged without gaps on a reference plane indicated by A (referred to as a reference plane). Each of the substantially semi-cylindrical objects B serves as a unit for forming a three-dimensional curved surface, and is referred to as a curved surface forming unit body here. In FIG. 8, a right-handed three-dimensional orthogonal coordinate system (x, y, z) is used for this, and the reference plane A is on the plane of z = 0. O represents the origin of this three-dimensional orthogonal coordinate. The longitudinal direction of the curved surface forming unit B is the x-axis direction, which is arranged without a gap in the y-axis direction. If such a thing is seen from the direction of the arrow shown by D in FIG. 8, the curved surface formed by the continuous surface of the plurality of curved surface forming units B arranged without gaps is a three-dimensional curved surface. Although only four curved surface forming units B are shown in FIG. 8, it is a matter of course that a larger number may be arranged.
[0007]
Thus, it is assumed that such a three-dimensional curved surface is irradiated with striped white parallel light rays as indicated by an arrow E in FIG. Striped white parallel light can be obtained by passing the white parallel light through a slit provided with a plurality of rectangular openings S as shown in FIG. Although only four openings S are shown in FIG. 9, it is a matter of course that more openings may be provided.
[0008]
In this three-dimensional orthogonal coordinate system, if the viewpoint is set to z = ∞ and the three-dimensional curved surface is viewed from the upper side of FIG. 8, some geometric pattern can be observed. In FIG. 8, depending on the irradiation direction of the stripe-shaped parallel light rays, a geometric pattern as shown in FIG. 10 may be observed if the shadow is not taken into consideration. In FIG. 10, the part shown in black is the part that does not appear to be irradiated with light, the part shown in white is the part that appears to be irradiated with light, and the pattern of parallel rays is not linear, It looks distorted.
[0009]
In this way, when the state of irradiating a three-dimensional curved surface with a certain pattern of parallel rays at an angle is viewed from directly above the three-dimensional curved surface, the shape of the three-dimensional curved surface, the pattern of parallel rays, It can be considered that a geometric pattern corresponding to the relationship between these three elements can be observed by the mutual relationship between the three elements in the irradiation direction. As can be seen from FIG. 10, it can be seen that such a geometric pattern is effective in design.
[0010]
Therefore, considering the creation of a geometric pattern as shown in FIG. 10, if only the geometric pattern shown in FIG. 10 is to be created, commercially available paint software or drawing software is used as described above. However, since this kind of geometric pattern is generated by the interrelation between the three elements of the shape of the three-dimensional curved surface, the pattern of parallel rays, and the irradiation direction as described above, By changing even one of the three elements, a geometric pattern with various variations can be obtained.
[0011]
For example, the shape of the three-dimensional curved surface can be variously changed from the shape shown in FIG. 11 (a) to 11 (e) are diagrams showing examples thereof. FIG. 11 (a) is a diagram in which every other curved surface forming unit B is determined based on the arrangement of the curved surface forming unit bodies B shown in FIG. In this configuration, the surface A is inverted to the lower side of the reference surface A, and in this way, a three-dimensional curved surface having a wave can be obtained.
[0012]
FIG. 11B shows an arrangement in which an appropriate gap is provided between the adjacent curved surface forming unit bodies B from the arrangement of the curved surface forming unit bodies B shown in FIG. 8, and FIG. ), Every other curved surface forming unit B is inverted to the lower side of the reference surface A with the reference surface A as a center. It can be seen that the shape of the three-dimensional curved surface can be changed by appropriately changing the arrangement. 11B and 11C show cross sections along the zy plane when a plurality of curved surface forming units B are arranged as described above.
[0013]
Further, when one curved surface forming unit B is considered, the shape of the surface is not limited to a substantially semicircular shape, but may be a half period of a sine wave as shown in FIG. As shown to (e), it can also be set as a semi-ellipse, Furthermore, it can be set as another shape, It is possible to change the shape of a three-dimensional curved surface also by this. 11D and 11E show cross sections along the zy plane for one curved surface forming unit B. FIG.
[0014]
As described above, the shape of the three-dimensional curved surface can be changed by changing the arrangement of the curved surface forming units B or the surface shape of the curved surface forming units B. Even if the pattern and the irradiation direction are kept constant, different geometric patterns can be obtained.
[0015]
Further, if the length in the short direction of the curved surface forming unit B is referred to as the width, the width of the curved surface forming unit B shown in FIG. 8 or FIG. 11A is constant, and the arrow D in FIG. When viewed from the direction, it is rectangular as shown in FIG. However, even if the width of the curved surface forming unit B is constant, as shown in FIG. 12 (b), it is possible to give overall undulation along an appropriate curve. The shape of the curved surface can be changed. 12 (a) and 12 (b), the alternate long and short dash line indicates the central axis of the curved surface forming unit body B. In FIG. 12 (a), the central axis is a straight line, but in FIG. 12 (b) the central axis. Is wavy along a sine wave. Furthermore, as shown in FIGS. 12C and 12D, the width of the curved surface forming unit B may be changed according to the position in the x direction, and this also changes the shape of the three-dimensional curved surface. can do. In FIGS. 12A to 12D, the shape of one curved surface forming unit B on the reference plane A is shown.
[0016]
As described above, the shape of the three-dimensional curved surface can be changed by changing the arrangement and shape of the curved surface forming unit B, and thereby the viewpoint, the pattern of parallel rays, and the irradiation direction can be kept constant. Even so, different geometric patterns can be obtained.
[0017]
To obtain a different geometric pattern, the pattern of parallel rays may be changed. For example, in FIG. 9, the opening S of the slit is rectangular, but as shown in FIG. 13A, even if the width of the opening S is constant regardless of the position, the central axis thereof has an appropriate curve. As shown in FIG. 13B, the width of the opening S can be changed according to the position, and the shape of the opening S is thus changed. By changing the pattern, the pattern of parallel light rays irradiated on the three-dimensional curved surface can be changed variously.
[0018]
In addition, as shown in FIG. 13C, a slit in which the openings S are arranged in a checkered pattern can be used, and this can also change the pattern of parallel rays irradiated to the three-dimensional curved surface in various ways. Furthermore, the shape of each opening S of the slit shown in FIG. 13C is not limited to a rectangle, but can be variously changed.
[0019]
Even when the shape of the three-dimensional curved surface and the irradiation direction of the parallel rays are kept constant, it is easy to change the observed geometric pattern by changing the pattern of the parallel rays irradiating the three-dimensional curved surface. This is where you can expect.
[0020]
Similarly, if the irradiation direction of the parallel light beam is changed in a state where the shape of the three-dimensional curved surface and the pattern of the parallel light beam are kept constant, it can be easily predicted that the observable geometric pattern will be different.
[0021]
In this way, when a certain three-dimensional curved surface shape is considered and the surface is irradiated with a parallel beam of a certain pattern from a certain angle, the observation is performed when the three-dimensional curved surface is viewed from directly above. The geometric pattern is useful in design even when only one specific situation is set, but the 3D curved surface shape can be changed or the pattern of parallel rays can be changed. By changing the angle and / or changing the irradiation direction, geometric patterns with various variations can be obtained.
[0022]
However, it is very troublesome to create a geometric pattern as a variation obtained by changing at least one of the three elements as described above by handwriting or commercially available software as in the past. It is necessary.
[0023]
Therefore, the present invention creates a geometric pattern that can be observed when a parallel light beam having an appropriate pattern is irradiated on a three-dimensional curved surface from a certain direction and a geometric pattern of a variation thereof easily and in a short time by simulation. The present invention relates to a method and apparatus for creating a geometric pattern.
[0024]
[Means for Solving the Problems]
  In order to achieve the above object, the geometric pattern creating method according to claim 1 comprises:
  From the input means,At least a first function C (x, y) that defines a pattern of parallel rays at a position (x, y) on the xy plane of the three-dimensional orthogonal coordinate system, and x of the three-dimensional orthogonal coordinate system; A second function Z (x, y) for determining the height at a position (x, y) on the y plane, and a three-dimensional polar coordinate with the origin of the three-dimensional orthogonal coordinate system as the origin as the irradiation direction of the parallel rays Two angles defined by the system φ, θIs entered,
  By means of simulation,Based on the input creation image size, the first function C (x, y), the second function Z (x, y), and the two angles φ and θ,
  One pixel of the created image as the pixel of interest
  A position on the three-dimensional curved surface determined by the second function Z (x, y), and the x coordinate value and the y coordinate value are the same as the x coordinate value and the y coordinate value of the target pixel of the created image Find a first position having a value;
  A straight line passing through the first position and parallel to the irradiation directions φ and θ is obtained.
  Find the second position where this straight line intersects the xy plane,
  Substituting the x-coordinate value and y-coordinate value of the second position into the first function C (x, y) that defines the pattern of parallel rays, and obtaining the light defined for the second position;
  The obtained light value is used as the pixel value of the target pixel on the created image.
Perform processing on all pixels in the created image
ByWith respect to the three-dimensional curved surface defined by the second function Z (x, y), the parallel rays of the pattern defined by the first function C (x, y) on the xy plane are in the directions of φ and θ. Simulating a geometric pattern that can be observed at z = ∞ without performing shadow calculation
It is characterized by providing.
  The geometric pattern creating apparatus according to claim 2 is:
  At least a first function C (x, y) that defines a pattern of parallel rays at a position (x, y) on the xy plane of the three-dimensional orthogonal coordinate system, and x of the three-dimensional orthogonal coordinate system; A second function Z (x, y) for determining the height at a position (x, y) on the y plane, and a three-dimensional polar coordinate with the origin of the three-dimensional orthogonal coordinate system as the origin as the irradiation direction of the parallel rays Input means for inputting two angles φ and θ defined in the system;
  Based on the input creation image size, the first function C (x, y), the second function Z (x, y), and the two angles φ and θ,
  One pixel of the created image as the pixel of interest
  A position on the three-dimensional curved surface determined by the second function Z (x, y), and the x coordinate value and the y coordinate value are the same as the x coordinate value and the y coordinate value of the target pixel of the created image Find a first position having a value;
  A straight line passing through the first position and parallel to the irradiation directions φ and θ is obtained.
  Find the second position where this straight line intersects the xy plane,
  Substituting the x-coordinate value and y-coordinate value of the second position into the first function C (x, y) that defines the pattern of parallel rays, and obtaining the light defined for the second position;
  The obtained light value is used as the pixel value of the target pixel on the created image.
Perform processing on all pixels in the created image
ByWith respect to the three-dimensional curved surface defined by the second function Z (x, y), the parallel rays of the pattern defined by the first function C (x, y) on the xy plane are in the directions of φ and θ. And a simulation means for simulating a geometric pattern that can be observed at z = ∞ without performing a shadow calculation.
A geometric pattern creating apparatus comprising:
[0025]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the invention will be described with reference to the drawings.
FIG. 1 is a diagram showing an embodiment of a geometric pattern creating apparatus according to the present invention. In the figure, 1 is input means, 2 is control means, 3 is display means, 4 is simulation means, and 5 is image output means. Indicates.
[0026]
First, each part of the configuration shown in FIG.
[Input means 1]
As described above, the input unit 1 simulates the geometric pattern that can be observed when viewed from directly above the three-dimensional curved surface when the three-dimensional curved surface is irradiated with parallel rays having an appropriate pattern from a certain direction. This is for inputting various parameters to be created by.
[0027]
The input means 1 constitutes an interactive graphical user interface (GUI) together with the display means 3 by the control means 2. By operating the input means 1, it is possible to select a menu for processing such as parameter input and simulation execution start, and input parameters described below.
[0028]
The main parameters input from the input means 1 will be described below.
(1) Created image size (x-direction size: xsize, y-direction size: ysize)
The created image size is the size of the geometric pattern image to be created, and its x-direction size xsize and y-direction size ysize are input. Also, the resolution of the created image is input in relation to the created image size. Here, as shown in FIG. 2, the position in the region of the created image is represented by an orthogonal coordinate system in which the upper left corner of the created image is the origin O, the vertical direction is the x axis, and the horizontal direction is the y axis. To.
[0029]
(2) Irradiation direction of parallel rays: φ, θ
The irradiation direction of a parallel light beam having a certain pattern that irradiates a three-dimensional curved surface is defined by two angles φ and θ defined by a three-dimensional polar coordinate system with the origin O of the three-dimensional orthogonal coordinate system described above as the origin. Here, the relationship between the three-dimensional orthogonal coordinate system and the three-dimensional polar coordinate system is as shown in FIG. 3, and the coordinates of the point P in the three-dimensional orthogonal coordinate system are represented by (x, y, z). When the coordinates in the system are represented by (r, θ, φ),
x = r × sin θ × cosφ (1)
y = r × sinθ × sinφ (2)
z = r × cos θ (3)
There is a relationship. In FIG. 3, r is the distance between the point P and the origin O. P ′ (x, y, 0) is a perpendicular foot dropped from the point P to the xy plane, and the counterclockwise angle formed by the x axis and the line segment OP ′ is φ, and z The angle formed by the axis and the line segment OP is θ.
Therefore, the values of φ and θ are input from the input unit 1 as the irradiation direction of the parallel rays.
[0030]
(3) Pattern of parallel rays: C (x, y)
This defines the shape of the slit through which the light beam is irradiated, defines the shape of the slit openings, the arrangement of the openings, and the transmission color, and further defines the slit as described above. It is only necessary to define the angle at which the light is arranged with respect to the parallel rays from the irradiation direction, and to define what the light that has passed through the slit will be. It is very cumbersome and difficult to do such a thing, and even if it can be done, it takes time and can be said to be unrealistic.
[0031]
Therefore, in this geometric pattern creating apparatus, how the light strikes on the xy plane, which is the z = 0 plane of the three-dimensional orthogonal coordinate system, that is, each position (x, The pattern of parallel rays is defined by defining whether or not y) is exposed to light or not, and what color of light is applied.
[0032]
In this way, defining whether or not light hits each position on the xy plane, conversely, defines the shape of the slit openings as described above, its arrangement, transmitted light, and the like. There is nothing else. In fact, if it can be determined whether or not light hits each position on the xy plane and the irradiation direction of the parallel rays is determined, the shape of the slit aperture, its arrangement, transmitted light, and the like can be calculated backward. However, this geometric pattern creating apparatus does not need to do such a thing at all.
[0033]
Specifically, the pattern of parallel rays is defined by defining the color of light at position (x, y) on the xy plane as a function C (x, y) of that position (x, y). To do.
Two examples are shown below. Here, the operator “mod” is introduced, A and B are real numbers, and “AmodB” represents a remainder when A is divided by B. That is, m is an integer greater than or equal to 0, and n is a real number satisfying 0 ≦ n <B.
A = m × B + n (4)
Is expressed as
AmodB = n (5)
It is. Therefore, “4.2 mod 1.1 = 0.9”. The same applies to this point.
[0034]
(Example 1 of parallel light pattern)

Here, the parallel light is assumed to be white light, and the value of C (x, y) is “1”, the position (x, y) on the xy plane is white, and the light is hit. “0” is black and indicates no light. The same applies to this point.
In this case, i = 0,1,2, ...
8i ≦ x <4 + 8i (7)
In this range, light hits, and no other light hits. Therefore, the way the light hits on the xy plane, that is, the pattern of parallel rays is striped as shown in FIG. Become. In addition, the part shown by the oblique line in Fig.4 (a) has shown the part which does not receive light.
[0035]
(Example 2 of parallel light pattern)

In this case, the parallel light beam pattern is a checkered pattern as shown in FIG. This can be easily understood from Example 1 above. In addition, the part shown by the oblique line in FIG.4 (b) has shown the part which does not receive light.
[0036]
Thus, the definition of the pattern of parallel rays is by defining the color of light at the position (x, y) on the xy plane as a function C (x, y) of the position (x, y). For this input, a desired function C (x, y) may be created and its expression may be input.
[0037]
In addition, some general formulas of the function C (x, y) are registered in the control unit 2 in advance, a desired function is selected from the input unit 1 and a parameter value in the function is input. It may be. For example, as a pattern of parallel rays, α and β are used as parameters.

When the general formula is registered and a striped pattern is desired, this function is selected by the input means 1 and the values of the parameters α and β in the general formula are input. The same applies to other patterns of functions.
[0038]
In the above example, the value of the function C (x, y) is assumed to be 1 (white) or 0 (black), but red (R), green (G), and blue (B). The values of these three colors, or the values of cyan (C), magenta (M), yellow (Y), and black (K) may be determined as desired. For example,

Then, the white part in FIG. 4A is red, and the shaded part is green.
[0039]
(4) Three-dimensional curved surface shape: Z (x, y)
This is a parameter for determining the shape of a three-dimensional curved surface irradiated with parallel rays having a desired pattern. In this geometric pattern creating apparatus, x−, which is a z = 0 plane of a three-dimensional orthogonal coordinate system. The shape of the three-dimensional curved surface is defined by defining the height Z from the y plane as a function Z (x, y) of the position (x, y) on the xy plane. Here, the height from the xy plane includes not only the positive direction of z but also the negative direction of z.
For example,
Z = (x, y) = 5 × | sin (πy / 20) | (11)
Then, the three-dimensional curved surface represented by the function Z (x, y) is as shown in FIG. 8, but the surface shape of each curved surface forming unit B is a sign as shown in FIG. 11 (d). It is a half cycle of the wave, its amplitude is 5, and its width is 20 in coordinate value.
[0040]
As described above, the definition of the three-dimensional curved surface shape is defined by defining the height from the position (x, y) on the xy plane as a function Z (x, y) of the position (x, y). In this input, a desired function Z (x, y) may be created and the expression may be input, or a number of general expressions of the function Z (x, y) may be set in advance. Alternatively, it may be registered in the control means 2, a desired function is selected from the input means 1, and a parameter value in the function may be input. For example, as a three-dimensional curved surface shape, α and β are used as parameters.
Z = (x, y) = α × | sin (πy / β) | (12)
This function is selected by the input means 1 if desired, and the values of the parameters α and β in the general formula are input. In this case, it is clear that α is a parameter that determines the amplitude, and β is a parameter that determines the period.
[0041]
[Control means 2]
The control means 2 controls the overall operation of the geometric pattern creating apparatus. Further, as described above, the control means 2 constitutes a GUI together with the input means 1 and the display means 3.
[0042]
[Display means 3]
The display unit 3 includes an appropriate display device such as a color CRT or a color liquid crystal display device and its display control unit. The control unit 2 forms a GUI together with the input unit 1.
[0043]
[Simulation means 4]
This is a direction (φ, θ) so that a three-dimensional curved surface having a shape represented by Z (x, y) has a pattern represented by a function C (x, y) on the xy plane. The image data of the geometric pattern that can be observed when the viewpoint is viewed at z = ∞ when the parallel rays are irradiated from is obtained by simulation. However, shadow calculation is not performed in this simulation. That is, based on the generally used Lambert's cosine law, shadow calculation depending on the normal direction is not performed, and the intensity of light irradiated to the position is directly adopted as a pixel value.
[0044]
The simulation process will be described with reference to FIG. In FIG. 5, it is assumed that parallel rays are irradiated from the direction (φ, θ) indicated by the arrow E, and a function that determines the pattern of parallel rays is C (x, y), and a function that determines the three-dimensional curved surface shape is Z ( x, y).
[0045]
[Step S1]
Focus on one pixel on the created image. Let the coordinate value of the pixel of interest on this created image be (x, y).
[0046]
[Step S2]
A position on the three-dimensional curved surface, the x coordinate value and the y coordinate value of which are the same as the x coordinate value and the y coordinate value of the target pixel of the created image, is obtained. It is easy to obtain such a position. The x-coordinate value and y-coordinate value of the position on the three-dimensional curved surface are the same as the x-coordinate value and y-coordinate value of the target pixel, respectively, and the z-coordinate value is the height at the position (x, y). Since it is nothing else, it can be obtained by a function Z (x, y) that determines the three-dimensional curved surface shape. Therefore, the coordinate value of the position on the three-dimensional curved surface is (x, y, Z). In FIG. 5, the position is indicated by P.
[0047]
[Step S3]
A straight line L passing through the position P (x, y, Z) obtained in step S2 and parallel to the determined irradiation direction (φ, θ) is obtained, and the straight line L intersects with the xy plane at z = 0. Ask for. It is easy to obtain such a straight line L. That is, since the irradiation directions are φ and θ, considering a unit vector having angles φ and θ, the x component Ix, y component Iy, and z component Iz of the unit vector are respectively
Ix = sinθ × cosφ (13)
Iy = sinθ × sinφ (14)
Iz = cosθ (15)
Therefore, from this, the inclination of the straight line L with respect to the x-axis, y-axis, and z-axis is known, and this straight line L passes through the point P (x, y, Z). An equation can be obtained, and a position Q where the straight line L intersects the xy plane can be obtained. Since such processing is well known, detailed description is omitted.
Here, the coordinate value of the position Q thus obtained is assumed to be Q (x ′, y ′, 0) as shown in FIG.
[0048]
[Step S4]
By substituting the x-coordinate value x ′ and y-coordinate value y ′ of the position Q obtained in step S3 into the function C (x, y) that determines the pattern of parallel rays, the position Q (x ′, y ′, 0 The light C ′ (x ′, y ′) defined with respect to () is obtained, and the obtained value of the light C ′ is used as the pixel value of the pixel on the created image focused in step S1.
[0049]
By performing the above processing for all the pixels of the created image, geometric pattern image data is created.
[0050]
Examples of geometric patterns created by the above simulation process are shown in FIGS. 6 and 7, the horizontal direction is the y-axis direction, and the vertical direction is the x-axis direction. The irradiation direction (φ, θ), the function C (x, y) for determining the pattern of parallel rays, and the function Z (x, y) for determining the three-dimensional curved surface shape are as follows. .
[0051]

[Image output means 5]
The image output means 5 outputs the geometric pattern image data created by the simulation means 4 and can be constituted by a printer, a film output device, or an external storage device such as a hard disk device. Of course, all of these may be provided as the image output means 5.
[0052]
The outline of each part of the geometric pattern creating apparatus shown in FIG. 1 has been described above, but the geometric pattern creating apparatus shown in FIG. 1 can be configured by a computer system. That is, the input means 1 can be constituted by a keyboard and a pointing device, the display means 3 can be constituted by a monitor and a display control means, and the simulation means 4 is described in the above description or the explanation to be described later in a control device including a CPU. It can be configured by installing software that operates.
[0053]
Next, the operation when creating a geometric pattern image using the geometric pattern creating apparatus shown in FIG. 1 will be described.
[0054]
Step 1: Parameter input and simulation execution instruction
First, the operator inputs a predetermined parameter value by the input means 1. Here, at least the above parameters are input. Then, when the operator inputs predetermined parameters, the input means 1 instructs execution of the simulation.
As a result, the control means 2 passes the input parameters to the simulation means 4 and instructs the execution of the simulation.
[0055]
Process 2: Simulation
When the simulation unit 4 receives a parameter from the control unit 2, the simulation unit 4 executes a simulation. This simulation process is as described above. Thereby, image data of a geometric pattern is created. Then, when the simulation is completed, the simulation unit 4 displays the created geometric pattern image on the display unit 3.
[0056]
Process 3: Output or correction of geometric pattern image data
The operator observes the image of the geometric pattern displayed on the display means 3 and outputs it to the image output means 5 if it is satisfactory. As described above, since the image output means 5 can be a printer, a film output device, an external storage device or the like, the output of the created geometric pattern image data can be stored in an external storage device. It is possible to print out with a printer or output film with a film output device.
[0057]
However, when the created geometric pattern is undesirable or when it is desired to create various variations from the created geometric pattern, the irradiation direction φ, θ, and parallel beam pattern of parallel rays are determined. The desired parameter among the three parameters of the function C (x, y) and the function Z (x, y) defining the three-dimensional curved surface shape may be changed as desired, and the simulation may be performed again.
[0058]
As described above, according to this geometric pattern creating apparatus, the irradiation directions φ and θ of parallel rays, the function C (x, y) that determines the pattern of parallel rays, and the function Z (that determines the three-dimensional curved surface shape When three parameters x, y) are set and input as desired, and a parallel light beam having a desired pattern is automatically irradiated from a desired direction onto a three-dimensional curved surface having a desired shape. It is possible to create a geometric pattern that can be observed easily.
[Brief description of the drawings]
FIG. 1 is a diagram showing an embodiment of a geometric pattern creating apparatus according to the present invention.
FIG. 2 is a diagram for explaining that a position in a created image is represented by an orthogonal coordinate system in which an upper left corner of the created image is an origin O, a horizontal direction is a y-axis, and a vertical direction is an x-axis.
FIG. 3 is a diagram for explaining a relationship between a three-dimensional orthogonal coordinate system and a three-dimensional polar coordinate system.
FIG. 4 is a diagram illustrating an example of a pattern of parallel rays.
FIG. 5 is a diagram for explaining a simulation process executed by a simulation unit 4;
FIG. 6 is a diagram illustrating an example of a geometric pattern created by a simulation process.
FIG. 7 is a diagram illustrating an example of a geometric pattern created by a simulation process.
FIG. 8 is a diagram for explaining a geometric pattern to be created by the geometric pattern creating apparatus according to the present invention, and a substantially semi-cylindrical curved surface forming unit B is arranged on the reference plane A without a gap; It is a figure which shows the state which carried out.
FIG. 9 is a diagram illustrating an example of a slit that forms a pattern of parallel light rays that irradiate a three-dimensional curved surface.
FIG. 10 is a diagram showing an example of a geometric pattern to be observed.
FIG. 11 is a diagram for explaining a change in the shape of a three-dimensional curved surface.
FIG. 12 is a diagram for explaining a change in the shape of a three-dimensional curved surface.
FIG. 13 is a diagram illustrating an example of changing the opening of a slit.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Input means, 2 ... Control means, 3 ... Display means, 4 ... Simulation means, 5 ... Image output means.

Claims (2)

A first function C (x, y) for determining a pattern of parallel rays at least at a position (x, y) on the xy plane of the three-dimensional orthogonal coordinate system from the input means , the three-dimensional orthogonal A second function Z (x, y) that determines the height at a position (x, y) on the xy plane of the coordinate system, and the origin of the three-dimensional orthogonal coordinate system as the origin as the irradiation direction of the parallel rays When two angles φ and θ defined in the three-dimensional polar coordinate system are input,
Based on the input created image size, the first function C (x, y), the second function Z (x, y), and the two angles φ, θ by the simulation means ,
One pixel of the created image as the pixel of interest
A position on the three-dimensional curved surface determined by the second function Z (x, y), and the x coordinate value and the y coordinate value are the same as the x coordinate value and the y coordinate value of the target pixel of the created image Find a first position having a value;
A straight line passing through the first position and parallel to the irradiation directions φ and θ is obtained.
Find the second position where this straight line intersects the xy plane,
Substituting the x-coordinate value and y-coordinate value of the second position into the first function C (x, y) that defines the pattern of parallel rays, and obtaining the light defined for the second position;
The obtained light value is used as the pixel value of the target pixel on the created image.
Perform processing on all pixels in the created image
Thus, with respect to a three-dimensional curved surface defined by the second function Z (x, y), parallel rays having a pattern defined by the first function C (x, y) on the xy plane are represented by φ, θ A method of creating a geometric pattern comprising a step of simulating a geometric pattern that can be observed at a viewpoint of z = ∞ without performing a shadow calculation when it is irradiated from the direction of. At least a first function C (x, y) that defines a pattern of parallel rays at a position (x, y) on the xy plane of the three-dimensional Cartesian coordinate system, and x of the three-dimensional Cartesian coordinate system. A second function Z (x, y) for determining the height at a position (x, y) on the y plane, and three-dimensional polar coordinates with the origin of the three-dimensional orthogonal coordinate system as the origin as the irradiation direction of the parallel rays Input means for inputting two angles φ and θ defined in the system;
Based on the input created image size, the first function C (x, y), the second function Z (x, y), and the two angles φ, θ,
One pixel of the created image as the pixel of interest
A position on the three-dimensional curved surface determined by the second function Z (x, y), and the x coordinate value and the y coordinate value are the same as the x coordinate value and the y coordinate value of the target pixel of the created image Find a first position having a value;
A straight line passing through the first position and parallel to the irradiation directions φ and θ is obtained.
Find the second position where this straight line intersects the xy plane,
Substituting the x-coordinate value and y-coordinate value of the second position into the first function C (x, y) that defines the pattern of parallel rays, and obtaining the light defined for the second position;
The obtained light value is used as the pixel value of the target pixel on the created image.
Perform processing on all pixels in the created image
Thus, with respect to a three-dimensional curved surface defined by the second function Z (x, y), parallel rays having a pattern defined by the first function C (x, y) on the xy plane are represented by φ, θ And a simulation means for simulating a geometric pattern that allows observation of the viewpoint at z = ∞ without performing a shadow calculation.

Images