FORM CREATING SYSTEM

Abstract: A single form creating system provides for free access to a form to be created throughout its whole process ranging from its first or design step to its final or manufacturing step. The position of a third point and the direction of a third straight line are first decided in accordance with the posi­ tions of first and second points as well as the directions of first and second lines, and then such third points are connected successively to create a desired form.

Description: The present invention relates to a form creating system, i.e. to an improved and advanced system which is capable of creating a desired form or modifying its created form in the field of CAD (Computer Aided Design) and/or CAM (Computer Aided Manufacturing), NC machine tool, computer graphics, computer vision and the like. In CAD/CAM, computer vision or the like, conventionally there are well known three types of modellings to express a desired or predetermined form; that is, a wire frame modeller, a surface modeller, and a solid modeller. Briefly, as for the wire frame modeller, the above kinds of forms, can be expressed by using constracted points which are roughly populated as a finite type of a set which has lower density. As for the surface modeller, these forms can be also expressed by the same type of a set which has higher density. In these cases, the two modellers of the above type can be performed by the way of estimating the lacked points among the given points obtained so as to express the form, that is by means of interpolation operation based on the functional approximation. The solid modeller piles up simple or primitive forms obtained as the typical sets in which the points are densly populated in a manner similar to a building-blocks-work to express a predetermined form. Each of these three conventional methods features a function to express forms for solid bodies. However, when used to express a three-dimensional form, the above-mentioned prior art methods lack in flexibility of expression so that they are unable to perform their functions sufficiently. Also, it is well known that a form expression is one embodiment of a form producing/finishing process while a form creation is also another one embodiment of the same process. All of the three conventional modellings however, are incapable of performing a continuous and throughout processing operation between these two embodiments. For example, even when the prior art of solid modeller is used, some of three-dimensional forms can be indeed expressed by means of combination of simple forms, but the solid model method inherently can not provide a free and detailed expression of such three-dimensional form. Thus, it can be naturally said that it is almost impossible to carry out a continuous and throughout processing operation from the form expression step to the form creation step. The Article "A New Method for Vector Generation" by R.L.T. Cederberg from Computer Graphics and Image Processing, Vol. 9, pages 183-195 (1979) describes a method of approximating a straight line between two fixed points. The straight line is approximated by a series of short vectors, whereby the first and last vectors pass through the first and second fixed points respectively. The vectors are determined so that they are centred to the straight line i.e. they straddle the straight line uniformly. The disadvantage of this approach for operating an NC machine is that the zig-zag nature of the approximated line results in the NC tool being driven in along a zig-zag path rather than along a smooth line or around a smooth curve. Accordingly, it is a principal object of the present invention to provide an improved unique form creating system which is freely accessible throughout its whole process ranging from design of a model or the like to manufacture of an actual form, while eliminating the drawbacks in the above-mentioned prior art methods. The object of the invention is solved by a two-dimensional or three-dimensional form creating system comprising: a reference point setting means for setting a position of a point in a formative space, said reference point setting means setting each position of both a first point and a second point at arbitary but different positions, each said position being a constructive point lying on a contour of a forming solid or figure a reference line setting means for setting a reference straight line passing through said reference point, said reference line setting means setting a first and second straight line passing separately through said first point and said second point respectively, input means for determining the position of a plurality of intermediate reference points, which lie on a contour of said solid or figure between the first and second points, characterized by said reference line setting means setting said first and second straight lines in arbitrary directions but not parallel to each other; triangle form setting means for setting a triangular wire frame-like form which is formed by a constructive procedure in accordance with both the position of said second point and the direction of said second line as well as both the position of said first point and the direction of said first line; said input means inputting shape control parameters as control variables; said intermediate point operating means determining said intermediate point based on the triangular wire frame-like form set by said triangle form setting means and the shape control parameters set by said input means; and said controlling means controlling repetitively each of said reference point setting means, said reference line setting means, triangle form setting means, and intermediate point operation means to determine the position of the plurality of intermediate points based on previously set or determined points and lines, these operations being repeatedly formed until the contour of said solid or figure is represented by the determined intermediate points within a predetermined accuracy. If such form creating process is displayed in a display unit, it is naturally understood that such form creating process itself is a CAD (Computer Aided Design) and also that data on the form created, as they are, can be used to operate an NC machine tool. It should be noted that the term "create" is used in the sense of "create and/or generate". The above object and features of the invention will be more apparent from the following description, from the disclosure found in the accompanying drawings and from further claims. The drawings illustrate as follows: Fig. 1 is a general view of an embodiment of the invention; Fig. 2 is a graphical representation illustrating the first setting step required to create a form; Fig. 3 is a graphical representation of fundamental und isosceles triangles both formed from the setting in Fig. 2; Fig. 4 is a graphical representation illustrating how to determine a constant α necessary to find a third point constituting a part of a form to be created; Fig. 5 is a graphical representation illustrating how to find an incenter of said isosceles triangle; Fig. 6 is a graphical representation illustrating how to find an incenter of said fundamental triangle; Fig. 7 is a graphical representation illustrating how to determine an unequilibrium amount S; Fig. 8 is a graphical representation illustrating how to find a distance d from the incenter of the fundamental triangle to a third point to be found; Figs. 9 and 10 are graphical representations illustrating how to find a third line at a third point; Fig. 11 is a graphical representation illustrating how to find a new third point; Fig. 12 is a graphical representation illustrating how a form can be changed when only the directions of the first and second lines among parameters are varied; Fig. 13 is a graphical representation illustrating how a form can be changed when only a position control parameter β is varied; Fig. 14 is a graphical representation illustrating how a form can be changed when only a tangent control parameter δ is varied; Fig. 15 is a graphical representation illustrating a principle to find a third straight line in a simplified manner; Fig. 16 is a graphical representation illustrating a state in which the first and second points as well as the first and second lines are set so as to create a three-dimensional form; Fig. 17 is a graphical representation illustrating a state in which the first straight line is orthogonally projected on a surface formed by a chord and the second straight line; Fig. 18 is a graphical representation illustrating a state in which the second straight line is orthogonally projected on a surface formed by the chord and the first straight line; Fig. 19 is a graphical representation illustrating how to form a fundamental triangular pyramid; Fig. 20 is a graphical representation illustrating how to form a temporary triangle; Fig. 21 is a graphical representation illustrating how to form a fundamental triangle in the temporary triangle; Fig. 22 is a graphical representation illustrating how to find a third point in creating a three-dimensional form; Fig. 23 is a block diamgram of an embodiment of the present invention; Fig. 24 is a block diagram of another embodiment of the present invention; and, Fig. 25 is a block diagram of still another embodiment of the present invention. We will now describe the present invention in detail with reference to embodiments illustrated in appended drawings. In Fig. 1, a general view of a system or a first embodiment of the invention is illustrated. The illustrated embodiment is provided with keyboard 1 and light pen 2 which cooperate to input positional information on a point that corresponds to the end of a form to be created, that is, the first point of the form to be created. It also incorporates an operation circuit 3 to perform a predetermined operation in accordance with input signals from input means such as keyboard 1 and light pen 2. It further includes a display unit to display the thus-created forms, a printer 5 to print such forms, and an external memory unit 6 which stores such forms in the form of predetermined signals such as magnetic signals or light signals. Figs. 2 through 22 illustrate principles of the invention that are useful in creating a desired form and, in particular, Fig. 2 to 11 show the principles of the invention that can be used to obtain two-dimensional forms. Throughout Figs. 2 - 22, heavy lines are used to express lines that are newly found in the respective figures. Specifically, in Fig. 2, there is shown the first setting step necessary to create a form. We can see a first point 11 and a second point 12 both of which are set at their aribitrary but different positions respectively, as well as a first straight line L1 passing through the first point 11 and a second straight line L2 passing through the second point 12. All of these points and lines are present in the same plane, so that a desired form can be produced between these two points. To set these points and lines, light pen 2, for example, may be placed at an aribitrary position on the display unit 4 to set the first point 11. Similarly, the second point 12 can be established at an aribitrary position other than that of the first point 11. Then, a straight line passing through the first point 11, or L1, is set, with its direction being determined by means of keyboard 1. Likewise, a straight line passing through the second point 12, or L2, is set, with its direction determined by keyboard 1. A point where both lines L1 and L2 intersect with each other is set as an intersection point 13. Although in the above description the information on the positions of the points as well as on the directions of the straight lines is inputted by means of keyboard 1 and light pen 2, it should be understood that this is not limitative but other suitable input means such as a digitizer may also be used for this purpose. Fig. 3 illustrates a fundamental triangle and an isosceles triangle both formed from the setting shown in Fig. 2. First and second points 11 and 12 are connected to draw a line segment, which is denoted by L3 and called a chord. Here, the reason this line L3 is called a chord is that, when a part (a contour line) of a desired form is to be created between first and second points 11 and 12, if such contour line is considered as a circular arc, then line L3 corresponds to a chord thereof. A triangle enclosed by three lines L1, L2 and L3 is here called a fundamental triangle. In this case, a shorter one of the two sides other than the side formed by chord L3, among the three sides of this fundamental triangle, is one formed by line L1. This shorter side is a line segment connecting points 11 and 13. Then, an isosceles triangle having two equilateral sides each equal to the above-mentioned shorter side is so formed as to be superposed on the fundamental triangle. In other words, a new point which is equi-distant from intersection point 13 as with line L1 is set on line L2. This new point is represented by 21. Thus, the other of the equilateral sides of this isosceles triangle is a line segment connecting point 21 and intersection point 13 in Fig. 2. A line segment between first point 11 and new point 21 is called L4. Fig. 4 illustrates how to determine a constant α necessary to find a third point constituting a part of a form to be created. Specifically, a straight line bisecting an internal angle of an isosceles triangle at point 11 is denoted as L5, and such internal angle is denoted as <(13)(11)(21). Here <(13)(11)(21) expresses an angle included by a line segment between points 13 and 11, and a line segment between points 11 and 21. This way of expression on angles will be employed hereinafter as well. The constant α is found: α = { area of ▵ (21)(11)(13)} / { area of ▵ (12)(11)(22)} where ▵ (21)(11)(13) denotes a triangle enclosed by points 21, 11 and 13. Also, this way of expression on triangles will be employed hereinafter as well. Fig. 5 illustrates how to find an incenter of the above-mentioned isosceles triangle. Generally, an incenter of a triangle is a point of bisectors of its respective internal angles and the three bisectors intersect at one point. A bisector of the internal angle of the isosceles triangle at point 21 is denoted by L6. A point of intersection of the two bisectors L5 and L6, or, the incenter of the isosceles triangle is represented by 23. A middle point between point 11 and incenter 23 is denoted as 24 and a middle point between point 21 and incenter 23 is denoted as 25. Fig. 6 illustrates how to find an incenter of the above-mentioned fundamental triangle. In this figure, a bisector of the internal angle of the fundamental triangle at point 11 is represented by a straight line L7; a bisector of the same at point 12 by a straight line L8; and, an intersection point of the two bisectors L7 and L8 or the incenter of the fundamental triangle by point 14. Fig. 7 illustrates how to decide an unequilibrium amount S. Not only the parameter α but also a parameter β is necessary to find a third point constituting a part of the form to be created. To obtain this parameter β, it is necessary to decide the unequilibrium amount S, which depends on the difference between the attributes of the fundamental and isosceles triangles. To set up the unequilibrium amount S, first Figures 4 and 5 are superposed on each other. Then, bisectors L7 and L8 are respectively extended. A perpendicular L9 is drawn at point 24, and a perpendicular L10 is drawn at point 25. Let a triangle enclosed by perpendicular L9, bisector L8 and line L1 be S1 and a triangle enclosed by perpendicular L10, bisector L7 and line L2 be S2. Then, the unequilibrium amount S is found as follows: S = (area of S1) - (area of S2) Alternatively, other suitable techniques than the above may be used to obtain such amount S. Fig. 8 illustrates how to obtain a distance d between the internal center 14 of the fundamental triangle and a third point to be found now. Let a straight line connecting incenter 14 and intersection 13 be L11. This line L11 is a bisector of the internal angle of the fundamental triangle at point 13. Let a third point to be found now be point 33, and suppose that this third point 33 is present on line L11. Conversely speaking, when assuming that there exists a point at which bisector L11 and a form to be created intersect with each other, we call this intersection point a third point 33 and try to find the third point 33. Let the distance between point 33 and incenter 14 be d. The distance d can be found as follows: d = β (α · S)/ γ where the parameter β denotes a position control parameter and the parameter γ stands for the length from the first point 11 to the second point 12. Figs. 9 and 10 illustrate how to find a third straight line L13 at the third point 33. Here, line L13 is a tangent to a form outline at point 33. In other words, when an outline of a desired form is drawn between points 11 and 12 , a tangent to the outline at point 33 is the third straight line L13. Conversely speaking, line L13 is a straight line required to produce a new third point between points 33 and 11. This third straight line is found as follows: Let a straight line passing through both points 11 and 33 be L9, a straight line passing through both points 12 and 33 be L10, and a bisector of the intersectional angle of lines L10 and L9 be L12. This bisector L12 is shown in Fig. 9. Let a straight line intersecting with bisector L12 at angle of ϑ and also passing through point 33 within the plane of the fundamental triangle be L13. The angle of ϑ can be found as follows: ϑ = δ · (α · S) /A where the parameter δ expresses a tangent control parameter, and A stands for the area of the fundamental triangle. The thus-obtained straight line is the third straight line L13. If the operation described in Figs. 2 through 8 is executed using this third straight line L13, then the position of a new third point can be found. Fig. 11 illustrates how to find a new third point in the above-mentioned manner. Specifically, considering point 33 as an alternative of point 12 in Fig. 1 and line L13 as an alternative of line L2, the operations described in Figs. 2 through 8 are executed repeatedly. Point 21a corresponds to Point 21 shown in Fig. 3, and point 13a corresponds to point 13 in Fig. 2. Therefore, ▵ (11)(33)(13a) is a new fundamental triangle and ▵(11)(21a)(13a) is a new isosceles triangle. Then, if the same operations as illustrated in Figs. 9 and 10 are carried out, then a new third straight line can be obtained. Also, similar operations are performed between point 12 and point 33 to find another new third point and straight line. In this way, a great number of points can be found between points 11 and 12. If these points are connected successively, then a predetermined form ( or, an outline for such form) is created between points 11 and 12. For higher accuracy, in this case, the number of repetition of the operations described in connection with Figs. 2 through 11 may be increased. When it is desired to modify the form once created in accordance with the above-described principles, its parameters may be varied, which include the position of the first point 11, the position of the second point 12, the direction of the first straight line L1, the direction of the second straight line L2 and constants β, δ. Examples modified by varying some of the parameters are shown in Figs. 12 to 14. Fig. 12 illustrates how the form can be modified when only the directions of lines L1 and L2 out of all the parameters are changed. In this figure, form C has been created by considering the first and second straight lines as L1 and L2 respectively in accordance with the above -described technique. (Of course, this form C may be considered as an outline of a desired form, not as the desired form itself.) Here, with the first and second points 11, 12, position control parameter β and tangent control parameter δ unchanged, if the first and second lines are changed to L1b and L2b respectively, then the form C is altered into a form represented by a two-dot chained line Cb. As shown, the feature of the form modified through change of the directions of the first and second lines L1 and L2 is that its convex portions are respectively shifted upwardly and downwardly with respect to the bisector L11. In other words, when line L1 is rotated clockwise (in this case, line L2 is rotated counter-clockwise), the convex portions of the form C b are displaced downwardly of bisector L11, as can be seen from comparison with the form C. On the contrary, when line L1 is rotated counter-clockwise (in this case, line L2 is rotated clockwise), the convex portions of the modified form are shifted upwardly of bisector L11. It is noted here that both lines L1 and L2 must not be parallel to each other after they have been respectively rotated. This is necessary to ensure that the form created has not inflection point at point 11 or 12. Therefore, when the form created may have an inflection point at either of point 11 or 12, no special restrictions are required on the rotational conditions between lines L1 and L2. Fig. 13 illustrates how a form can be modified when only the position control parameter β is changed. Change of the position control parameter β causes the degree of expansion of the entire form or the curvature of the form to vary. In Fig. 13, there is shown the change of the form which occurs when the position control parameter β is changed to a negative value after it is set as a positive value and the form C is once created. Form Cc, which is obtained after the parameter β is changed to a negative value, has a smaller degree of expansion than that of the form C and comes nearer the chord L3. In other words, if the position control parameter β is set as 0, then the form passes through the incenter 14 of the fundamental triangle. If the parameter β is set as a positive value, then the form expands out away from the internal center 14 to come closer to intersection point 13; the greater the parameter β, the closer the form comes to intersection point 13. Conversely, if the parameter is changed to a negative value, then the form contracts away from internal center 14 and approaches the chord L3; the greater the absolute value of the parameter, the closer it approaches chord L3, which means that the form C comes closer to a straight line. The term "position" included in "position control parameter" means a position at which the form to be created intersects with bisector L11. Thus, to change the position control parameter β means the change of this intersection point. Accordingly, in other portions of the created form than the intersection point, the form is altered only in curvature. Also, when the form created prior to the change of the position control parameter β is contained within the fundamental triangle, even if the parameter is thereafter changed, the form created will not be bulged out of the fundamental triangle. Fig. 14 illustrates how a form can be changed when only the tangent control parameter δ is varied. When the tangent control parameter δ is varied, the degree of the expansion of the form can be changed between two points used to create a form (or to modify a created form)(that is, two points corresponding to the then first and second points). In other words, assume that the form C is once created between the first and second points 11 and 12. In this case, the third straight line L13 is identical with a tangent to the form C at the third point 33. After such point 33 and line L13 have been determined, a new third point is decided between points 11 and 33 in accordance with the directions of this tangent L13 and line L1. In this way, the form is gradually determined or produced. By the way, to change the tangent control parameter δ means to change the direction of the above-mentioned tangent (or, the third line L13). Therefore, the change of the tangent control parameter is identical with the change of the direction of the second line L2 when originally creating a form, and thus this can be considered to be the same case as described in connection with Fig. 12. In this case, however, there exists discontinuity at a point (the third point 33) in the form because line L1 is not changed. Specifically, if the tangent control parameter δ is changed at point 33 to change line L13 into line L13d, for example, then a form being created is changed into one shown by a two-dot chained line Cd between points 33 and 11. That is, if line L13 is rotated clockwise by changing the tangent control parameter δ, then a form being created is expanded out to the right in the drawing within the lower portion of bisector L11. The tangent control parameter is useful to enhance the degree of freedom of the operation for creating a form. Also, it should be noted that the values of the above-mentioned position and tangent control parameters can be varied to create a form or modify a created form not only between points 33 and 11 or 33 and 12, but also between every point and any other point in the form C. Thus, it is possible to modify the entire form C as well as any desired portion of the form C in an easy and free manner. Fig. 15 illustrates a principle to find a third straight line in a simple manner. Let an intersection point of an extension of line L9 and line L2 be point 34, let an intersection point of an extension of line L10 and line L1 be point 35, connect these points 34 and 35 to draw a line L14, and let a line drawn by parallely displacing line L14 onto point 33 be L15. This new line L15 is used in place of line L13. When ϑ is ambiguous in terms of accuracy, it is convenient to employ line L15 as a third straight line. The above-mentioned manner is usually used to create or modify a planar form. This manner, however, can also be applied in creating or modifying a three-dimensional form. Specifically, the above manner is used to create a plurality of planar forms and then these planar forms are superposed on each other to produce a three-dimension form in the form of a so-called flexible wire frame or network. Although the above description relates to creation of a form, it may also applied in drawing a previously-existing form. Namely, at first a form similar to the existing form is once produced roughly and then its position control parameter or tangent control parameter is varied to adjust the shape of the roughly-produced form. As the case may be, the points 11 and 12 as well as the directions of the lines L1 and L2 may be varied. Next, we will describe a principle that is used to creat a three-dimensional form. In this case, the three-dimensional form is not directly created, but a plurality of outlines or three-dimensional outlines of the form are first obtained and then these outlines are connected successively to create the desired form. In Fig. 16, there are set a first point 51, a second point 52, a first straight line L51, and a second straight line L52. Here, L51 is a line that passes through point 51, while L52 is a line that passes through point 52. Points 51 and 52 are interconnected to produce a chord 50. Why this line segment connecting these two points is expressed as a chord is the same reason as has been described in connection with Fig. 3. Here, the extensions of the lines L51 and L52 are considered not to intersect with each other. That is, a form to be created here is a three-dimensional one and thus outlines to be drawn between points 51 and 52, in many cases, do not exist in one plane. Also, L51 should be a tangent to the outline at point 51, and L52 should be a tangent to the outline at point 52. For this reason, in most cases, lines L51 and L52 do not intersect with each other. Fig. 17 illustrates an orthographic view of the first line L51 projected in a plane composed of the chord 50 and the second line L52. Let the orthographically-projected line of the line L51 be L53. That is, when light is applied to a plane formed by chord 50 and line L52, the resultant shadow of line L51 is considered as line L53. Fig. 18 illustrates an orthographic view of the second line L52 projected in a plane composed of the chord 50 and the first line L51. Let the orthographic line of the line L52 be L54. That is, when light is applied to a plane formed by chord 50 and line L51, the resultant shadow of the second line L52 is considered as line L54. Fig. 19 illustrates how to form a fundamental triangular pyramid. Specifically, points 53 and 54 are connected to produce a line segment. Let this line segment be L55. As a result of this, four planes enclosed by line L50, L51, L52, L53, L54 and L55 can be produced, which in turn cooperate to enclose or form a triangular pyramid. This is interpreted as a fundamental triangular pyramid. Fig. 20 illustrates how to form a temporary triangle Σ. A torsion control parameter is used to find a point 55 on line segment L55. This torsion control parameter ε can be obtained from the following equation: ε = D 1 /D 2 where, D1 is the distance between points 54 and 55 and D2 is the distance between points 54 and 53. These distances D1 and D2 are determined depending on cases. If the ratio of D1 to D2, namely, the torsion control parameter ε is varied, then a form to be created is changed. Alternatively, the torsion control parameter ε may be obtained as a ratio of angles. Then, let a line segment between the thus-obtained point 55 and the first point 51 be L56, and a line segment between points 55 and 52 be L57. These line segments L50, L56 and L57 cooperate to enclose a triangle. This triangle is called a temporary triangle Σ. Fig. 21 illustrates how to form a fundamental triangle within the above-mentioned temporary triangle Σ. Let an orthograph of line L51 that is projected into the temporary triangle Σ be a straight line L58, and an orthograph of line L52 into the same temporary triangle be a straight line L59. Also, let an intersection point between these lines L58 and L59 be point 56. A triangle that is enclosed by line L50 and the thus-obtained lines L58 and L59 is a three-dimensional, fundamental triangle necessary for creation of a three-dimensional form. This three-dimensional fundamental triangle corresponds to the fundamental triangle formed in Fig. 3 to create the two-dimensional form. Fig. 22 illustrates how to form an isoseles triangle from the above-mentioned three-dimensional fundamental triangle. Specifically, the above-mentioned fundamental triangle can be operated similarly to the triangle in Fig. 3. Thus, when a form is created at the then time, the same idea as employed in the previously described two-dimensional form creation can be applied. That is, if the same operations as in Figs. 2 to 10 are performed based on the three-dimensional fundamental triangle ▵ (52)(51)(56) and isosceles triangle ▵(59)(51)(56), then three-dimensional third point 71 and third straight line L73 can be found. However, a torsion control auxiliary parameter  must used to create a three-dimensional form. Specifically, a tangent to an outline of a form to be created at point 71 has a certain angle relative line L73 within the plane of the three-dimensional fundamental triangle, and this certain angle is called the torsion control auxiliary parameter  . This parameter must be taken into consideration so as to obtain a three-dimensional form. Line L72 is a straight (tangent) line that is obtained as a result of consideration of the torsion auxiliary parameter  . In Fig. 22, references given within symbols [ ] respectively correspond to the points or straight lines shown in Figs. 2 through 11. Accordingly, if the operations shown in Figs. 16 to 22 are performed based on line L51 or L52 and the line obtained as a result of consideration of the torsion control auxiliary parameter  , then new third point and straight line can be obtained. These operations can be executed repeatedly to obtain a three-dimensional outline. The thus-obtained outlines can be connected one by one successively to provide a three-dimensional form. For example, let the coordinates of point 51 be (2.0, 0.0, 0.0), direction cosign of line L51 be (0.0, 0.7232, 0.6906), coordinates of point 52 be (0.0, 2.0, π), direction cosign of line L52 be (-0.7232, 0.0, 0.6906), position control parameter β be 0, tangent control parameter δ be 0, torsion parameter ε be 0.5, and torsion control auxiliary parameter  be -0.0467. Then, a form that is created by these factors provides an isoclinal form. In Fig. 23, a block diagram of an embodiment of the invention is illustrated. This embodiment comprises a first point setting means 81 to set up a first point 11 at an aribitrary position as shown in Fig. 2, and a second point setting means 82 to set up a second point 12 at an arbitrary position different from that of point 11. In this embodiment, there are also provided a first straight line setting means 83 to set up a first line L1 passing through point 11 in an arbitrary direction and a second straight line setting means 84 to set up a second line L2 passing through point 12 in an arbitrary direction. Examples of these setting means 81 - include input means such as keyboard 1 and light pen 2. As its principle is shown in Figs. 2 through 10, there is provided a third point/straight line decision means 85 which, in accordance with the positions of points 11 and 12 as well as the directions of lines L1 and L2, decides the position of a third point 33 and the direction of a third straight line L13 containing this third point 33. An operation circuit 3 serves as the third point/straight line decision means 85. In obtaining a two-dimensional form, the same principles as explained in Figs. 2 to 10 may be applied, while in order to set up a three-dimensional form(or its outline), the principles discussed in connection with Fig. 17 to 22 must be employed. The operation circuit 3 is adapted to be able to realize all of these principles. Alternatively, a computer may be used instead of the operation circuit 3. Third point/straight line decision means 85 is also provided with input means 86 for input of the parameters β, δ, ε, , and the like. Keyboard 1 may be used as this input means 86. There is further provided a memory unit 87 which stores information on each point decided by the decision means 85. As described above, the embodiment in Fig. 23 is constructed such that, as a first step, it can find a third point from the first and second points 11 and 12 as well as the first and second lines L1 and L2. Fig. 24 illustrates a block diagram of another embodiment of the invention. This embodiment is provided with a control means 38 which controls each of means 81 - 84 repetitively, in accordance with previously set or decided points and directions of lines at such points as well as a new point decided by the decision means 85 and direction of a new line at this new point, to provide a large number of points between the first and second points 11 and 12. This control means 83 can be operated by the same principle as explained in connection with Fig. 11. Fig. 25 illustrates a block diagram of still another embodiment of the invention, especially used to create a two-dimensional form. In this embodiment, there are provided a first point setting means 81 to set up a first point 11 at an arbitrary position, with its principle being illustrated in Fig. 2, and a second point setting means 82 to set up a second point 12 at a different arbitrary position from that of the first point 11. This embodiment also includes a first straight line setting means 83 to establish a first straight line L1 passing through point 11 in an arbitrary direction and a two-dimensional second straight line setting means 91 to establish a second straight line L2 passing through point 12 in an arbitrary direction within a plane formed by point 11 and line L1. Also, as its principles are shown in Figs. 2 to 4, there is provided an isosceles triangle forming means 92. In this forming means 92, at first a fundamental triangle is formed by a chord L3 between points 11 and 12, the first line L1 and the second line L2, and then an isosceles triangle having two equal sides each of which is equal to the shorter one of the fundamental triangle sides other than the side formed by the chord L3. Further, this embodiment includes a third point operation means 93 which, as its principle is illustrated in Figs. 5 through 11 and 15, calculates the position of a third point as well as the direction of a third line containing this third point in accordance with the attributes of the above-mentioned fundamental and isosceles triangles. Describing this third point operation means 93 in detail, it comprises the following components: that is, an internal center position operation means 93a (which applies the principles in Figs. 5 and 6) to calculate the positions of the incenters of the fundamental and isosceles triangles; a first triangle area operation means 93b (which applies the principle in Fig. 7) to calculate the area of a first triangle enclosed by a line connecting the incenter of the fundamental triangle and one of vertexes other than a vertex of a given angle commonly shared by the fundamental and isosceles triangles, a perpendicular bisector of a line connecting isosceles triangle incenter and a vertex of the fundamental triangle positioned opposed to said one vertex within the isosceles triangle, and a side positioned opposed to said one vertex; a second triangle area operation means 93c (which also applies the principle in Fig. 7) to calculate the area of a second triangle enclosed by a line connecting the fundamental triangle incenter with the other vertex other than said given angle vertex, a perpendicular bisector of a line connecting said isosceles triangle incenter with a vertex opposed to said other vertex within said isosceles triangle, and a side opposed to said other vertex; and, a calculation means 93d (which applies the principles in Figs. 8 to 10) to calculate, as the position of a third point, the position on a bisector of said given angle that is spaced apart from the position of the fundamental triangle incenter by a distance that depends on the difference between the areas of the first and second triangles as well as the distance between the first and second points. Third point operation means 93 further includes means for inputting the parameters β, δ, ε,  and a memory unit 87 to store information on each of points decided by the third point operation means 93 itself. Operation circuit 3 is adapted to be capable of performing functions of the above-mentioned fundamental and isosceles triangles forming means 92 as well as those of the third point operation means 93. Accordingly, the present invention is capable of creating a form or modifying a created form with ease. Thus, the invention can be effectively applied to a shape working machine, a form recognition device, an image processor, an auto-drawing instrument, an image creator and the like in NC machine tools or the like. When applied to these machines and devices, the invention can perform not only two-dimensional operations but also three-dimensional operations. As has been described hereinbefore, the present invention provides a single form creating system which provides for free access to a form to be created throughout the whole process ranging from its design step to its manufacturing step.

Claims: A two-dimensional or three-dimensional form creating CAD system comprising: a reference point setting means (81, 82) for setting a position of a point in a formative space, said reference point setting means setting each position of both a first point and a second point at arbitary but different positions, each said position being a constructive point lying on a contour of a forming solid or figure a reference line setting means (83, 84; 91) for setting a reference straight line passing through said reference point, said reference line setting means setting a first and second straight line passing separately through said first point and said second point respectively, input means (86,94) for determining the position of a plurality of intermediate reference points, which lie on a contour of said solid or figure between the first and second points, characterized by said reference line setting means (83,84;91) setting said first and second straight lines in arbitrary directions but not parallel to each other; triangle form setting means (92) for setting a triangular wire frame-like form which is formed by a constructive procedure in accordance with both the position of said second point and the direction of said second line as well as both the position of said first point and the direction of said first line; said input means (86,94) inputting shape control parameters as control variables; said intermediate point operating means (85,93) determining said intermediate point based on the triangular wire frame-like form set by said triangle form setting means (92) and the shape control parameters set by said input means (86,94); and said controlling means (88) controlling repetitively each of said reference point setting means (81,82), said reference line setting means (83,84,91), triangle form setting means (92), and intermediate point operation means (85,93) to determine the position of the plurality of intermediate points based on previously set or determined points and lines, these operations being repeatedly formed until the contour of said solid or figure is represented by the determined intermediate points within a predetermined accuracy. A two-dimensional or three-dimensional form creating system according to claim 1 wherein said controlling means (88) controls said reference point setting means (81,82), said reference line setting means (83,84,91), said triangle form setting means (92) and said intermediate point operation means (85,93) to determine a first intermediate point and a first intermediate line passing through said first intermediate point and determines a further intermediate point and a further intermediate line passing through said intermediate point by repeating the above procedure using the first intermediate point and the first intermediate line and one of the previously set reference points and the corresponding previously set reference lines; these operations being repeated to define the contour of said solid or figure by the plurality of determined intermediate points. A two-dimensional or three-dimensional form creating system according to claims 1 or 2, wherein: said triangle form setting means (92) further comprises: a fundamental triangle constructing means for determining a fundamental triangle enclosed by a straight line between said first point and said second point, which is a third edge, said first straight line or alternative line projected on a control plane of said triangle form for said first line, which is a first edge and said second straight line or alternative line projected on said plane, which is a second edge; and an isosceles triangle constructing means for determining an isosceles triangle having equilateral edges equal to a length of a shorter side edge of said fundamental triangle between said first edge and said second edge, which is made by putting the vertex of the longer side edge of said fundamental triangle between said first edge and said second edge and taking said shorter side edge as a common edge included between said fundamental triangle and said isosceles triangle. A form creating system according to claim 3, wherein said intermediate point operating means further comprises: an internal center position operating means (93a) for calculating both a position of an internal center of said fundamental triangle and a position of the internal center of said isosceles triangle; a first triangle area operating means (93b) for calculating an area of a first triangle enclosed by a set of three lines, one of said three lines is the shorter side edge of said fundamental triangle, another line is a line crossing between said internal center of said fundamental triangle and the longer side vertex but not the intersection of said first straight line and said straight line and a last line is perpendicular to the line segment between said internal center of said isosceles triangle and the shorter side vertex but not said intersection and passes through a point dividing a length of said line segment into two halves; and a second triangle area operating means (93c) for calculating the area of a second triangle which is constructed at the opposite side of said first triangle according to the opposite operation corresponding to the disposing relation used by said first triangle. A form creating system according to claims 1, 2, 3 or 4, wherein said intermediate point operating means further comprises: a calculation means (93d) for calculating and controlling both the position of said intermediate point and the direction of an intermediate straight line through said intermediate point, and for setting both the position of said intermediate point at a distance from the internal center of said fundamental triangle and the direction of said intermediate straight line at an angle apart from a mean angle equal to a direction of the bisector between a line passing through both said first point and said intermediate point and a line passing through both said second point and said intermediate point in accordance with the difference between the areas of said first and second triangles and with the control variables.

Inventors: NAKAMURA, YOSHIAKI, SETOGUCHI, RYOZO
Applicants: SETOGUCHI, RYOZO
Application year: 1984
Main classification: G06F15
IPC codes: G06F17, G06T11, G05B19