JPS60211543A - Coordinate converting system - Google Patents

Abstract

PURPOSE:To attain coordinate conversion of plural points at a high speed in a multi-dimension space by calculating a coordinate value after coordinate conversion from a vector group and plural points generated by a vector generating means. CONSTITUTION:A coordinate value 121 is read from a coordinate storage means 120 and a vector 131 is read from a conversion matrix storage means 130 by the start of a vector generating means 140, a vector 141 is generated by the product between the vector and a scalar and the result is stored in a vector storage means 150. When the processings above are repeated and the processing for all coordinates of a storage means 120 is finished, a coordinate calculating means 160 is started, and address information 111 having a quantity equal to the number of dimensions of a space representing one point is read from a point storage means 110, a vector group 151 is read from the storage means 150 by using the addresses and they are added to calculate a position vector applying coordinate conversion to one point. The processings above are conducted all points stored by the point storage means and the result is fed to a drawing display means 190.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a coordinate transformation method necessary for displaying figures and objects registered as data in any position and in any orientation on a display.

[Prior art]

Conventionally, when converting the coordinates of multiple points in a multidimensional space,
First, each point is represented by a vector whose components are coordinate values, then these vectors are sequentially extracted and multiplied by a transformation matrix representing the transformation, and the resulting vector is used to obtain the position after the coordinate transformation, and the above process is This was done by repeating the points.

On the other hand, a coordinate transformation method devised to perform coordinate transformation processing at high speed has appeared. For example, when converting the coordinates of one point using the coordinate conversion method described above, before multiplying a vector and a matrix, check for elements with a value of zero in the matrix before performing the calculation; There is a method of omitting the process of multiplying one element of a vector by a zero element of a matrix in the middle of the calculation, thereby reducing the number of calculations required for the process and executing coordinate transformation at high speed.

[Problems with conventional technology]

However, in the coordinate transformation method described above, unless there is an element with a value of zero in the transformation matrix, speeding up of processing cannot be expected.

[Purpose of the invention]

An object of the present invention is to perform coordinate transformation at high speed by eliminating redundancy of a plurality of points in a multidimensional space, regardless of the characteristics of a transformation matrix.

[Structure of the invention]

The present invention expresses a plurality of points in a multidimensional space by a vector whose components are addresses of locations where coordinate values are stored, and stores coordinate values for the plurality of points for each coordinate in the multidimensional space. , generate a vector group from a transformation matrix representing coordinate transformation of a point in a multidimensional space and the coordinate values, and calculate coordinate values after the coordinate transformation from the vector group generated by the vector generation means and the plurality of points. This configuration allows coordinate transformation of multiple points in a multidimensional space.

The explanation will be given below in the following order. First, we will formulate the coordinate transformation of the rectangle 100 in the two-dimensional space illustrated in FIG. Explain. After that, the present invention will be explained in detail using an embodiment of the present invention in which the rectangle is displayed after coordinate transformation.

[Operation and principle of the present invention]

The conventional method uses a rectangle 10 in the two-dimensional space shown in Figure 1.
For example, 0 is represented by four row vectors (1) whose components are coordinate values. Next, if we take the transformation matrix T, the calculations performed in the conventional method are as follows: multiplication is performed 16 times and addition is performed 8 times.

Here, we convert the matrix of equation (2) into two row vectors f(tl
l + 1llll) *le, = (1 circle, wo) (4)
If we express the coordinate transformation again using the calculations performed by the conventional method, we get 5-.If we examine these formulas, we can see that the conventional method has a-ship construction,
It can be seen that the row vectors b-1tx, e-1ta, and d-1ta are each calculated twice, which is wasteful.

The principle of the present invention is to reduce the number of calculations required for coordinate transformation processing by eliminating the above waste. In other words, point P=(x,y) in two-dimensional space is converted to transformation matrix T=(t
: t: ), when converting T to f(tll
*tll) e, f (t@et@).

The coordinate transformation of P is P T = xaz + y tt y, so.

The ytt a is prepared in advance and synthesized later.

Therefore, when a plurality of points have duplicate coordinate values, high-speed processing is possible by avoiding duplicate calculations.

〔Example〕

FIG. 2 is a block diagram of an embodiment in which the coordinates of the rectangle illustrated in FIG. 1 are transformed and displayed using the coordinate transformation method of the present invention based on the above principle.

6- In FIG. 2, 170 is a control means, which is constructed using a computer. Further, 180 is a control signal, and using this control signal, the control means 170 first activates the vector generation means 140. The vector generating means reads the coordinate value 121 from the contents of the coordinate value storage means 120 and the vector 131 from the transformation matrix storage means 130, generates a vector 141 by multiplying the vector and the scalar, and then reads the coordinate value 1
The generated vector 141 is stored in the storage location of the vector storage means 150 determined by the address . Repeating the above processing for all coordinate values stored in the coordinate value storage means,
When the vector generation means completes its processing, the control means next activates the coordinate calculation means 160. The coordinate calculation means reads address information 111 in a number equal to the number of dimensions of the space from the part representing one point out of the contents of the point storage means 110, and then uses these address information to read a vector group 151 from the vector storage means 150. By reading and adding up these vectors, the position resulting from the coordinate transformation of the single point of interest is calculated as a position vector. The coordinate calculation means performs the above processing on all points stored in the point storage means and sends the results to the graphic display means 190. The graphic display means displays a line drawing according to the position vector 161 sent by the coordinate calculation means, and can be realized by a buffer for temporarily holding the position vector, a CRT, and conventional display means.

The details of this method will be further explained in the following content which shows the operation of this method.

In this method, first, the rectangle 100 illustrated in FIG.
Bo ), P F = (At, Bt).

These four points are stored as the contents of a point storage means constituted by one memory chip, for example. A conceptual diagram representing this situation on the memory is shown in FIG.

Next, for example, the contents of the coordinate value storage means constituted by one memory chip are separated into an X coordinate value part and a y coordinate value part, and the address A indicating the X coordinate value part is A1.
The coordinate value a is stored in the storage location determined by .

Coordinate values c and d are stored in storage locations determined by addresses Bo and B1 indicating the b and y coordinate values, respectively.

Also, the number of coordinate values stored in the X coordinate value part is stored at the beginning of the X coordinate value part, and the number of coordinate values included in the y coordinate value part is stored at the beginning of the y coordinate value part. put. This conceptual diagram is shown in FIG.

On the other hand, the transformation matrix of equation (2) is converted into two row vectors f(t
ll + tll ) + is also P(tr+ , t@ )
In (7), T is considered to be divided and stored in the transformation matrix storage means into two parts: T and HORI. FIG. 5 is a conceptual diagram in which the transformation matrix storage means is represented by, for example, one memory chip.

The process begins when the control means activates the vector generation means 140 illustrated in FIG. 6, for example. As a first process, the activated vector generation means extracts the vector 8x shown by equation (7) from the contents of the transformation matrix storage means 130 according to the command signal of the coordinate selector 200, and performs the above-mentioned 1.
1 is held in the vector holder 210, and the current coordinates are notified to the coordinate value storage means 120 and the vector storage means 150.

The second process of the vector generation means is the address generator 220
The coordinate value storage means 12 illustrated in FIG.
Out of the contents of 0, 2, which is the number of coordinate values of the coordinate indicated by the coordinate selector, is taken out to the counter 23o1, 1 is added to the contents of the address generator, and the contents of the coordinate value storage means are The scalar holder 240 stores the first coordinate value a of the coordinate of interest stored in the location indicated by the contents of the address generator.
Take it out.

The third process of the vector generation means is the vector holder 210
The vector containing the contents of the vector and the coordinate value containing the contents of the scalar holder 240 are sent to the vector/scalar multiplier 250, and a vector is calculated by multiplying the above vector by the above scalar. Among the contents of 150, the X component of the resultant vector is placed on the memory chip M1 determined by the contents of the address generator, and the
Store the y component of the resulting vector above.

The vector generating means then subtracts 1 from the contents of the counter and repeats the same process until the result becomes zero,
Next, in the same manner as before, a vector value is extracted from the contents of the transformation matrix storage means, and the same processing as before is performed, and when the contents of the counter become zero, the processing is completed.

When the vector generation means completes the processing, the control means next activates the coordinate calculation means 160 illustrated in FIG. 8, for example. The coordinate calculation means is the point storage means 110 illustrated in FIG.
For each of the plurality of points represented by the contents of 150, the vector stored at the location indicated by the contents of the address holder is extracted, added to the vector represented by the contents of the vector adder 320, and the above process is repeated for the y component of the point of interest. Then, the vector indicated by the contents of the vector adder is sent to the display means, and the above processing is executed for all points to complete the processing.

When the coordinate calculation means completes the processing, the control means finally activates the display means 190. The display means is composed of, for example, a buffer memory for temporarily holding a group of vectors sent by the coordinate calculation means and a CRT, and connects the points pointed by the vectors held in the buffer memory with line segments in order and displays them on the CRT. By displaying, the figure after coordinate transformation is displayed.

The coordinate selector 200 used in the above explanation can realize a method of holding a base address for each coordinate and changing the pace address for each coordinate using conventional digital circuit technology using TTL, etc. The components of the vector generation means and the coordinate value calculation means can also be realized by conventional digital circuit technology using TTL or the like.

〔Effect of the invention〕

In the arithmetic processing of the coordinate transformation using the present invention, the vector generation means performs a total of 8 times, and the coordinate value calculation means performs a total of 8 times. Table 1 summarizes the results in comparison with the conventional method.

Table-1 Table 2 is a summary of the results.

Table 2 13- As shown in the above two tables, the present invention has the effect of reducing the number of multiplications required in coordinate transformation processing when a plurality of points have duplicate coordinate values. Since multiplication requires more time to process than addition, the effects of the present invention are believed to be significant in speeding up processing.

[Summary of effects]

In the above explanation, the dimensions are limited to two dimensions, the contents of the point storage means are a plurality of row vectors, and the contents of the transformation matrix storage means are a matrix divided into 1×2 row vector groups. , the vector generation means generates coordinate values stored in the coordinate storage means for coordinates determined in the same order as the row vectors sequentially extracted from the group of row vectors constituting the matrix represented by the contents of the transformation matrix storage means. One by one, the above process was performed for all the row vectors that constitute the matrix represented by the contents of the transformation matrix storage means. is a plurality of column vectors, the contents of the transformation matrix storage means are a matrix divided into 2×1 column vector groups 14-, and the vector generation means constructs a matrix represented by the contents of the transformation matrix storage means. Column vectors taken out sequentially from a group of column vectors are multiplied one by one by the coordinate values stored in the contents of the coordinate storage means for the coordinates determined in the same order. The same holds true for all column vectors that make up the representing matrix.

In a system for displaying figures, basic figures having duplicate coordinate values are often registered in advance in data held by the system, which is an effective field of application of the present invention.

In addition to the method of displaying figures, 3D CAD often uses a method of generating new objects by combining basic objects registered as data, and in this case, coordinate transformation that moves the basic objects in 3D space is used. Processing is required and the present invention can be applied.

[Brief explanation of drawings]

Fig. 1 is an explanatory diagram of the rectangle used in the example, Fig. 2 is a block diagram of a system for converting the coordinates of a figure and displaying it using the present invention, and Fig. 3 is a point representing each vertex of the rectangle used in the example. Figure 4 shows the contents of the storage means for each vertex of the rectangle used in the example. Figure 5 shows the transformation matrix used in the example divided into row vectors and stored. FIG. 6 is a diagram showing the contents of the transformation matrix storage means, FIG. 6 is a diagram showing an example of the configuration of the vector generation means, FIG. 7 is a diagram showing the contents of the vector storage means for storing vector groups generated by the vector generation means, and FIG. The figure shows an example of the configuration of the coordinate calculation means, and FIG. 9 shows an explanatory diagram of figures used to show the effect. In the figure, 100 is the rectangle used in the example, 110 is the point storage means, and 11 is the rectangle used in the example.
1 is a group of addresses indicating the location where each coordinate value for one point is stored; 120 is a coordinate value storage means; 121 is a coordinate value taken out from the coordinate value storage means; 130 is a transformation matrix storage means;
131 is a vector constituting a transformation matrix; 140 is a vector generation means; 141 is a vector generated by the vector generation means; 150 is a vector storage means; 151 is a vector group retrieved from the vector storage means using the address group 111; 160 161 is a coordinate calculation means, 161 is a position vector after coordinate transformation, 170 is a control means, 180 is a control signal,
190 indicates the graphic display means 17 = 71-1 Figure 7I-3 Figure 71-4 Figure O 7 (α) (b)

Claims (1)

[Claims] Express multiple points in a multidimensional space with a vector (IXn (or n×1) row (or column) vector (n indicates the dimension of the space)) whose components are addresses of locations where coordinate values are stored. Then, the coordinate values for the plurality of points are stored for each coordinate in the multidimensional space, and a transformation matrix representing the coordinate transformation of the points in the multidimensional space is stored in 1×n (or n×1) rows (or columns). ) is expressed as a matrix divided into vector groups, and the rows of the above transformation matrix (
Generate a vector group by applying the coordinate values of the coordinates determined in the same order to the row (or column) vectors one by one from the vector group, and sequentially calculate each point from multiple points. , read the address that is each component of the vector representing the above point, find the vector generated for each component using the coordinate values stored at the location indicated by the above address, and add the found vectors. A coordinate transformation method characterized by calculating coordinate values after coordinate transformation.