JPH0478973A - Method for calculating cosine value from vector - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed description of the invention] [Industrial application field]

The present invention relates to a method for calculating a cosine value of a rotation angle in image rotation.

[Conventional technology]

The following is a method for calculating the cosine value of the rotation angle when rotating and displaying a bitmap image in a personal computer that constitutes a bitmap system.
Conventionally, there are methods as shown below. ■Directional vectors (a, b) as shown in Figure 7 (a)
) is given, cosθ=a/Va+b” ・(1)
A method of calculating the value of by using a floating point representation and a numerical calculation algorithm such as the Newton-Raphson method. ■Calculating the above formula (1) using fixed-point representation,
A method using a method such as a spread calculation as exemplified in Figure (b). (2) A method in which a table of cosine values is prepared for each direction as shown in FIG. 7(c), and the cosine value for a given direction vector is determined by referring to the table. The characteristics of these methods are that ■ is capable of high-precision calculations, ■ is capable of medium-precision calculations, and ■ is capable of deriving cosine values faster than ■ and ■. can give.

[Problem to be solved by the invention]

By the way, the above methods (1) and (2) have the drawback that the calculations are complicated and require a large execution module, and the calculations take a long time. Furthermore, method (2) requires a large data area, and furthermore, the cosine values that can be calculated are limited to those in a specific direction listed in the table. Therefore, when it is necessary to rotate relatively small bitmap images (characters, icons, etc.) at high speed, for example when displaying character strings diagonally, which is often seen in applications such as architectural CAD systems, the above-mentioned conventional Neither method is suitable. SUMMARY OF THE INVENTION An object of the present invention is to provide a method for calculating a cosine value of a rotation angle from a vector, which does not require a large data area and can be performed at high speed with a small execution module.

[Means to solve the problem]

In order to achieve the above object, a method of calculating a cosine value from a vector according to the present invention is a method of calculating a cosine value of an angle in a direction given by a vector with respect to a reference coordinate axis in order to rotate and display an image on an image display device. There it is,
Set a numerical value to give the calculation accuracy, calculate the coordinate points sequentially according to Bresenham's algorithm based on the direction given by the vector above, calculate the square value of the distance of the calculated coordinate point from the coordinate origin, and calculate the square value. is compared with the square value of the above set value, and when the square value is greater than or equal to the square value of the above set value, the square value and the coordinate origin of the coordinate point calculated one point before that coordinate point are calculated. Find which of the squared values of the distance is closer to the square of the above set value, and calculate the above cosine value from the coordinate value corresponding to the above reference coordinate axis of the coordinate point that gives the closer square value and the above set value. It is characterized by the fact that it is made to do so.

【Example】

Hereinafter, the present invention will be explained in detail with reference to illustrated embodiments. FIG. 1 is a system configuration diagram for realizing a cosine value calculation method according to an embodiment of the present invention. In FIG. 1, l is an input device, through which a direction vector (a 1 , b 2 ) and a numerical value M for giving calculation accuracy (hereinafter referred to as accuracy M) are input. In addition, 2 is a discrete straight line drawn from the coordinate origin (0, 0) toward the coordinate point (a, b) according to Bresenham's algorithm, as shown in FIG. 3 is a device that calculates discrete coordinate values in the traveling direction (coordinate values of points indicated by black circles in the figure), and 3 is a device that calculates the traveling distance (the square of This is a device that calculates the square of the distance from the coordinate origin.As will be described later, the device 2 outputs the X coordinate value of the coordinate point that is calculated by the device 3 and is closest to 1, I22 or M2. This is output by
The coordinate values give an approximate value of Mcosθ. FIG. 2 is a flowchart showing the procedure of this embodiment. In step S1, input vectors (a 1 , b 2 ) and precision M are input, and in step S2, each control parameter required for Bresenham's algorithm is initialized. Then, in step S3, the calculation start coordinates (Xa,
Yo) is set to (0,0), and the square of the traveling distance g is set to 0. Next, the process advances from step S4 to step s6. In step S4, coordinates (xo, yo) on a series of discrete straight lines are determined according to Bresenham's algorithm. (X r, Y +), .-, (Xn, Yn), =- is generated (see Fig. 3). In step S5, step S
Calculate C based on the coordinate values obtained in step 4. this("
The calculation is performed using the previous coordinate values. That is, (X
n. When the next point (Xn+,, Yn++) of (Xn-. Yn+,) and (0,0) is derived, the distance M 1 n +, between (Xn-. , 0) using the distance I2n. As shown in Fig. 4(a), if the vehicle moves in the X direction, Qn"1'・ρn'÷2Xn+1, and the
As shown in figure (b), when proceeding in the Y direction, ln
+12・ln2+ 2 Yn〒1. In addition, if it progresses in an oblique direction as shown in Figure 4(c), (l
n+, 2=Qn'+ 2 (Xn+ Yn+ 1). In step S6, ln obtained in step s5
+, 2 is closest to Ml+. That is, determine whether (ln"15M2), and
If 2n"H"<M', return to step S4 and In+
, 12M'', compare which of i2n 4, ! and Qn2 is closer to M2, and output the X coordinate value of the coordinate point that gives the square value of the closer one in step S7. Output in step S7 above. The X coordinate value obtained gives an approximate value of McSθ, and if this value is Lc, then Lc=Mcosθ−EC−(2) However, it can be expressed as j Ec 1<1. The value can be determined by Lc/M, or because the cosine value is smaller than I, it cannot be used as is to calculate the coordinate values of the rotated image using binary calculation, and the above Lc value is used.In this case, the value of Lc is used. , the coordinate values of the rotated image can be obtained by rotating the original image enlarged vertically and horizontally by M times and dividing the resulting coordinate values by M. For example, as shown in FIG. Considering the case where a binary image of size WXH is rotated to the left by θ, as shown in Figure 6, the grid spacing of the enlarged image is M, and by rotating the n-th point in the X direction, The X coordinate value (Xn) of the obtained point is Xn=n XLc
/M -...c3). In addition, the Y coordinate value (Yn) of the point obtained by the above rotation is given as the sine value of the Y coordinate value obtained at the same time as the X coordinate value by the algorithm in Figure 2, and this is set as Ls, then Yn = n x Ls /M - (4). Also, if the size of the rotated image is WrXHr, then the above (
From Equation 2) and Equation (3), Wr=W(Mcosθ-Ec)/M=Wcosθ-WEc/M Hr=H(Mcosθ-EC)/M=Hcosθ-HEc/M. Therefore, if W and F (of the original image are less than or equal to M),
It can be seen that Wr and Hr of the rotated image can be determined with an error of one dot. Furthermore, it can be seen that the direction of the rotated image is determined on average in units of about 45°/M. Therefore, for example, M=64=
2@, it can be rotated in approximately 0.7' units. This angle is indistinguishable to the human eye, and is accurate enough for practical use. Note that the larger M is, the higher the accuracy is, but if it is too large, the calculation speed will be slow, so it is desirable to set it to an appropriate value depending on the purpose. It has been confirmed that when M is about 64, calculation speed is considerably faster than that of the other methods described in the conventional example. [Effects of the Invention] As is clear from the above, the method of calculating a cosine value from a vector according to the present invention sets a numerical value to give calculation accuracy, and sequentially points coordinates according to Bresenham's algorithm based on the direction given by the vector. Along with seeking
Find the square value of the distance of the obtained coordinate point from the coordinate origin, compare the square value with the square value of the above setting value, and when the square value is greater than or equal to the square value of the above setting value, the square value is calculated. Find out which of the square values of the distance from the coordinate origin of the previous coordinate point and the previous coordinate point is closer to the square value of the above set value, and select the coordinate point that gives the closest square value. Since the cosine value is calculated from the coordinate value corresponding to the reference coordinate axis and the set value, the cosine value can be calculated by four arithmetic calculations based on the input data.
The calculation speed can be faster than when performing complex calculations as in the conventional example ■ and ■, and it does not require a large data area as in the conventional example ■, and the cosine value that can be calculated can be Because it is not limited to a specific orientation of the table, it is effective for printing on a hit map system using relatively small bitmap images such as characters and icons, and is especially effective for CAD, CAM
, is very effective for CAI.

[Brief explanation of the drawing]

FIG. 1 is a system configuration diagram for realizing an embodiment of the present invention, FIG. 2 is a flowchart showing the procedure of the above embodiment, and FIG. 3 is a diagram explaining how to obtain coordinate points in the above embodiment. Fig. 4 is a diagram explaining how to calculate the square of the distance between the above coordinate point and the coordinate origin, and Figs. 5 and 6 explain the error when rotating an image using the cosine value obtained in the above example. FIG. 7 is a diagram illustrating a conventional example.

Claims (1)

[Claims] (1) A method of calculating the cosine value of an angle with respect to a reference coordinate axis in a direction given by a vector in order to rotate and display an image on an image display device. Based on the direction given by Bresenham's algorithm, find the coordinate points sequentially, find the square value of the distance of the found coordinate point from the coordinate origin, compare the square value with the square value of the above setting value, and calculate the value. When the square value is greater than or equal to the square value of the above setting value, which of the square value and the square value of the distance from the coordinate origin of the coordinate point calculated one point before that coordinate point is the above setting value. Cosine from a vector, characterized in that the cosine value is calculated from the coordinate value corresponding to the reference coordinate axis of the coordinate point giving the closer square value and the set value. Value calculation method.