JPH05108833A - Elliptic scan converter - Google Patents

Abstract

PURPOSE:To plot an ellipse at a high speed by preliminarily predicting the number of maximum arithmetic digits based on the parameter of the ellipse to be plotted, and reducing the lower-order bits of an inside variable only in the prescribed number of digits according to the predicted number of digits in order to execute a scan conversion. CONSTITUTION:A parameter setting part 10 sets and inputs the parameter of the ellipse to be plotted, and initializes it. An arithmetic precision predicting part 12 receives the initial value and set value of the parameter, and searches the number of maximum arithmetic digits to be generated at the time of the scan conversion of the ellipse. A reduction number of digit calculating part 14 decides the number of digits of the lower order bits to be reduced from the inside variable used by the scan conversion of the ellipse to be plotted, based on the number of maximum arithmetic digits. An elliptic circumferential coordinate calculating part 16 reduces the lower-order bits of the inside variable only in the decided number of digits in order to execute the scan conversion, and decides the luster coordinate of the ellipse to be plotted. Then, an outputting part 18 transmits the searched elliptic luster coordinate to a display device, printing device, or storage device.

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION This invention relates to computer graphics, and more particularly to a scan conversion device for drawing ellipses on a raster scan display.

[0002]

2. Description of the Related Art In a raster scan display such as a CRT, pixels arranged in a matrix on a screen are made to emit light discretely to draw an image. So, for example,
Since it is impossible to draw a strict straight line from one point to another point, a pixel closest to the straight line is selected to draw a pseudo straight line. In this way, the grid point positions (raster coordinates) of a series of pixels to emit light are determined by repeating the procedure (rasterization) of determining the pixel with the shortest distance with respect to the straight line or curve to be drawn. The procedure for determining the raster coordinates on the raster scan display for the image to be drawn in this way is called scan conversion.

Conventionally, as scan conversion for drawing an ellipse on a raster scan display, it has been considered to apply the Bresenham circle drawing algorithm to the ellipse as it is. The ellipse drawing algorithm will be described below.

Now, as shown in FIG. 5, it is assumed that an ellipse centered on the origin and having a diameter of Rx in the X-axis direction and a diameter of Ry in the Y-axis direction is drawn. Since the ellipse is symmetric in four directions,
If only the quadrant in the first quadrant is scan converted,
By inverting and folding the minute ellipse, it is possible to draw each quadrant of the other three quadrants. This elliptic equation is expressed as the following equation. (X / Rx) ² + (y / Ry) ² = 1 (1.01) This equation can be transformed into the following equation. When Ry ² · x ² + Rx ² · y ² = Rx ² · Ry ² (1.02) Rx ² = a and Ry ² = b, the following equation is obtained. bx ² + ay ² = ab (1.03)

At this time, in FIG. 6, the square of the distance Eh between the true ellipse L0 or L1 and the adjacent grid point Ph in the right direction Eh.
, The squared distance Ed from the adjacent grid point Pd in the lower right direction
, And the squared Ev of the distance from the adjacent lattice point Pv in the direct downward direction is as follows. Ph: Eh = | b (xi + 1) ² + a (yi) ^2- ab | (1.04) Pd: Ed = | b (xi + 1) ² + a (yi-1) ^2- ab | (1.05) Pv: Ev = | B (xi) ² + a (yi -1) ² -ab | (1.06) where Δi = b (xi +1) ² + a (yi -1) ² -ab (1.07) is defined, and the sign of this Δi Based on the above, the lattice points closest to the true ellipse among Ph, Pd, and Pv are determined by classifying as follows.

When Δi <0, this means that the true ellipse is Pd as shown by the curve L0 in FIG.
This is the case when passing outside of. Therefore, the grid point to be selected is either Pd or Ph. To determine either Pd or Ph, the difference .delta.i between the square of the distance Eh between Ph and the true ellipse L0 and the square of the distance between Pd and the true ellipse L0 Ed is examined. .delta.i = Eh-Ed = | b (xi + 1) ² + a (yi) ^2- ab |-| b (xi + 1) ² + a (yi-1) ² -ab | = 2 {b (xi + 1) ² + a (Yi -1) ² -ab} -a (-2yi +1) = 2Δi + 2ayi -a (1.08) Then, when δi <0, Eh <Ed, so P
Select h, and set xi + 1 = xi +1 and yi + 1 = yi,
Find the next error term Δi + 1. That, Δi + 1 = b (xi + 1 +1) 2 + a (yi + 1 -1) 2 -ab = b (xi + 1 2 + 2xi + 1 +1) + a (yi + 1 -1) 2 -ab = b (Xi + 1) ² + a (yi-1) ^2- ab + b (2xi + 1) = [Delta] i + b (2xi + 1 + 1) (1.09) [delta] i≥0, Eh≥Ed, so Pd is selected,
The next error term .DELTA.i + 1 is obtained with xi + 1 = xi + 1 and yi + 1 = yi-1. That is, Δi + 1 = b (xi + 1 + 1) ² + a (yi + 1-1) ² -ab = Δi + b (2xi + 1 + 1) -a (2yi + 1-1) (1.10)

In the case of Δi> 0 This means that the true ellipse is P as shown by the curve L1 in FIG.
This is the case of passing inside d. Therefore, the grid point to be selected is either Pd or Pv. To determine either of these, the square of the distance Ev between Pv and the true ellipse L1 and the square of the distance Ed between Pd and the true ellipse L1 Ed.
Check the difference δi with. .delta.i = Ev-Ed = | b (xi) ² + a (yi-1) ^2- ab |-| b (xi + 1) ² + a (yi-1) ² -ab | = 2 {b (xi + 1) ² + A (yi -1) ² -ab} -b (2xi +1) = 2Δi -2bxi + b (1.11) Then, when δi <0, Ev <Ed, so P
Select v, and set xi + 1 = xi, yi + 1 = yi -1,
Find the next error term Δi + 1. That is, if Δi + 1 = b (xi + 1 + 1) ² + a (yi + 1-1) ² -ab = Δi-a (2yi + 1-1) (1.12) δi ≧ 0, then Ev ≧ Ed. , Pd,
The next error term .DELTA.i + 1 is obtained with xi + 1 = xi + 1 and yi + 1 = yi-1. That is, Δi + 1 = b (xi + 1 + 1) ² + a (yi + 1-1) ² -ab = Δi + b (2xi + 1 + 1) -a (2yi + 1-1) (1.13)

Case of Δi = 0 This is a case where the true ellipse passes directly above Pd. Therefore, Pd is selected. Further, Δi + 1 is given by the following equation. Δi + 1 = b (xi + 1 + 1) ² + a (yi + 1 + 1) ² -ab = Δi + b (2xi + 1 + 1) -a (2yi + 1-1) (1.14)

As described above, the elliptical scan conversion can be performed by the digital differential analysis method (DDA: Digital Differential Analysis) similar to the Presentham's circle drawing algorithm. FIG. 7 is a flowchart showing the elliptic scan conversion processing by the above ellipse drawing algorithm.

[0010]

As described above, it is possible to draw an ellipse by the scan conversion in which the Presentham's circle drawing algorithm is directly applied. However, according to such an ellipse drawing algorithm, the calculation including the quaternary term of the input parameter is performed by the internal calculation (Equation (1.03)), and therefore, a large-scale arithmetic device is required as compared with the expected output value accuracy. Had to use. In a small-scale system such as a personal computer, the calculation accuracy on hardware is often limited to about 16 bits, and when the required calculation accuracy exceeds this, it is processed by software. In that case, there was a problem that the throughput was significantly reduced.

The present invention has been made in view of the above problems, and an object of the present invention is to provide an ellipse scan conversion device capable of drawing an ellipse at high speed with a small-scale circuit and improving throughput.

[0012]

In order to achieve the above object, the ellipse scan conversion apparatus of the present invention draws an ellipse on a raster scan display by scan conversion based on a digital differential analysis method. In an apparatus for determining the coordinates of an ellipse to be drawn, a calculation accuracy prediction unit that predicts in advance the maximum number of calculation digits that can occur in the scan conversion based on the parameters set for the ellipse to be drawn, and the calculation accuracy prediction unit. A truncation digit number calculation means for determining the number of digits of the lower bits to be truncated from the internal variable used in the scan conversion based on the maximum computation digit number predicted by Rounded down the lower bits of the internal variable by the number of digits Has a configuration comprising a elliptical circumferential coordinate calculating means for constant.

[0013]

When parameters such as the major axis, the minor axis, and the center coordinate of the ellipse to be drawn are given, the maximum value of the internal variables that can occur in scan conversion can be obtained from those parameters and the algorithm of the digital differential analysis method.
The maximum number of calculation digits can be obtained from the maximum value. When this maximum number of calculated digits occurs, the overflow amount becomes maximum. In the present invention, the scan conversion operation is performed by rounding (truncating) the internal variable so as not to cause overflow or to minimize the overflow. As a result, an ellipse can be drawn at high speed even with a small arithmetic unit.
Further, in the case of processing by software, throughput can be improved by suppressing the number of calculation digits.

[0014]

Embodiments of the present invention will be described below with reference to FIGS. FIG. 1 shows the configuration of an elliptical scan conversion device according to an embodiment. This ellipse scan conversion device includes a parameter setting unit 10, a calculation accuracy prediction unit 12, a number of digits to be truncated calculation unit 14, an ellipse circumferential coordinate calculation unit 16 and an output unit 18.

The parameter setting unit 10 sets and inputs the parameters of the ellipse to be drawn (major axis, minor axis, center coordinates, etc.) and initializes the parameters. Calculation accuracy prediction unit 12
Receives the set value and initial value of the parameter from the parameter setting unit 10 and obtains the maximum number of calculation digits that can occur in scan conversion of the ellipse to be drawn by a predetermined calculation formula described later. The truncation digit number calculation unit 14 includes the calculation accuracy prediction unit 12
Determine the number of lower-order bits to be truncated from the internal variable used in scan conversion of the ellipse to be drawn, based on the maximum number of calculated digits obtained in. Ellipse circumference coordinate calculation unit 16
Cuts the lower bits of the internal variable by the number of digits determined by the truncated digit number calculation unit 14 and executes scan conversion to determine the raster coordinates of the ellipse to be drawn. Output part 1
A display device, a printing device, or a storage device (not shown) displays the elliptic raster coordinates obtained by the elliptic circle coordinate calculation unit 16.
To send to.

Next, the operation of the elliptical scan conversion apparatus of this embodiment will be described with reference to the flow chart of FIG. Also in this example, as shown in FIG. 5, an ellipse centered on the origin and having a diameter of Rx in the X-axis direction and a diameter of Ry in the Y-axis direction is scan-converted in the first quadrant in the clockwise direction by an ellipse of 4 minutes. Each quadrant of the other three quadrants can be drawn by inverting and folding the quadrant of the first quadrant.

When the scan conversion is started, the parameter setting unit 10 first initializes (20). In this initialization, the start coordinates (x = 0, y = Ry) are determined, and the initial value (Rx * Rx * (1-2 * Ry) of Δi (equation (1.07)) corresponding to the start coordinates is determined. + Ry × Ry) is required.

Next, the operation accuracy predicting unit 12, a maximum value delta _MAX of Δi which may occur in this scan conversion are determined (22). The maximum value of Δi in equation (1.07) occurs when Eh in equation (1.04) becomes maximum, or
It is either when Ev of 6) becomes the maximum. As shown in FIG. 3, Eh is maximum near the X axis and Ev is maximum near the Y axis. Which maximum value is larger is determined by the aspect ratio of the ellipse, that is, the ratio of Rx and Ry. Therefore, for example, as shown in FIG. 5, when drawing a horizontally long ellipse, the coordinates (Rx, Rx,
0) maximum delta _MAX of Δi is obtained by. In this scan conversion, most since the value is larger internal variable of a Δi including fourth-order terms, the maximum value delta _MAX of Δi is also the maximum value of the internal variable. Then, the number of calculation digits of Δ _MAX is [log (Δ
_MAX ) +1]. Here, [x] is a Gaussian symbol, and for a real number x, [x] represents the maximum integer not exceeding x. Therefore, if [x] = n, n ≦
The relationship of x <n + 1 is established.

Next, in the cutoff digit number calculation unit 14, the maximum calculation digit number [log (Δ
_{Based on (MAX} ) +1], the number k of lower order bits to be truncated from the internal variable used in scan conversion of the ellipse to be drawn is determined (24). If the calculation in the elliptic circle coordinate calculation unit 16 of the present scan conversion apparatus is performed with an integer type of 32 bit length, the maximum number of overflow bits k
Is, k = is determined as _{[log (Δ MAX) +1]} -32 (2.01). Maximum number of bits that overflows k
Is the number k of lower order bits to be truncated from the internal variable.

The elliptic circle coordinate calculation section 16 is supplied with the above-mentioned initial value from the parameter setting section 10 and the cut-off digit number calculation section 14 with the above-mentioned data of the cut-off digit number k. In the elliptic circle coordinate calculation unit 16, the digital differential analysis method (D
Before performing the scan conversion by DA), the recurrence tolerances h _del , v _del , h _eps , and v _eps used in the scan conversion are defined as the following values (26). h _del = R _x × R _x × (1-2 × R _y ) (2.02) v _del = R _y × R _y × (2 × R _x −1) (2.03) h _eps = R _y × R _y × ( 3-2 × R _x ) (2.04) v _eps = R _x × R _x × (2 × R _y -3) (2.05) where the tolerance h _del of the formula (2.02) is the second term of the formula (1.09). (B
(2x i + 1 +1)), and the tolerance v _{del in} equation (2.03) is
Corresponding to the second term (-a (2yi + 1-1)) of (1.12), the equation (2.
Tolerance h _{eps of} 04) is the second and third terms of equation (1.11) (-
2bxi + b), and the tolerance v _eps of equation (2.03) is
This corresponds to the second and third terms (2ayi-a) of (1.08).

Equations (1.08), (1.09), (1.11), and Equation (1.12) are x
Since a term having i and yi as variables is included, it is possible to express a variation in which xi and yi change by one. Hold xi and yi separately,
The lower bits may be rounded (truncate) and used for each calculation, but it is difficult to do this each time one dot is drawn. Therefore, in the present embodiment, the variation of the recurrence formula used in the scan conversion is transformed into a tolerance in accordance with the third-order term.

The elliptic circle coordinate calculation unit 16 rounds the lower bits of the calculated tolerances h _del , v _del , h _eps , v _eps by k digits (26). Also, with respect to the initial value Δi from the parameter setting unit 10, the lower bits are rounded by k digits (28).

After rounding the internal variables in this way, the elliptic circle coordinate calculation unit 16 uses the digital differential analysis method (DDA).
Scan conversion is performed to determine the elliptical raster coordinates (30 to 54). Each step 3 of this scan conversion
0 to 54 correspond to steps 106 to 132 of FIG. 7, respectively. In the scan conversion of this embodiment, Δiδi
, H _del , v _del , h _eps , v _eps, etc. are rounded to within 32 bits, so that an ellipse can be drawn at high speed by a 32-bit processor. Further, the burden on software is small, the overhead is small, and the throughput can be improved.

FIG. 4 shows that when a 640 × 818 dot size ellipse is drawn on a CRT, it is 2646 × 3 on A4 size paper.
In each case of drawing an ellipse having a size of 742 dots and when drawing an ellipse having a size of 3238 × 4586 dots on a sheet of B4, the calculation speed according to the conventional method and the calculation speed according to the present embodiment are compared. According to this experimental result, it is possible to achieve a speedup of 6.0 to 8.2 times.

In the present embodiment, the number of rounded digits k is obtained from the equation (2.01), but the number is not limited to this, and may have an appropriate value α (integer) width. _{, k = [log (Δ MAX} ) +1] may be -32 (2.06).

[0026]

As described above, according to the present invention,
The maximum number of calculation digits is predicted in advance based on the parameters of the ellipse to be drawn, and the lower bit of the internal variable is cut off by a predetermined number of digits according to the maximum number of calculation digits, and scan conversion is executed. The ellipse can also be drawn at high speed by the arithmetic unit of (1), and the throughput can be improved even when processing by software.

[Brief description of drawings]

FIG. 1 is a block diagram showing the main configuration of an elliptical scan conversion device according to an embodiment of the present invention.

FIG. 2 is a flowchart showing a process of an ellipse scan conversion device according to an embodiment.

FIG. 3 is a diagram for explaining an operation of a calculation accuracy prediction means of the embodiment apparatus.

FIG. 4 is a diagram showing an effect of speeding up drawing by the apparatus of the embodiment.

FIG. 5 is a diagram showing an elliptical figure drawn by the embodiment and the conventional method.

FIG. 6 is a diagram for explaining a Bresenham's drawing algorithm for a circle or an ellipse.

FIG. 7 is a flowchart showing a scan conversion process by a conventional ellipse drawing algorithm.

[Explanation of symbols]

 10 Parameter Setting Section 12 Calculation Accuracy Prediction Section 14 Truncated Digit Number Calculation Section 16 Elliptic Circular Coordinate Calculation Section 18 Output Section

Claims (1)

[Claims] 1. An apparatus for determining raster coordinates of an ellipse to be drawn by scan conversion based on a digital differential analysis method for drawing an ellipse on a raster scan display, wherein the ellipse to be drawn is set. Calculation accuracy prediction means for predicting in advance the maximum number of calculation digits that can occur in the scan conversion based on parameters, and an internal variable used in the scan conversion based on the maximum number of calculation digits predicted by the calculation accuracy prediction means Truncation digit number calculating means for determining the number of lower-order bits to be truncated from, and performing the scan conversion by truncating the lower bits of the internal variable by the number of digits determined by the cutting-off digit number calculating means, And an elliptic circle coordinate calculating means for determining raster coordinates of an ellipse to be drawn. Conversion device.