JPH0830797A - Antialiasing method - Google Patents

Abstract

PURPOSE:To prevent the stoppage of the plotting of the line part of a grid stripe due to an aliasing by providing a step deciding whether light beam steps over the line part of a grid stripe model or not on the assumption that light beam is shifted from one intersected point to the other intersected point. CONSTITUTION:Based on the intersected point Qn-1 of light beam passing an arbitrary first picture element from a viewpoint location and a grid stripe model and the intersected point Qn of light beam passing a second picture element adjacent to the first picture element from the viewpoint location and the grid stripe model, whether light beam steps over the line part of the grid stripe model or not is decided on the assumption that light beam is shifted from one intersected point Qn-1 and the other intersected point Qn. When it is decided that light beam steps over the part, the information on the distance between the both intersected points Qn-1 and Qn on the grid stripe model is calculated and the information on the average of the density value between the both intersected points Qn-1 and Qn on the grid stripe model is calculated. Based on the information on the distance between the both intersected points Qn-1 and Qn and the information on the average of the density value between the both intersected points Qn-1 and Qn, the luminance value of the second picture element is calculated.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an anti-aliasing method used when a reflection image for a curved surface shape model of a lattice fringe model is generated by determining the brightness of each pixel on the projection surface by a ray tracing method.

[0002]

2. Description of the Related Art In order to examine a reflection image of a three-dimensional free-form surface object such as an automobile windshield, it is conceivable to generate a reflection image of lattice stripes for the three-dimensional free-form surface object by simulation.

A ray tracing method may be used as a method of generating a lattice fringe reflection image for a three-dimensional free-form surface object by simulation. That is, the ray from the viewpoint position to the lattice fringe is traced, and the brightness on the projection plane is determined depending on whether the intersection point of the lattice fringe and the ray is white or black.

[0004]

When a lattice fringe reflection image for a three-dimensional free-form surface object is generated using the ray tracing method, aliasing may occur due to insufficient sampling. That is, the line portion of the checkered pattern may not be drawn.

It is an object of the present invention to provide an anti-aliasing method which can prevent the line portion of the lattice fringes from being drawn due to aliasing.

[0006]

The anti-aliasing method according to the present invention is used when a reflection image for a curved surface shape model of a lattice fringe model is generated by determining the brightness of each pixel on the projection surface by the ray tracing method. An anti-aliasing method, wherein an intersection of a ray passing through an arbitrary first pixel from the viewpoint position and a lattice fringe model, and an intersection of a ray passing through a second pixel adjacent to the first pixel from the viewpoint position and the lattice fringe model Based on the above, if it is assumed that the ray has moved from one intersection to the other, the step of determining whether the ray has straddled the line portion of the checkered model, and the ray has straddled the line portion of the checkered model. When the judgment is made, the information on the distance between the intersections on the checkerboard model is calculated and the information on the average of the density values between the intersections on the checkerboard model is calculated. Steps and information about the distance between the both intersections, on the basis of the information about the average of the density values between the two intersection points, characterized in that it comprises the step of calculating the luminance value of the second pixel.

[0007]

Based on the intersection of the ray passing through the arbitrary first pixel from the viewpoint position and the lattice fringe model, and the intersection of the ray passing through the second pixel next to the first pixel from the viewpoint position and the lattice fringe model, If it is assumed that the ray has moved from one intersection to the other, it is determined whether or not the ray crosses the line portion of the checkered model.

When it is determined that the light ray straddles the line portion of the checkered model, the information on the distance between the two intersections on the checkered model is calculated and the information on the average of the density values between the two points on the checkered model is calculated. To be done.

Then, the brightness value of the second pixel is calculated based on the information on the distance between the two intersections and the information on the average of the density values between the two intersections.

[0010]

FIG. 1 shows an optical system model of a reflected image when a reflected image for a curved surface shape model of a lattice fringe model is created by simulation.

In this optical system model, a viewpoint 1, a projection plane 2 for creating a reflected image, a three-dimensional free-form curved glass 3 such as a glass for automobiles, and a black and white lattice striped screen 4 are arranged from the near side.

The projection plane 2 is divided into a plurality of areas on a pixel-by-pixel basis. In this example, the three-dimensional free-form glass 3 is Y
The cross section along the -Z plane has a curved semi-cylindrical shape. As shown in FIG. 2, the checkered screen 4 is composed of a plurality of vertical and horizontal black line portions and a plurality of white rectangular portions surrounded by the black line portions. The width of the black line portion is Hb, and the height of the white rectangular portion is Hw.

The brightness value of each pixel on the projection plane 2 is basically determined by the ray tracing method. That is, a ray from the viewpoint position through each pixel to the screen surface is traced, and the brightness value of the pixel is determined depending on whether the intersection position of the ray and the screen surface is the white part or the black part of the checkered pattern. It

When the brightness value of each pixel on the projection plane 2 is determined only by the ray tracing method, aliasing may occur due to insufficient sampling, and the black portion of the grid pattern may not be drawn. In particular, the three-dimensional free-form glass 3 is shown in FIG.
In the case of the shape and arrangement shown in (1), of the vertical and horizontal black line portions of the checkered pattern, the horizontal black line portion may not be drawn.

Such aliasing is performed in the position Q _n-1 of the intersection of the ray traced for one pixel and the screen surface 4 among the vertically adjacent pixels in the projection plane 2 and the other pixel. This occurs when the traced position of the ray and the intersection position Q _n of the screen surface 4 have the relationship shown in FIG.

That is, among the vertically adjacent pixels in the projection plane 2, assuming that the light ray has moved from the intersection point position Q _n-1 for one pixel to the intersection point position Q _n for the other pixel, the lattice stripes Aliasing occurs when a light ray crosses a black line portion. In such a case, the horizontal black line portion between the intersections Q _n-1 and Q _n is not drawn.

Therefore, in this embodiment, the black line portion in the horizontal direction is prevented from being undrawn in the following manner. In this embodiment, the brightness value of each pixel in the projection plane 2 is sequentially determined by scanning the pixels in the projection plane 2 for each column from the top to the bottom. Therefore, in the case where aliasing as described above is generated, if it is assumed that light is shifted to the intersection Q _n for the current pixel of interest from the intersection Q _n-1 for the previous pixel of interest,
This is the case when the light beam straddles the black portion in the horizontal direction of the plaid model.

In such a case, based on the following equation 1,
The luminance value P _{n of the} pixel of interest this time is determined.

[0019]

## EQU1 ## P _n = PA / L

However, PA is the sum of densities between the intersection point position Q _n-1 and the intersection point position Q _n . L is the intersection point Q
the distance between the _n-1 and the point of intersection Q _n. Therefore,
The luminance value P _n of the target pixel is the average value of the densities on the screen surface 4 between the intersection point position Q _n-1 for the previous target pixel and the intersection point position Q _n for the previous target pixel. As a result,
Since the luminance value for the pixel of interest this time becomes darker than the luminance value for the white portion, the horizontal black line portion between the intersections Q _n−1 and Q _n is drawn.

As for the distance L between the intersection point position Q _n-1 and the intersection point position Q _n , the Y coordinate value of the intersection point position Q _n-1 is y _n-1 , and the Y coordinate value of the intersection point position Q _n is y _n . Then, it is roughly obtained by the following equation 2.

[0022]

## EQU2 ## L = y _n-1 -y _n

Further, the density sum PA between the intersection point position Q _n-1 and the intersection point position Q _n is expressed by the following equation 3 between the intersection point position Q _n-1 and the intersection point position Q _n. It is calculated as the sum of the density sum P of the black portion in the area and the density sum Pw of the white portion between the intersection position Q _n-1 and the intersection position Q _n .

[0024]

[Formula 3] PA = Pb + Pw

The density sum Pb of the black portion is obtained as follows. A serial identification number M (= 1, 2, 3, ...) Is preliminarily assigned to the white rectangular portion in order from top to bottom for each row of the checkered pattern. Assuming that the identification number of the white rectangular portion where the intersection Q _n-1 with respect to the previous pixel of interest exists is M _n-1 and the identification number of the white rectangular portion where the intersection Q _n with respect to the current pixel of interest is M _n , the intersection point From the position Q _n-1 to the intersection position Q _n , the number Nb of black line portions that the light ray straddles is represented by the following mathematical formula 4.

[0026]

## EQU00004 ## Nb = _Mn - _Mn-1

Assuming that the width of the black line portion is Hb and the image intensity for the black line portion is Ib, the density sum Pb due to the black portion is expressed by the following equation 5.

[0028]

(5) Pb = Nb × Hb × Ib

The density sum PW of the white portion between the intersection point position Q _n-1 and the intersection point position Q _n is obtained as follows.
The density sum Pw is the density sum Pw1 by the white rectangular portion included from the intersection position Q _n-1 to the intersection position Q _n , and the intersection position Q.
the concentration sum Pw2 by the white portion of the _n-1 to the nearest black line portion at the bottom, is the sum of the concentration sum Pw3 using the white portion of the intersection Q _n to the nearest black line portion of the upper side.

The density sum Pw of the white rectangular portion between the intersection point position Q _n-1 and the intersection point position Q _n is obtained as follows.

The number Nw of light rays straddling the white quadrangle between the previous time and this time is expressed by the following mathematical expression 6.

[0032]

(6) Nw = Nb-1

The white rectangular portion height Hw, the image intensity for the white rectangular portion and Iw, density sum by white-block portion contained in the intersection Q _n-1 to the intersection point position Q _n Pw1
Is expressed by the following Equation 7.

[0034]

[Equation 7] Pw1 = Nw × Hw × Iw

In addition, the density sum Pw2 by the white part from the intersection point position Q _n-1 to the lower black line portion is the Y coordinate value of the intersection point position Q _n-1 , y _n-1 , Mod (a / b) When is defined as the remainder of a / b, it is expressed by the following formula 8.

[0036]

## EQU8 ## Pw2 = {Hw-Mod (y _n-1 / (Hw + H
b)} × Ib

[Hw-Mod (y
_n-1 / (Hw + Hb)} corresponds to L1 in FIG.

Also, the density sum Pw of the white portion from the intersection point position Q _n to the upper black intersection point position Q _n-1 to the lower black line segment
3 is the Y coordinate value of the intersection point position Q _n , y _n , Mod (a /
If b) is defined as the remainder of a / b, it is expressed by the following Equation 9.

[0039]

## EQU9 ## Pw3 = {Mod (y _n / (Hw + Hb)} × Ib

[Mod (y _n / (H
w + Hb)} corresponds to L2 in FIG.

FIG. 3 shows the overall procedure of the brightness value determination process.

As described above, the brightness of each pixel on the projection surface 2 is determined by scanning from the top to the bottom for each column of the pixel group on the projection surface 2. FIG. 4 shows a brightness value determination process for pixels in one column.

First, the uppermost pixel in the column to be scanned is set as the pixel of interest (step 1). Then, the coordinates of the position of the intersection of the ray passing through the pixel of interest from the viewpoint and the screen surface of the grid pattern are obtained (step 2).

Next, if it is assumed that the light beam is moved from the intersection point position for the previous pixel of interest to the intersection point position for the current pixel of interest, it is determined whether or not the line crosses the black line portion (step 3).

If the pixel of interest is the uppermost pixel,
Since the last pixel of interest does not exist, move to step 4,
The ray tracing method determines the luminance of the pixel of interest this time. That is, the brightness of the current pixel of interest is determined depending on whether the intersection point position of the current pixel of interest obtained in step 2 is within the white rectangular portion or the black line portion.

After this, the routine proceeds to step 6, where it is judged if the pixel of interest this time is the pixel at the bottom. If the pixel of interest this time is not the lowermost pixel, the pixel one lower than the pixel of interest this time is regarded as the pixel of interest (step 7), and then the process returns to step 2. And a ray passing through the pixel of interest from the viewpoint,
The coordinates of the position of the intersection of the checkered pattern with the screen surface are obtained.

Next, if it is assumed that the light beam is moved from the intersection point position for the previous pixel of interest to the intersection point position for the current pixel of interest, it is determined whether or not the light beam crosses the black line portion (step 3).

When it is determined that the pixel does not cross the black line portion, the brightness of the pixel of interest this time is determined by the ray tracing method as described above (step 4). After this, it is judged whether or not the pixel of interest this time is the lowermost pixel (step 6). If the pixel of interest this time is not the lowermost pixel, the pixel one lower than the pixel of interest this time is regarded as the pixel of interest (step 7), and then the process returns to step 2.

When it is determined in step 3 that the black line portion is crossed, the density average value between the intersection point position with respect to the previous pixel of interest and the intersection point position with respect to the current pixel of interest is calculated based on the above equations 1 to 9. It is calculated (step 5). Then, the calculation result is determined as the luminance value of the pixel of interest this time.

After this, the routine proceeds to step 6, where it is judged whether or not the pixel of interest this time is the lowermost pixel. If the pixel of interest this time is not the lowermost pixel, the pixel one lower than the pixel of interest this time is regarded as the pixel of interest (step 7), and then the process returns to step 2.

The above-described processing is sequentially repeated, and when the processing for the lowermost pixel is completed, YES is determined in step 6, and the brightness value determination processing for one column is completed.

According to the above-described embodiment, it is possible to prevent the black line portion in the horizontal direction of the checkered pattern from becoming undrawn, and a more realistic image can be obtained.

In the above embodiment, the pixel groups on the projection surface are scanned in the vertical direction in order to prevent the black line portions in the horizontal direction of the lattice stripes from being drawn by aliasing, but the black lines in the vertical direction of the lattice stripes are scanned. When it is desired to prevent the line portion from being drawn due to aliasing, the pixel group on the projection surface may be scanned in the horizontal direction.

If it is desired to prevent the black line portion in the horizontal direction of the checkered pattern and the black line part in the vertical direction of the checkered pattern from being prevented from being drawn due to aliasing, the following may be done. The pixel group on the projection surface is scanned in one of the horizontal direction and the vertical direction, and the brightness value of each pixel is determined by the same method as in the above-described embodiment. After this,
By scanning in the other direction, the brightness value of the pixel of interest may be corrected by the anti-aliasing method of the present invention (processing of step 5 in FIG. 5) only in the area where aliasing occurs.

Although a three-dimensional free-form curved surface glass is used as the object model in which the lattice fringes are reflected, an object model other than glass may be used as long as the object has a three-dimensional free-form curved surface shape.

[0056]

As described above, according to the present invention, it is possible to prevent the line portions of the lattice fringes from becoming undrawn due to aliasing.

[Brief description of drawings]

FIG. 1 is a schematic diagram showing a configuration of an optical system model of a reflected image.

FIG. 2 is a schematic diagram showing an example of the positional relationship between the intersection points and the lattice stripes for vertically adjacent pixels when antialiasing occurs.

FIG. 3 is a flowchart showing a procedure of a brightness value determination process.

[Explanation of symbols]

 1 viewpoint 2 projection plane 3 three-dimensional free-form glass 4 lattice screen

Claims (1)

[Claims] 1. An anti-aliasing method used when a reflected image of a curved surface shape model of a lattice fringe model is determined by determining the brightness of each pixel on the projection surface by a ray tracing method, the method being an arbitrary method from a viewpoint position. The intersection of the ray passing through the first pixel and the lattice fringe model, and the second pixel next to the first pixel from the viewpoint position.
Based on the intersection of the ray passing through the pixel and the plaid model,
If it is assumed that the ray has moved from one intersection to the other, the step of determining whether the ray has straddled the line portion of the checkered model, when it is determined that the ray has straddled the line portion of the checkered model, Calculating information about the distance between the intersections on the checkered model and calculating information about the average density value between the intersections on the checkered model, and information about the distance between the intersections and the density between the intersections Calculating the luminance value of the second pixel based on the information about the average of the values.