JP2718784B2 - Drawing method of contour and / or edge - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image generation method using a computer, and more particularly to a method for drawing contour lines and / or ridge lines using a line drawing (wire frame display).

[Conventional technology]

When drawing a three-dimensional shape as a two-dimensional image, a method of drawing only the object and the outline with a wire frame (drawing method by line drawing-also called a drawing method), or drawing by painting the surface of the object with different shades and colors (Drawing method using a screen). Here, the contour line indicates a boundary line between the visible surface and the invisible surface of the object, and the ridge line indicates an inner shape line representing an angular portion other than the contour line of the object.

When the purpose is to create a realistic image, a method of calculating the brightness of each point on the object surface based on the position of the light source and the reflectance of the object surface and drawing it as a shaded face drawing, Usually used. On the other hand, when the purpose is to display an object in an easy-to-understand manner, the object is often drawn as a line drawing, or the face drawing and the line drawing are sometimes combined.

In the line drawing method, in order to make it easy to understand,
Often, only lines that are visible from the viewpoint are drawn, that is, hidden line elimination is performed. There are several known hidden line elimination methods. All of them are as follows: (1) For all contour lines and ridge lines, determine whether or not each is hidden by the front surface, and draw only non-hidden lines (2) a method combining a process of drawing a line and a process of painting a front surface with a background color and erasing the previously drawn line.

Also, when drawing a glossy object such as a metal or a transparent object such as a glass, it is often necessary to draw an image that is reflected on the surface of the object or an image that is transmitted through the object and refracted on the surface. Will be needed. A ray tracing method is widely used as a method for drawing including such reflection and refraction images. The ray tracing method is a method of tracing a light beam reaching a viewpoint from each pixel direction in the opposite direction from the viewpoint to determine a luminance value of each pixel and generate an image. In order to determine the luminance value of a certain pixel, first, an object where a half line extending from the viewpoint to the pixel direction intersects first, and the intersection thereof are obtained. If there is no intersecting object, the background color is taken as the luminance value of the pixel. If there is no reflection or refraction on the intersecting object surface, a luminance value is obtained from the relationship between the surface attribute and the light source. When there is reflection on the surface, the luminance of the object itself obtained from the relationship between the surface attribute and the light source is combined with the luminance of the reflection image obtained by recursively tracing the ray coming from the reflection angle, The brightness of the pixel is used. In the case where there is refraction on the surface, in addition to the above-described case, by tracing light rays coming from the refraction angle recursively, the luminance of the obtained refraction image is also synthesized to be the luminance of the pixel. By the above processing, the reflection and refraction images of the object can be drawn.

[Problems to be solved by the invention]

When a line drawing is generated using the above-described hidden line elimination method according to the prior art, there are the following three problems: (1) a complicated surface (for example, a tertiary or higher-order surface or a fractal such as a mountain); Shape, etc.), it is necessary to obtain the outline stably and efficiently, and to perform hidden line elimination.
Extremely difficult.

(2) When combining a screen and a line drawing, it is necessary to simultaneously erase the hidden surface of the face drawing and the hidden line of the line drawing without inconsistency. Since these two processes are similar to each other, it is wasteful to perform them completely independently. However,
When both the hidden line and the hidden surface are erased by one process, the selection of the hidden surface erasing method is restricted. For example, it is practically very difficult to apply ray tracing to line drawings.

(3) When creating a screen, the shadow on the object surface is often simulated based on a certain physical model. In this case, if the physical model is determined, the image to be created is uniquely determined. . In contrast, line drawing
It is always performed as a means of artificial emphasis, and the appropriate color, depth, thickness, etc. of the line differ for each purpose. In the case of combining a face image and a line image by a conventional technique, it is difficult to separate such a physical model and an artificial factor in a process of processing.

With the hidden line elimination method or the ray tracing method according to the prior art, it is extremely difficult to draw the contour lines and ridge lines of the object in the reflection and refraction images. If the situation is limited, for example, if only reflection on a plane is used, it can be realized relatively easily by combining coordinate transformation with the conventional hidden line elimination method. Handling reflection and refraction is not possible with this method. Further, capturing a line having no thickness by the ray tracing method requires complicated processing such as tracing a ray as a light beam such as a cone, which is practically difficult.

An object of the present invention is to create a contour line and a ridge line of a three-dimensional object.
It is an object of the present invention to provide a means for stably and efficiently drawing without depending on the complexity of an object shape and the direction in which a face image is generated. Also, the contours and ridges of the three-dimensional object are
The purpose is to efficiently draw images including those in reflection and refraction images.

[Means for solving the problem]

In the present invention, a two-dimensional data array (distance image) having, as an element, distance information from a viewpoint to an object at each pixel
Is generated by pre-processing, a differential operator is operated on the pre-processing, and post-processing is performed on those output images in consideration of nearby differential values.

In addition, a two-dimensional data array (optical path length image) is created by ray tracing, which uses the information on the optical path length from the object (or background) that is finally reflected on each pixel to the viewpoint, as an element. The differential operator is operated to make an appropriate correction.

FIG. 1 is a diagram illustrating the principle of the present invention. Three-dimensional object 41
, A distance image 1 is obtained. Differential processing 102 is performed on the distance image 1 to obtain an outline image and / or
Alternatively, a ridge image 103 is obtained.

(Operation)

The contour is a set of points at which the distance from the viewpoint changes discontinuously. Therefore, when the first derivative operator is applied to the distance image 1, the contour appears as a peak value.
On the other hand, in the ridge line, the normal direction of the object surface changes discontinuously. That is, it is a set of points at which the first derivative of the distance from the viewpoint changes discontinuously. Therefore, when a second derivative operator is applied to the distance image 1, the ridgeline appears as a peak value.

However, simply by using these differential operators, (1) the density of the contour line on the primary differential image changes depending on the distance difference between the objects; (2) the object plane close to the line of sight , The primary differential value increases like the outline; (3) The outline appears as a positive / negative type line on the second derivative image; It cannot be used as a ridgeline image. The above phenomenon is
By observing the local behavior of the derivative, a significant portion can be corrected.

Also, when focusing on the optical path length from the viewpoint to the object finally reflected instead of the distance from the viewpoint, reflection,
Edges and contours in the refraction image have the same discontinuity. Therefore, when a first-order or second-order differential operator is applied to the optical path length image, the contour lines and ridge lines in the reflection and refraction images appear as peak values similarly to general contour lines and ridge lines.

〔Example〕

 Hereinafter, embodiments of the present invention will be described.

FIG. 2 shows the flow of the processing of one embodiment of the present invention. First, distance image 1 is prepared as preprocessing. This includes three-dimensional shape data 11 of the object and camera parameters 12 (viewpoint,
(A reference point, a viewing angle, a resolution, etc.) and a method of obtaining the existing object 41 by directly measuring the existing object 41 using a distance measuring device. Here, the distance measuring device means light (triangulation or interference measurement using a range finder or the like), ultrasonic waves, magnetic force, mechanical contact,
It refers to a device that measures the distance from a point to each point on the surface of a three-dimensional object by using such means, and obtains a distance image. In the case of the former method, the distance image 1 can be obtained by using the hidden surface removal processing 31 performed when drawing the screen. Hidden surface removal processing 31 appears to overlap 3
In this process, a visible line, that is, a plane closest to the viewpoint, is obtained for each pixel from the three-dimensional object plane, and a scan line method, a z-buffer method, a ray tracing method, and the like are widely used. Among these, in the z-buffer method and the ray tracing method, the closest object is determined by calculating and comparing the distance from the viewpoint to the surface of each object for each pixel. The distance value calculated at this time can be used as it is as the distance image 1. Even in the scan line method, distance values at both ends of a segment on a scan line are obtained during processing. Therefore, if interpolation processing is performed between them, the distance value of each pixel can be easily obtained.

The distance value is the actual distance from the viewpoint 61 to the object 41 as shown in Fig. 3 (however, the component in the direction perpendicular to the screen)
Can be used, but when drawing by the perspective projection method, it is better to use a value proportional to the projection distance, that is, the reciprocal of the actual distance. The reason is that it is easy to obtain by linear interpolation, and the relationship between the first derivative of the distance on the smooth object surface and the inclination of the object surface does not depend on the distance to the object. Therefore, it depends on two points. In addition, as in the case where the luminance value is obtained by performing the anti-aliasing process, 1
If a pixel is sampled at a plurality of points or the ratio of each surface to one pixel is calculated and the average value of the distance values within the pixel is used as the distance value of the pixel, the line drawing obtained by the processing described below is It will be smooth without jaggy.

For the distance image 1, primary differential processing 21 and secondary differential processing
22 to obtain primary differential image 2 and secondary differential image 3, respectively. In the first derivative processing 21, the Sobel operator g = | A + 2B + CF-2G-H | + | C + 2E + HA-2D-F | (1) Alternatively, the Prewitt operator g = | A + B + CFFG- H | + | C + E + H−A−D−F | (2) Used by selecting from various primary differential operators. The second derivative processing 22 includes a Laplacian ι = 4X-B-D-EG (3) or a modified operator ι = 8X-A-B-C-C-D-E-F-G- H ... (4) Select and use from various secondary differential operators such as (4). Here, A to H, X are the values of the neighboring pixels shown in FIG. That is, a 3 × 3 window 63 is prepared, and the center pixel X represents the pixel of interest, and A to H represent neighboring pixels.

Next, regarding the correction processing of the contour pixel and the edge pixel,
An example of each will be described.

First, for each pixel, the maximum value (process 23) and the minimum value (process 24) of the first derivative in the vicinity (for example, the nine pixels shown in FIG. 4) are obtained, and the first-order maximum differential image 4, 1 The next differential minimum image 5 is set.

The contour image 6 is obtained by performing a contour correction process 25 using the primary differential image 2, the primary differential maximum image 4, and the primary differential minimum image 5. First derivative value at a certain pixel
g, the maximum value of the first derivative near this pixel is g _max , and the minimum value of the first derivative is g _min , the value p of this pixel in the contour image 6 is Given by Here, g ₀ is the value of g on a plane inclined 45 degrees with respect to the screen, and is “8” when, for example, a Sobel operator is used. κp is a constant for discriminating between a contour line and a change in inclination. An appropriate value of κp varies depending on the target shape and the drawing purpose, but is, for example, a value of about “4” to “16”.

The ridge line image 7 is obtained by performing the ridge line correction processing 26 using the second-order differential image 3 and the first-order maximum differential image 4. Assuming that the secondary differential value at a certain pixel is ι and the maximum primary differential value near this pixel is g _max , the value e of this pixel in the edge image 7 is Given by Here, ι ₀ is the value of ι at an edge formed by two planes inclined at 45 degrees to the screen at right angles. For example, when the second derivative operator shown in the equation (4) is used, “6” ". kappa _l is the limit value of the first derivative for performing exception processing such as contour erased. Appropriate κ
The value of ₁ varies depending on the target shape and the purpose of drawing, but is, for example, about “2” to “4”. Note that when equation (6) is used, the sharper the ridgeline, the greater the absolute value of e and the darker the line, but if the correction is performed using the maximum and minimum values near the second derivative, Regardless of the dihedral angle of the ridge line, it is possible to draw a ridge line with a certain depth.

The pixel value of the outline image 6 obtained by the above method is 0 for the background and 1 at the maximum for the outline portion. The pixel value of the ridge image 7 is 0 for the background, positive for the convex ridge, and negative for the concave ridge. Operations appropriate for these pixel values (absolute value, linear operation,
If the luminance value is calculated (processing 27) by applying the maximum / minimum truncation, etc., an image 9 suitable for the purpose can be obtained. At this time, it is also easy to combine with the shaded screen 8 if necessary.

FIG. 5 shows a flow of processing in another embodiment of the present invention. First, a ray tracing process 131 and an optical path length calculation 133 are performed using the three-dimensional shape data 11 of the object and camera parameters 12 (viewpoint, reference point, viewing angle, resolution, etc.) as input data, and an optical path length image 101 is created. . A differential operator is operated on the optical path length image 101 (differential processing 102), and correction processing 1 is performed.
By applying 02, a contour line and a ridge line image 103 including the inside of the reflection and refraction images can be obtained. Further, the shaded face image 10 is shaded by the shading process 32.
4 and (Step 23), a combined image 105 is obtained.

Next, a specific method of the optical path length calculation 133 will be described. In the ray tracing method, the distance from the viewpoint or the object surface to the next object is calculated in the process of processing. By adding these distances from the viewpoint to the object finally reflected, the optical path length can be obtained. However, in some cases,
Instead of simply adding the actual distance, it is necessary to appropriately incorporate the following correction processing. Note that the distance referred to below refers to a distance from a viewpoint or an object to the next object or background.

(1 ′) The distance to the background is suppressed by a certain finite value. If this is not performed, the optical path directly from the viewpoint to the background and the optical path to the background due to reflection or refraction both have infinite lengths, so that the edge of the mirror cannot be extracted as a contour line.

(2 ′) When adding the distance, weighting is performed according to the reflectance and the transmittance.

(3 ') For the distance from the viewpoint, a component perpendicular to the screen at the actual distance is used.

(4 ′) For the distance from the viewpoint or the entire optical path length,
Use the reciprocal value. By this processing, on a smooth object surface directly visible from the viewpoint, the relationship between the first derivative and the inclination of the object surface does not depend on the distance to the object.

(5 ') One pixel is sampled at a plurality of points, and the average value of the optical path length at each point is used as the optical path length of the pixel in the same manner as in the case where the luminance value is obtained by performing anti-aliasing processing. As a result, the contour / ridge image becomes smooth without jaggies.

〔The invention's effect〕

As described above, according to the present invention, a contour line and a ridge line of a three-dimensional object can be stably and efficiently drawn regardless of the complexity of the object shape. Even in the case of combining with a face image, if a distance image is created by slightly changing the existing hidden surface elimination algorithm, the subsequent processing can be performed completely independently of the creation of the face image. The anti-aliasing processing of a line drawing can be realized only by reflecting the processing for a plane image on a distance image. Furthermore, if a range finder device is used, it is possible to perform drawing based on an existing object by the same processing.

Further, according to the present invention, the contour lines and ridge lines of the three-dimensional object, including those in the reflection and refraction images, can be efficiently drawn. It is easy to combine with a shaded drawing. In this case, the change of the enhancement effect (such as the density of the line) of the contour line and the ridge line can be performed completely independently of the creation of the face image. The anti-aliasing processing of a line drawing can be realized only by reflecting the processing for the plane drawing on the optical path length image.

INDUSTRIAL APPLICABILITY The present invention can be applied to creation of illustration images in many fields such as industrial design and architectural design.

[Brief description of the drawings]

FIG. 1 is an explanatory view of the principle of the present invention, FIG. 2 is a processing flow in an embodiment of the present invention, FIG. 3 is an explanatory view of distance values, FIG. 4 is an explanatory view of neighboring pixels, FIG. Shows a flow chart of processing in the case of another embodiment of the present invention. 1 to 9: two-dimensional data array (image), 11: three-dimensional shape data, 12: camera parameters, 21 to 27: processing for two-dimensional data array (image processing), 31: hidden surface removal processing 32, shading processing, 41, existing object, 51, distance measurement, 101, optical path length image, 102, differentiation processing, 102 ', correction processing, 103, contour line image and / or ridge line image , 104 …… shaded screen, 105 …… composite image,

Claims (3)

(57) [Claims] 1. A method of drawing a visible one of a contour line and / or a ridge line of a three-dimensional object as a two-dimensional image, wherein distance information from a viewpoint to an object at each pixel is used as an element. Preparing a dimensional data array as input data and applying a differential operator thereto to obtain an image of a contour line and / or an edge line as an output, wherein a contour line and / or a ridge line is drawn. 2. The contour and / or ridge line drawing method according to claim 1, wherein a distance image is generated by performing a hidden surface elimination process on the three-dimensional shape data. 3. A method of drawing a visible one of a contour line and / or a ridge line of a three-dimensional object as a two-dimensional image, the method comprising: Creating a two-dimensional data array having information on the length of the optical path up to the element by a ray tracing method and applying a differential operator to the array to obtain an image of a contour line and / or a ridge line as an output. How to draw contours and / or edges.