Wolfgang Leister

Computer Generated Copper Plates


Making computer generated copper plates with image generation algorithms is presented. The method uses a kind of volume texturing in connection with image processing algorithms, and is suitable for implementation in a ray tracing algorithm. Experience shows that this method is especially interesting for illustrations in books and for generating icons on user interfaces.

Keywords: I.3.3 image generation (rendering), I.3.7 ray tracing,
with applications in H.5.2 user interfaces, I.7.2 desktop publishing, J.5 fine arts


Copper plates were formerly used for presenting technical facts and for book illustrations. This technique is more than an old fashioned graphical presentation method influenced by former printing techniques. These images have a special aesthetical flair and have the power to present facts more tersely than raster reproductions of photographs, as some details can be emphasized in a special manner.

Look alike images can be made by image processing techniques out of the pixel values of a two dimensional raster image. But to imitate copper plates a three dimensional scene description has to be used. In the last few years image generation techniques have been studied, especially how to generate photo realistic images from three dimensional scene descriptions. One of these techniques is the well known ray tracing algorithm[1,2,3] that generates photo realistic images with shadows, mirror and glass effects.

The following considerations have their target in generating images that resemble copper plates. In Section 2 the term copper plate is defined. Section 3 illuminates suitable image generation techniques, while in Section 4 the integration of these techniques in a ray tracer is presented. Section 5 deals with implementation details and presents some results. Before some conclusions are given, Section 6 shows how to use copper plates for generating icons for user interfaces.

Copper Plates

The technique can be traced back to the middle ages, where it was used first to produce playing cards. Later many famous painters and artists used this technique, also for reproduction purposes. Before the reproduction technique for photographs came up, copper plates often were used for technical illustrations in scientific publications and as book illustrations.

Conventional copper plates are made by cutting lines into a metal sheet with the help of a graving tool. In the printing process these engraved lines are filled with paint, leaving the other parts clean. The colour is transfered to a sheet of paper when pressing the plate onto it. Three dimensional effects on the resulting figures are produced by the artist who draws the lines in a special manner and by hatchings. Besides the copper plates there are other, comparable techniques as etchings or woodcuts. More details on this subject are presented elsewhere[4].

In the following considerations the term copper plate refers to the result of the printing process, not to producing the printing sheet. A typical copper plate is therefore a drawing that consists of lines of varying thickness and of single points. It does not contain gray values. The objects represented are bordered by lines. The edges are partially more emphasized than the bare (realistic) presentation would afford. Shading is done by regular hatchings in several thicknesses and distances. Dashed lines and interspersed dots enlarge the spectrum of possibilities.

Often letters, sometimes longer explanations are included in the image. Sometimes invisible objects that are occluded by others are drawn with dashed lines. The copper plate technique is also used to produce printable black and white clichées from gray scale images, in modulating the thickness of the lines in hatchings with the pixel values. The following discussion will face on the subject of imitating three dimensional copper plates algorithmically.

Image Generation of Copper Plates

Copper plates can be generated from two dimensional pixel images with filter algorithms and image processing techniques. Good results for painting the edges as line graphics can be reached with the Gauß-Laplace- or with the Kirsch-Compass-Operator[1]. To get the hatchings is somewhat more difficult: first the images must be segmented into areas, that are later filled with patterns of parallel lines. Readers not familiar with the operators used in image processing find more about these techniques in textbooks[5]. Some of the algorithms are similar to colour reduction techniques used in desktop publishing.

At first we should discuss how to represent copper plates. From an artists view a 2D object description would be convenient, e.g. using a spline description of the lines with some drawing attributes. Scan conversion has then to be done later. The advantage would be a resolution and device independent representation. But as it could be complex to determine the projection of general lines on surfaces we chose a raster representation, and make use of standard rendering algorithms.

With image processing techniques all raster images can be handled, also such originated from a scanner, but the three dimensional scene information is not available when producing the hatchings. The two dimensional patterns can either be straight lines or follow border lines of the segmentation area, what is not satisfactory. As hatchings should express three dimensionality, a three dimensional model and a rendering algorithm should be used.

For imitating copper plates with computer algorithms, the geometry and colour part of a rendering algorithm has to deliver suitable information. Generally, there are two different kinds of image rendering algorithms, that generate images from three dimensional scenes: the image-centered and the scene-centered algorithms[1,6]. Scene centered algorithms project unoccluded objects onto the image plane and apply colours on these areas. For single objects the borders can be found easily. Hatchings can be generated by texture mapping. Such techniques are qualified for polygonal scenes. For other object kinds a special treatment is necessary, especially for free form surfaces, where a self occlusion without occluding edges is possible.

In case there are many surfaces with common borders present, as can arise from triangulating complex objects, not all border information should be used. Then for each edge has to be examined whether it is part of a border. This could be done by investigating the material properties for neighbouring objects. Another possibility is to introduce special object kinds for subdivided free form surfaces, a method that increases modeling and implementation efforts. The projection of hatching lines especially affords the calculation of curves in closed formulas.

A system that handles this kind of difficulties is proposed by Dooley and Cohen[7]. Objects in the scene are attached to a set of semantic attributes (importance, line style) that are interactively determined. The rendering algorithm works with illustration rules that are applied to the projected lines according to their attributes.

In what follows an image centered technique shall be investigated for its suitability to generate copper plates. Similar considerations to ameliorate presentation techniques for three dimensional scenes are presented by Saito and Takahashi[8], where an interim representation, the so called G-Buffer is used for storing a pixel image that contains additional scene information. Afterwards this representation is transformed into a black and white representation by appropriate operators.

Copper Plates by Ray Tracing

The kernel of the ray tracing method[1,3] consists of the ray query <p,r,s> that is done for each pixel, where p is the start point of the ray query, r is the query's direction and s is the scene of geometrical objects. The result of this query is the first intersection point t = <tx,ty, tz> of the ray with the scene:

lambda is the normalized length from the start point to the intersection point. The geometric data, the material description parameters and the illumination model determine the resulting colour values (i.e. RGB) for the ray. For copper plates this basic algorithm has to be modified, introducing new parameters into the illumination formula. The geometrical values at the intersection point are the basis for determining the lines for edges and hatchings of a copper plate.

For each ray query the rendering process can be divided into the following phases:

Phase 1:
Geometrical query. Intersection coordinates, object id, material description class, and according illumination formula are determined. This part is the most calculation time consuming. For rendering copper plates no changes with respect to the basic algorithm are necessary.
Phase 2:
Determine colour values, brightness values, etc. from the geometric information according to the illumination formula.
Phase 3:
Geometric and colour calculations for textures and copper plates (hatches).
Phase 4:
Filter phase; the channels and neighbouring pixels are mixed. Image processing operators are used.
Phase 5:
Discretizing the colour values and output. I.e. setting the resulting pixels to black or white.




The available information on hatches will be called the kappa value in what follows. For each pixel kappa is calculated, stored in a pixel file, and later discretized to black and white values with a simple threshold operator in the post processing step.

A first possibility is to calculate a value

 if an intersection has taken place, where a0 is a newly introduced parameter in the material description class for the object that was hit. When the resulting pixel image is treated with a threshold operator the result is a interference pattern with a circular structure, caused by some properties of central projection. This method offers only few variation possibilities, as the direction of the hatchings cannot be changed.

The following suggestion comes close to the conventional texture techniques. The object that was hit by the query ray is geometrically overlayed with parallel, plane laminae (Figure 1). The laminae consist of shares of parallel and equidistant planes in 3D space. As an extension also other lamina objects are possible, e.g. sphere shells stacked into each other or whatever spatial texture.


Figure 1: Hatchings with the ray tracing method

Let t = <tx,ty, tz> the intersection point of the query ray with an object: t = p +  · r. The lamina share i is described by the plane coefficients ei,1,ei,2,ei,3,ei,4 of the first lamina and the distance parameter ai of the parallelly placed laminae. Then the normalized distance bi is given by:

fi := ei,1·tx + ei,2·ty + ei,3·tz + ei,4

 bi is put out as pixel value and treated with a threshold operator in the postprocessing phase. A structure of parallel lines will then be seen on the object's surface.

Several hatches can be combined by summing up the values bi multiplied by the weight factor ci (a parameter in the material class). The hatches are first calculated separately and then later combined. Chosing negative factors ci (desirable) nullifications can be reached. Summing up two hatches will result in a typical triangle pattern after applying the threshold operator on the pixel image.

Overlay of two hatches without producing the triangle pattern is reached by applying the following operator:


In copper plates fluctuations of image values depending on the pixel value in the corresponding RGB image are expressed by different thickness of lines. To reach this we add a weighted amount of the RGB colour value. We introduce the parameters hf and hb to the material description class for scaling the brightness values. Be h the value of a weighted sum of the RGB value, then we add the term (h-hb) · hf to manipulate the thickness.

Be bi and ci weight factors that are newly introduced parameters in the illumination formula. Then we get the following formula for kappa using the parameter r from Equation 2 and bi from Equation 3:



The general method is here first to collect information on the pixel as colour, depth, angles, numbers of light sources, etc., and store this information as a pixel image. In the postprocessing step an edge detection algorithm is applied. In what follows we discuss what kind of information is usefull for getting the edges.

Edges are sudden changes in the image domain, that are difficult to determine with an image centered method. Often neighbouring pixel values are combined with an edge detection operator in image domain. The resulting image depends on the illumination formula and the illumination situation. Alternatively changes of the material description class or of the object id in neighbouring pixels can be marked. For drawing shadows the number of visible light sources can be given out.

By using the  value in an edge detection operator sudden depth changes are detected. But it is undesirable that also objects with a normal vector nearly perpendicular to the query rays are marked. Common edges of neighbouring polygons (e.g. polyhedra) cannot be detected with this method.

As the  value only varies in a small range, and the query ray is relatively long, the control input for the algorithm must contain a range for scaling the  value. An automatic determination is not possible, as there is no global reference in the scene.

Sudden changes of the value cos phi, i.e. the angle between query ray and normal vector, are marked. Actually, it is better to use the value  instead, to avoid the use of negative factors in second order rays. This method can detect edges of neighbouring polygons and strongly curved objects, but no sudden changes in depth. Disadvantages are given by the non linearity of this value. This operator is blind with respect to direction. Therefore in some situations edges cannot be detected. To avoid this, the normal vector can be put out in three separate channels.

Pixels can also be marked when the distance of the intersection point to the object border is smaller than a given threshold. This works only when polygonal scenes are used, but not on objects with curvatures or on combined objects. This method does not need information on neighbouring pixels. Near the edges the minimum of the distance values has to be chosen; but this makes only sense for convex polygons.

To get a satisfactory result several of the proposed types of information have to be merged. Actually, one can get good results when combining the edge-detected mu and lambda.

Second Order Rays

An advantage of the ray tracing method is its easy treatment of second and higher order rays, i.e. rays from reflection and refraction. In most implementations the calculation procedure for these rays is called recursively for each new ray generation. The collected information on the pixel is then combined with the already calculated values. In a first approach the copper plate properties  were treated similar to the RGB values, i.e. they were scaled by a factor and then added. This holds for lambda and mu. For  similar to the overlay of laminae bothering triangle pattern appear. To avoid this we use the  operator from Equation 4.

Be  the value for the current ray generation according to Equation 5 the value for the jth ray (reflection, refraction, xray) in generation i, and accordingly ci,j and di,j factors from the material description class. Then  calculates from


Thus hatchings and border lines can be exposed on mirror surfaces and through glass objects. For modeling with second order rays we propose some design rules. The object that is the mirror should have no hatches or only hatches with a wide distance, so as not to interfere with the finer grain hatches of the objects in the mirror. When chosing scaling factors ci,j, di,j less than 1.0 for the  value, the hatchings in the mirror will appear thinner than usual (thicker when using factors greater than 1.0). For the lambda and mu values one should be aware that the value can reach the maximal value. The phi value would be critical in this case as it is 1.0 for planes perpendicular to the query ray. Therefore we use mu instead to avoid negative scale factors.


Some of the optical properties of copper plates are determined by the image processing operators when combining the channels, and neighbouring pixel relations. In the post processing step the discretizing of raster images takes place, mostly using threshold and edge detecting operators. With smaller objects hatches can be suppressed using a kind of bluescreen technique. Eventually some fluctuations in image space can be simulated by overlaying the image with a random function.

For readers unfamiliar with image processing algorithms we will refer to introducing textbooks on the subject[5]. Mainly a threshold operator, and convolution algorithms with different stencils will be used, e.g an approximation of the Gauß-Laplacian and the Kirsch-Compass operator.

Especially when using low resolutions and fine grain hatches there is a danger of interference patterns and alias problems. The characteristics of the images will be different when printed on different output media: while these images resemble copper plates on laser printers they look like woodcuts on pin printers.

As conventional copper plates have no grey values a black and white representation can be convenient, if the resolution ist high enough. At low resolution severe aliasing problems occur, especially with hatches. If all channels are anti-aliased (especially kappa) then the postprecessing can be adapted to deliver grey values, using a threshold for each grey value.

To investigate the aliasing problems a series of original copper plates werde scanned in at various resolutions. Using high resolution all lines were reproduced, while the low resolution images had more the look of an ordinary grey scale image, and the characteristic copper plate hatches disappeared. So the hatches information is very sensitive with respect to the alias effect.

Implementation and Results

The implementation of the graphical method discussed here was done on the basis of the ray tracer VERA [1,2]. The structure of the program had not to be changed much, but the input routines had to be completed, as new key words for the material description classes had to be added. The colour calculations needed most of the changes, due to a new illumination equation. In addition a second pixel raster file is given out, that contains normalized  values in the range 0..255.

In the current implementation the formula 5 is fully implemented with the restriction that three lamina shares can be specified. The syntax of the new parameters in the VERA input language is given in Appendix A.

The calculation of the final result is done in a separate image processing program, in order not to change the structure of the ray tracer too much. Threshold and edge detection operators are used channelwise. The resulting bitmaps are merged bitwise by an or-Operator.


Figure 2: A sphere with different hatchings and as (dithered) raster image

To illustrate the potential of the new technique a sphere is treated with different hatches in Figure 2. The sphere is illuminated from the upper right side. A glossy spot can be seen in the reproduction of the RGB pixel image. Upper: hatching without (1a) and with brightness modulation (1b), two hatchings added without (2a) and with brightness modulation (2b). The characteristic triangle pattern can be seen. Lower: two hatchings overlayed without (3a) and with brightness modulation (3b). Using a negative weight factor for the second hatching, inverse lines and special patterns can be produced (4).

Note: The original images of the article are not presented here. We show some other images instead, that are more propriate for a Web-document. Until these are prepared, we refer to a document on nonrealistic rendering.

Copper Plates as Icons

The modern user interface technique offers a further field of use for the presented technique. Icons are used in graphical user interfaces to symbolize objects or methods. Icons are mostly realized as small raster images at low resolution. Typically these images will have a resolution between 50x50 and 150x150 pixels (sometimes even less), depending on the purpose. For icons often a rough sketch is enough to symbolize an object or an action. Icons are often produced manually with bitmap editors, but using the copper plate method a characteristic and unitary style on the user interface can be reached.

The copper plate method has been adapted for making icons. Caused by the low resolution of the icons there is a danger for interferences between the hatchings and the image raster, and there is nearly no possibility for anti rastering methods in this case. The designer should be aware of this while modeling.

Note: The illustration images are currently under preparation


With the method presented images can be produced that resemble to copper plates. The method is based on the ray tracing method and can easily be implemented. The resulting images can be used for illustration purposes, where 3D scenes can be presented concisely in black and white images. Another application is their use as icons in user interfaces. The image examples presented are used with success in the user interface of the MNS system from Metronor.

The next step could be to research how to use this technique for computer animations. This is also interesting in connection with interaction techniques, where short animation sequences can be shown in icons. Especially the problems occurring due to motion blur and interferences should be inquired. It could also be interesting to use this technique in visualization technique.


This work was partially done while the author was employed at Institut für Betriebs- und Dialogsysteme, Universität Karlsruhe, Germany. The author is grateful to his colleagues both at Universität Karlsruhe and at Metronor for their support. The author also wishes to thank Heinrich Müller at Universität Dortmund for his advice. The Figures 5--7 are by courtesy of Achim Stößer (Universität Karlsruhe).


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Note: This article is prepared from the original that appeared in Computer Graphics Forum, Volume 13, Number 1 March 1994, pp. 69-77, Blackwell, ISSN 0167-7055. However, the appendix (extensions to the Vera modeling language) and some of the illustrations are not included with this article.
Dr. Wolfgang Leister

Tue Oct 2 22:46:47 MEST 1997