EP1297520B1 - Method for representing and image on a stepped surface and staircase - Google Patents

Abstract

To represent an image on a stepped surface, an eyepoint on the axis of sight in front of partial surfaces of the stepped surface is selected. The image is divided into partial images that are assigned to the partial surfaces. Each partial image is projected from the eyepoint onto the partial surface to which it has been assigned. Alternatively, the image is divided into partial images that are assigned to the partial surfaces so that the first partial image, which is assigned to the first partial surface closest to the eyepoint, is modified by a specified factor. Each additional partial image is enlarged relative to the first partial image based on the distance from the eyepoint of the partial surface to which it is assigned and is then represented on its respective partial surface.

Description

The invention relates to a method for imaging an image on a stair-like area with at least two partial areas that are transverse to one Visible axis run and offset along the visual axis relative to each other and a staircase with a picture on it.

Such a method and such a staircase are, for example, out Department stores and sports stadiums known. In these known stairs a picture is put up on a set surface in a department store a lettering with the name of the department store or a note such as "Zur Children's department "and in a sports stadium the specification of the row of seats Can be grandstand. Such a procedure is described, for example, in the documents DE-A-4 314 772 and US-A-5 685 412. In this known method, the Partial surfaces of the stair and the line of sight runs in essentially horizontal through the eyes of a person before the upward leading staircase stands.

A disadvantage of these known methods and stairs is that the maximum size of the image by the size and shape of a single Settling area is defined so that the height of the image is at the step height the stairs are limited, which is usually about 18 cm.

It is therefore an object of the invention to provide a method of the type mentioned at the beginning Art as well as creating a staircase of the type mentioned at the beginning, the enable larger images.

• ein Augpunkt gewählt wird, der auf der Sichtachse vor den Teilflächen liegt;
• das Bild dadurch in Teilbilder, die den Teilflächen zugeordnet sind, unterteilt wird, dass es ausgehend vom Augpunkt auf die Teilflächen projiziert wird; und
• jedes Teilbild auf seine ihm zugeordnete Teilfläche abgebildet wird.

This task is solved in the method according to a first variant by the steps that:

• an eye point is chosen which lies on the visual axis in front of the partial areas;
• the image is divided into partial images which are assigned to the partial areas by projecting it onto the partial areas starting from the eye point; and
• each drawing file is mapped to its assigned area.

• ein Augpunkt gewählt wird, der auf der Sichtachse vor den Teilflächen liegt;
• das Bild derart in Teilbilder, die den Teilflächen zugeordnet sind, unterteilt wird, dass das erste Teilbild, das der ersten, dem Augpunkt am nächsten liegenden Teilfläche zugeordnet ist, entsprechend einem vorgegebenen Maßstab verändert wird und dass jedes weitere Teilbild relativ zu dem ersten Teilbild entsprechend dem Abstand seiner ihm zugeordneten Teilfläche von dem Augpunkt vergrößert wird; und
• jedes Teilbild auf seine ihm zugeordnete Teilfläche abgebildet wird.

In the method according to a second variant, this task is solved by the steps that:

• an eye point is chosen which lies on the visual axis in front of the partial areas;
• the image is subdivided into partial images which are assigned to the partial areas in such a way that the first partial image which is assigned to the first partial area closest to the eye point is changed according to a predetermined scale and that each further partial image relative to the first partial image is changed accordingly the distance of its partial area assigned to it from the eye point is increased; and
• each drawing file is mapped to its assigned area.

These two variants are based on the following considerations, the example of a staircase, the seating areas used for the illustration will be explained, although they also apply to other stair-like surfaces be valid.

In contrast to the known method, in which the image is only on a set surface of the stairs is shown and therefore at most the The height of this placement area can be found in these two variants for the illustration the seating areas are available, which together form a total area form, the height of which is the sum of the individual set area heights equivalent. The image can therefore be relative to the known method are shown on a larger scale.

In both variants, the perspective distortion becomes more precise said compensation compensates for the eye of a beholder, if it looks at the seating areas from the eye point, because the setting surfaces are offset relative to each other along the visual axis and are therefore at different distances from the eye point. For example, the area of the lowest, first step is around Step depth, which is usually about 27 cm, closer to the eye point than the setting area of the second stage, which in turn is around the Step depth closer to the eye point than the setting surface of the third step, etc.

The eye point is the starting point for the illustration of the image on the stair-like surface or on the partial surfaces, and he defines thus the position from which a viewer can view the picture with the perceives slightest perspective distortions. He will be accordingly chosen the respective circumstances, and can, if it is the partial areas are the setting areas of a staircase in a department store, for example at eye level with an average customer, i.e. in about 1.70 m in height, and at a horizontal distance from that on this height of about 3 m.

In the first variant, the image is divided into the partial areas with the help of a central projection. The second variant is done the subdivision of the image into the partial areas with the help of magnification scales, which result from the geometric relationships of the individual case, in particular the different distances of the partial areas from to the eye point.

In the second variant it can be provided that the magnification scale a field relative to the first field equal to that Quotient from the distance of its assigned partial area from the Eye point and the distance of the first partial area from the eye point.

In both variants it can be provided that the surface is covered by the Surface of a stair is formed.

In this case it can be provided that the staircase is an escalator, or that the stairs in a grandstand of a sports stadium or event hall lies.

In this case, it can also be provided that the partial surfaces are formed by the setting surfaces of the steps, or that the partial surfaces are formed by the treads of the steps.

Furthermore, it can be provided that the eye point through the position a camera is defined.

The partial images are preferably generated by dividing the Image using a computing device.

• das Bild in Teilbilder unterteilt ist, die den Setzflächen zugeordnet und auf den ihnen zugeordneten Setzflächen abgebildet sind; und
• jedes Teilbild relativ zu dem untersten Teilbild entsprechend dem horizontalen Abstand seiner ihm zugeordneten Setzfläche von der untersten Setzfläche vergrößert ist.

According to a first variant, the task mentioned above is achieved in the case of the stairs in that:

• the image is subdivided into partial images which are assigned to the setting areas and are depicted on the setting areas assigned to them; and
• each partial image is enlarged relative to the lowermost partial image in accordance with the horizontal distance of its associated setting area from the lowest setting area.

• das Bild in Teilbilder unterteilt ist, die den Trittflächen zugeordnet und auf den ihnen zugeordneten Trittflächen abgebildet sind; und
• jedes Teilbild relativ zu dem obersten Teilbild entsprechend dem vertikalen Abstand seiner ihm zugeordneten Trittfläche von der obersten Trittfläche vergrößert ist.

This task is solved with the stairs according to a second variant in that:

• the image is subdivided into partial images which are assigned to the treads and are depicted on the treads assigned to them; and
• each partial image is enlarged relative to the uppermost partial image in accordance with the vertical distance of its tread surface assigned to it from the uppermost tread surface.

These two variants are based on the same considerations that already explained in connection with the two process variants have been.

The first variant concerns the use of the seating area of a staircase. This can be in the field of view of a viewer who, for example, is watching the stairs descends, or lie on a television camera, for example on the Ceiling of an event hall is attached.

The second variant concerns the use of the steps of a staircase. This can be in the field of view of a viewer who, for example, is watching Going up stairs, or lying on a television camera, for example mounted on a grandstand of a sports stadium and on the opposite lying grandstand is directed.

In the first variant it can be provided that the magnification scale of a sub-picture equal to the quotient from the sum of the horizontal Distance of its assigned seating area from the lowest Seated area and the horizontal distance of the lowest seated area from a given eye point in front of the stairs and the is the horizontal distance of the lowest setting surface from the eye point.

In the second variant it can be provided that the magnification scale of a sub-picture equal to the quotient from the sum of the vertical distance of its associated tread from the top Tread and the vertical distance of the top tread of a given eye point above the stairs and the vertical Distance of the top step from the eye point.

In both variants it can be provided that the stairs are an escalator is, or that the stairs in a grandstand of a sports stadium or an event hall.

It can also be provided that the eye point through the position a camera is defined.

The invention primarily enables the use of stairs for imaging large-format advertising motifs.

In both method variants, it can also be provided that the step-like surface has at least one rear partial surface, the from the point of view of the eye so offset behind a front partial surface is that a portion of the back face is through the front face is covered, and that this covered area of the rear face not for the depiction of the drawing file assigned to the rear partial area is used. Hence, only the one seen from the eye point becomes Area of the rear seating area used for illustration.

• die Fläche durch die Oberfläche einer Treppe gebildet wird;
• die Sichtachse horizontal verläuft;
• die Teilflächen durch Setzflächen der Stufen gebildet werden, von denen wenigstens eine Setzfläche aus Sicht des Augpunktes hinter derjenigen Setzfläche, auf die die Sichtachse trifft, liegt und somit an ihrem unteren Rand einen streifenförmigen Bereich aufweist, der von der nächst vorderen Setzfläche verdeckt wird; und
• die Höhe F_i des verdeckten Bereiches, gemessen von der Unterkante der hinteren Setzfläche, durch die folgende Formel bestimmt wird: Fi = t × Gi-1 / Wi-1

   worin:

i der Index für die Stufen ist und i=1 für die erste, unterste Stufe steht,

t die Tiefe der Trittflächen der Treppe ist,

G_i-1 der vertikale Abstand zwischen der Oberkante der nächst vorderen Setzfläche und der Sichtachse ist, und

W_i-1 der horizontale Abstand zwischen der Oberkante der nächst vorderen Setzfläche und dem Augpunkt ist.

In this case it can be provided that:

• the surface is formed by the surface of a staircase;
• the line of sight is horizontal;
• the partial surfaces are formed by setting surfaces of the steps, of which at least one setting surface from the point of view of the eye lies behind that setting surface which the visual axis meets and thus has at its lower edge a strip-shaped area which is covered by the next front setting surface; and
• The height F _{i of} the hidden area, measured from the lower edge of the rear seating area, is determined by the following formula: F i = t × G i-1 / W i-1

wherein:

i is the index for the levels and i = 1 stands for the first, lowest level,

t is the depth of the steps of the stairs,

G _{i-1 is} the vertical distance between the upper edge of the next front seating surface and the visual axis, and

W _{i-1 is} the horizontal distance between the upper edge of the next front seating surface and the eye point.

• der vertikale Abstand G_i-1 durch die folgende Formel bestimmt wird: Gi-1 = (i-1)×h - H    worin:
• h die Höhe der Setzflächen der Treppe ist, und
• H der vertikale Abstand zwischen der Sichtachse und dem unteren Treppenabsatz ist; und
• der horizontale Abstand W_i-1 durch die folgende Formel bestimmt wird: Wi-1 = (i-2)×t + XA    worin:
• X_A der horizontale Abstand zwischen der Oberkante der Setzfläche der ersten Stufe und dem Augpunkt ist.

In this case it can further be provided that:

• the vertical distance G _{i-1 is} determined by the following formula: G i-1 = (i-1) × h - H wherein:
• h is the height of the seating surface of the stairs, and
• H is the vertical distance between the line of sight and the lower landing; and
• the horizontal distance W _{i-1 is} determined by the following formula: W i-1 = (i-2) × t + X A wherein:
• X _{A is} the horizontal distance between the top of the first stage seating area and the eye point.

In both stair variants, it can also be provided that the Stairs has at least one rear partial surface, which from the perspective of Eye point so offset behind a front partial surface that a Area of the rear partial area is covered by the front partial area, and that this hidden area of the rear face is not for the Image of the drawing file assigned to the rear partial area is used becomes.

• die Sichtachse horizontal verläuft;
• von den Setzflächen wenigstens eine Setzfläche aus Sicht des Augpunktes hinter derjenigen Setzfläche, auf die die Sichtachse trifft, liegt und somit an ihrem unteren Rand einen streifenförmigen Bereich aufweist, der von der nächst vorderen Setzfläche verdeckt wird; und
• die Höhe F_i des verdeckten Bereiches, gemessen von der Unterkante der hinteren Setzfläche, durch die folgende Formel bestimmt wird: Fi = t × Gi-1 / Wi-1    worin:
• i der Index für die Stufen ist und i=1 für die erste, unterste Stufe steht,
• t die Tiefe der Trittflächen der Treppe ist,
• G_i-1 der vertikale Abstand zwischen der Oberkante der nächst vorderen Setzfläche und der Sichtachse ist, und
• W_i-1 der horizontale Abstand zwischen der Oberkante der nächst vorderen Setzfläche und dem Augpunkt ist.

In this case, it can be provided for the first variant of the stairs that:

• the line of sight is horizontal;
• At least one seating area of the seating areas from the point of view of the eye lies behind that seating area which the visual axis meets and thus has at its lower edge a strip-shaped area which is covered by the next front seating area; and
• The height F _{i of} the hidden area, measured from the lower edge of the rear seating area, is determined by the following formula: F i = t × G i-1 / W i-1 wherein:
• i is the index for the levels and i = 1 stands for the first, lowest level,
• t is the depth of the steps of the stairs,
• G _{i-1 is} the vertical distance between the upper edge of the next front seating surface and the visual axis, and
• W _{i-1 is} the horizontal distance between the upper edge of the next front seating surface and the eye point.

• der vertikale Abstand G_i-1 durch die folgende Formel bestimmt wird: Gi-1 = (i-1)×h - H    worin:
• h die Höhe der Setzflächen der Treppe ist, und
• H der vertikale Abstand zwischen der Sichtachse und dem unteren Treppenabsatz ist; und
• der horizontale Abstand W_i-1 durch die folgende Formel bestimmt wird: Wi-1 = (i-2)×t + XA    worin:
• X_A der horizontale Abstand zwischen der Oberkante der Setzfläche der ersten Stufe und dem Augpunkt ist.

In this case it can further be provided that:

• the vertical distance G _{i-1 is} determined by the following formula: G i-1 = (i-1) × h - H wherein:
• h is the height of the seating surface of the stairs, and
• H is the vertical distance between the line of sight and the lower landing; and
• the horizontal distance W _{i-1 is} determined by the following formula: W i-1 = (i-2) × t + X A wherein:
• X _{A is} the horizontal distance between the top of the first stage seating area and the eye point.

Further features and designs of the invention are in the subclaims described.

FIG. 1

zeigt ein Bild im Originalzustand, das auf die Stufen einer Treppe abgebildet werden soll;

FIG. 2

ist eine Seitenansicht einer Treppe, auf deren Stufen das Bild der FIG. 1 abgebildet ist;

FIG. 3

zeigt die Teilbilder, die in einer Ebene übereinander angeordnet sind;

FIG. 4

ist eine zentralperspektivische Vorderansicht der Treppe der FIG. 2, wie sie für ein Auge im Augpunkt erschient; und

FIG. 5

ist eine Seitenansicht einer Treppe, auf deren Stufen ein Bild gemäß einem anderen Verfahren abgebildet ist.

Preferred exemplary embodiments are described in more detail below with reference to the accompanying drawings.

FIG. 1

shows an image in the original state, which is to be displayed on the steps of a staircase;

FIG. 2

is a side view of a staircase, on the steps of which the image of FIG. 1 is shown;

FIG. 3

shows the partial images, which are arranged in a plane one above the other;

FIG. 4

is a central perspective front view of the stairs of FIG. 2, as it appears to an eye in the eye point; and

FIG. 5

is a side view of a staircase, on the steps of which an image is shown according to another method.

In FIG. 1 is a picture 10, which here is simply a square with its two Diagonals is shown in its original state, on the seating areas 11 of three adjacent stages 12, 13, 14 of a conventional one Stairs to be mapped.

In FIG. 2 shows this staircase, from which it is assumed below that the step height h = 18 cm and the step depth t = 27 cm. The three stages 12-14 comprise the ninth, tenth and eleventh stages of the staircase, each counted from the lower landing 15, so that the center of the seating area 11.10 of the tenth stage 13, that of the center of the three corresponding seating surfaces 11.9. 11.10, 11.11 corresponds to the total area formed, at a height of H = 1.71 m (= 10 × 0.18 m - 0.5x0.18 m) above the lower landing 15. The horizontal distance of this tenth seating area 11.10 from the lower landing 15, that is to say from the seating area 11.1 of the first, lowest step 16, is accordingly X ₁₀ = 2.43 m (= 9 × 0.27 m).

The choice of three levels 12-14 was made here with regard to the above-mentioned height H, since at this height H there are often the eyes 17 of many people 18 who are standing on the lower landing 15 and are just about to climb the stairs. For the eye point AP, which is required for the subdivision of the image 10 (indicated by a thick dotted line in FIG. 2) into the three partial images 10.1, 10.2, 10.3 (indicated by thin dotted lines in FIG. 2) in the following, this height H is chosen as the z coordinate. For the choice of the x coordinate of the eye point AP, the one shown in FIG. 2 shown viewer 18, who stands on the lower landing 15 shortly before the first step 16, so that the horizontal distance X _{A of} his eyes 17 from the first seating surface 11.1 is approximately 15 cm. The sum of this horizontal distance X _A and the previously calculated horizontal distance X _{10 of} the tenth setting surface 11.10 from the first setting surface 11.1 is 2.58 m (= 0.15 m + 2.43 m), and this is the sum that follows chosen as the x coordinate for the eye point AP.

At this point it is pointed out that the one previously made Selection of the eye point AP is only to be seen as an example and after Needs can be changed.

According to a first embodiment of a method for imaging the image 10 on the three setting surfaces 11.9-11.11, the image 10, as shown in FIG. 2 can be seen, arranged at right angles to the visual axis A, which here corresponds to the horizontal connecting line between the eye point AP and the center M of the tenth setting surface 11.10, in such a way that the visual rays S originating from the eye point AP are _{at the bottom} and point to the lower edge of the ninth Meet the setting surface 11.9, cut the lower edge of the image 10 and that the visual rays S _above , which meet the upper edge of the eleventh setting surface 11.11, cut the upper edge of the image 10. This arrangement makes the best use of the total area made available for the illustration by the three setting areas 11.9-11.11, as will become clear from the further explanations.

Now the individual pixels on the stair-like total area are projected from the eye point AP, whereby the image 10 in three drawing files 10.1, 10.2, 10.3 is divided: the first drawing file 10.1 is created through those visual rays that both image 10 and the Cut the ninth setting surface 11.9, the second drawing 10.2 is created by those visual rays that represent both the image 10 and the tenth placement surface 11.10 cut, and the third drawing 10.3 is created by those Visual rays that represent both image 10 and the eleventh seating area 11.11 cut.

In FIG. 3 (which is not true to scale to FIG. 2), these three partial images 10.1-10.3 are arranged one above the other for better comparison, so that they match well with the one shown in FIG. 1 shown image 10 can be compared in the original state. As can be clearly seen, all three drawing files 10.1-10.3 have the same height, which is determined by the height h of the three setting surfaces 11.9-11.11, but have different widths. This is due to the different horizontal distances of the three setting surfaces from the eye point AP (hereinafter also referred to as "eye point distances"), so that in the projection described above the beam set applies, after which the magnification scale with which the image 10 is projected onto a setting surface 11 , is equal to the quotient of the eye point distance of this setting surface 11 and the eye point distance X _{0 of} the image 10. It follows from this that the relative scale of a partial image to the first, that is to say the partial image 10.1 projected onto the ninth setting surface, is equal to the quotient of the eye point distance of this partial image and the eye point distance of the first partial image 10.1. With the previously assumed values, the scale of the second partial image 10.2 is a factor of 1.12 (= 2.58 / 2.31 = [0.15 m + 9 × 0.27 m] / [0.15 m + 8x0 , 27 m]) larger than that of the first partial image 10.1 and the scale of the third partial image 10.3 by a factor of 1.23 (= 2.85 / 2.31 = [0.15 m + 10 × 0.27 m] / [ 0.15 m + 8 × 0.27 m]) larger than that of the first sub-picture 10.1.

This increases with the distance between the eye points the perspective reduction compensated for the eye 17th of the viewer 18 when looking at the stairs with the partial images 10.1-10.3 results. This is good in FIG. 4 can be seen in the three stages 12-14 starting from the stairs in a central perspective front view are shown from the eye point AP. Although the three seating areas 11.9-11.11 seem to be getting narrower upwards Image 10 for viewer 18 to be undistorted.

According to a second embodiment of a method for imaging of the picture 10 on the three setting surfaces 11.9-11.11 are those previously explained Formulas used to draw up the individual drawing files 10.1-10.3 to generate mathematically.

In contrast to that shown in FIG. 2 to 4 represented stairs Image 10 not on the seating 11, but on the tread 19 Stages, then an eye point can be selected, which lies above these treads 19 and, for example, the position of the Lens corresponds to a television camera.

In FIG. 5 a staircase is shown in which the image 10 on the seating surfaces 11.2, 11.3, 11.4 and 11.5 of the second to fifth stage from the first, lowest level 16. This for the picture The procedure used builds on the procedures above in connection with the stairs of FIG. 2 have been described.

The starting point for this supplementary procedure is the knowledge that it in the case of stair-like surfaces to at least partially cover one Partial area by a partial area closer to the eye point AP can come. This masking effect, also called a shading effect can be referred to, for example, is easy for the stairs FIG. 5: The total staircase area used for the illustration there consists of the second to fifth seating areas 11.2-11.5, of which the second seating surface 11.2 is completely below the visual axis A lies, the third setting surface 11.3 lies on the line of sight A and is cut by it and the fourth and fifth seating areas 11.4 and 11.5 are complete lie above the visual axis A. Consequently, the total area at least a rear partial surface - namely the two setting surfaces 11.4 and 11.5 - which, from the perspective of the eye point AP, are offset behind a front partial surface - namely the setting surfaces 11.3 or 11.4 - is that an area 20 of the rear partial surface 11.4 / 11.5 is covered by the respective front partial surface 11.3 / 11.4.

Since the hidden areas 20 cannot be seen from the eye point AP are, according to the supplemented procedure, that it is not for the mapping of the respective rear partial area 11.4, 11.5 Sub-images 10.3, 10.4 are used.

In FIG. 5 is also clearly visible that the hidden areas 20 of the rear setting surfaces 11.4 and 11.5 at their upper edge, respectively are limited by visual rays that cover the top of each Cut the next front seating surface 11.3 and 11.4. The stairs have here Steps with straight front edges, which are also the top edges of the setting surfaces 11, so that the hidden areas 20 are horizontal, right-angled stripes on the lower edge of the rear setting surfaces 11.4, 11.5 are.

In the following, the formula for calculating the height F _{i of} the hidden area 20 of the i-th setting surface 11. I, measured from its lower edge, is derived.

t die Tiefe der Trittflächen 19 der Treppe ist,

G₃ der vertikale Abstand zwischen der Oberkante der dritten Setzfläche 11.3 und der Sichtachse A ist, und

W₃ der horizontale Abstand zwischen der Oberkante der dritten Setzfläche 11.3 und dem Augpunkt AP ist.

For the height F _{4 of} the concealed area 20 of the fourth setting surface 11.4, as is easily shown in FIG. 5, the following ray set can be seen for the visual axis A and the line of sight, which intersects the upper edge of the next front, i.e. third, setting surface 11.3: F 4 / t = G 3 / W 3 wherein:

t is the depth of the steps 19 of the stairs,

G _{3 is} the vertical distance between the upper edge of the third setting surface 11.3 and the visual axis A, and

W _{3 is} the horizontal distance between the upper edge of the third setting surface 11.3 and the eye point AP.

G₄ der vertikale Abstand zwischen der Oberkante der vierten Setzfläche 11.4 und der Sichtachse A ist, und

W₄ der horizontale Abstand zwischen der Oberkante der vierten Setzfläche 11.4 und dem Augpunkt AP ist.

Correspondingly, for the height F _{5 of} the concealed area 20 of the fifth setting surface 11.5, the following set of rays applies for the visual axis A and the line of sight, which intersects the upper edge of the next front, ie fourth, setting surface 11.4: F 5 / t = G 4 / W 4 wherein:

G _{4 is} the vertical distance between the upper edge of the fourth setting surface 11.4 and the visual axis A, and

W _{4 is} the horizontal distance between the upper edge of the fourth setting surface 11.4 and the eye point AP.

i der Index für die Stufen ist und i=1 für die erste, unterste Stufe 16 steht,

G_i-1 der vertikale Abstand zwischen der Oberkante der nächst vorderen Setzfläche 11.(i-1) und der Sichtachse A ist, und

W_i-1 der horizontale Abstand zwischen der Oberkante der nächst vorderen Setzfläche 11.(i-1) und dem Augpunkt AP ist.

From these two equations, the following general formula for the height F _{i of} the hidden area 20 of the i-th setting surface 11.i can be derived: F i = t × G i-1 / W i-1 wherein:

i is the index for the levels and i = 1 for the first, lowest level 16,

G _{i-1 is} the vertical distance between the upper edge of the next front seat 11 (i-1) and the line of sight A, and

W _{i-1 is} the horizontal distance between the upper edge of the next front seat 11 (i-1) and the eye point AP.

• für den vertikalen Abstand G₃ der dritten Setzfläche 11.3 gilt: G3 + H = 3×h    worin:
• h die Höhe der Setzflächen 11 der Treppe ist, und
• H der vertikale Abstand zwischen der Sichtachse A und dem unteren Treppenabsatz 15 ist; und
• für den horizontalen Abstand W₃ der dritten Setzfläche 11.3 gilt: W3 = 2×t + XA    worin:
• X_A der horizontale Abstand zwischen der Oberkante der Setzfläche der ersten Stufe 16 und dem Augpunkt A ist.

In FIG. 5 is also easy to see that:

• for the vertical distance G _{3 of} the third setting surface 11.3: G 3 + H = 3 × h wherein:
• h is the height of the set surfaces 11 of the stairs, and
• H is the vertical distance between the line of sight A and the lower landing 15; and
• the following applies to the horizontal distance W _{3 of} the third setting surface 11.3: W 3 = 2 × t + X A wherein:
• X _{A is} the horizontal distance between the upper edge of the setting surface of the first step 16 and the eye point A.

• für den vertikalen Abstand G₄ der vierten Setzfläche 11.4: G4 + H = 4×h ; und
• für den horizontalen Abstand W₄ der vierten Setzfläche 11.4: W4 = 3×t + XA

The following applies accordingly:

• for the vertical distance G _{4 of} the fourth seating surface 11.4: G 4 + H = 4 x h; and
• for the horizontal distance W _{4 of} the fourth setting surface 11.4: W 4 = 3 × t + X A

The following general formulas for the vertical distance G _i-1 and the horizontal distance W _{i-1 of} the (i-1) th setting surface 11. (I-1) can accordingly be derived from these four equations: G i-1 = (i-1) × h - H W i-1 = (i-2) × t + X A

With the formulas explained above, the size of the hidden ones can Areas 20 are calculated, which is preferably done with the aid of a computing device can happen. From the hidden areas 20 can also in a simple manner the size of the for the illustration of the drawing files 10.3, 10.4 required areas on the rear seating surfaces 11.4, 11.5 be what is preferably done with the help of a computing device can.

LIST OF REFERENCE NUMBERS

10

Image, drawing files

11

setting surfaces

12

ninth level

13

tenth stage

14

eleventh stage

15

lower landing

16

first stage

17

eye

18

observer

19

treads

20

covered area

H

step height

t

Tread depth

AP

eye point

A

visual axis

X ₀

Eye distance of the image

Claims (22)

1. A method for the representation of an image (10) on a stepped surface with at least two partial surfaces (11.9,11.10,11.11;19) which run at right angles to an axis of sight (A) and are offset relative to each other along the axis of sight (A); said method is characterized by the steps that:

   Selecting an eye point (AP) which lies on the axis of sight (A) in front of the partial surfaces (11);

   Dividing the image (10) into partial images (10.1, 10.3, 10.3) which are assigned to the partial surfaces (11.9-11.11) by being projected from the eye point (AP) onto the partial surfaces; and

   Representing each partial image (10.1-10.3) on the partial surface (11.9-11.11) to which it is assigned.
2. A method for the representation of an image (10) on a stepped surface with at least two partial surfaces (11.9,11.10,11.11;19) which run at a right angle to an axis of sight (A) and are offset relative to each other along the axis of sight (A); said method is characterized by the steps that::

   Selecting an eye point (AP) which lies on the axis of sight (A) in front of the partial surfaces (11.9-11.11);

   Dividing the image (10) into partial images (10.1, 10.2, 10.3) which are assigned to the partial surfaces (11.9-11.11) so that the first partial image is assigned to the first partial surface (11.9) lying closest to the eye point (AP); modifying the first partial image (10.1) according to a specified factor; enlarging each additional partial image (10.2, 10.3) relative to the first partial image (10.1) corresponding to the distance of its assigned partial surface (11.10; 11.11) from the eye point (A) and

   Representing each partial image (10.1, 10.2, 10.3) on the partial surface to which it is assigned.
3. Method according to claim 2, wherein the enlargement factor of a partial image (10.2,10.3) relative to the first partial image (10.1) is equal to the quotient of the distance of its corresponding partial surface (11.10,11.11) from the eye point (AP) and the distance of the first partial surface (11.9) from the eye point (AP).
4. Method according to one of the aforementioned claims characterized in, that the surface is formed by the surface of a staircase.
5. Method according to one of the aforementioned claims characterized in, that the staircase is an escalator.
6. Method according to claim 4, characterized in, that the staircase lies in a grandstand of a sports stadium or an exhibition or performance venue.
7. Method according to one of the claims 4 to 6 characterized in, that the partial surfaces are formed by the riser surfaces (11.9-11.11) of the steps (12,13,14).
8. Method according to one of the claims 4 to 6 characterized in, that the partial surfaces are formed by the tread surfaces (19) of the steps (12,13,14).
9. Method according to one of the aforementioned claims characterized in, that the eye point (AP) is defined by the position of a camera.
10. Method according to one of the aforementioned claims characterized in, that the stepped surface has at least one rear partial surface (11.4,11.5) which, from the point of view of the eye point (AP) is offset behind a forward partial surface (11.3,11.4), so that an area (20) of the rear partial surface (11.4,11.5) is concealed by the forward partial surface (11.3,11.4) and that this concealed area of the rear partial surface (11.4,11.5) is not used for the representation of the partial image (10.3,10.4) assigned to the rear partial surface (11.4,11.5).
11. Method according to claim 10 characterized in, that:

    The surface is formed by the surface of a staircase;

    The axis of sight (A) runs horizontally;

    the partial surfaces are formed by riser surfaces (11) of the steps (12,13,14), at least one riser surface (11.4,11.5) of which, from the point of view of the eye point (AP), lies behind the riser surface (11.3,11.4) on which the axis of sight (A) alights, and thus has on its lower edge a strip-shaped area (20), which is concealed by the next-forward riser surface (11.3,11.4); and

    The height (F_i) of the concealed area (20) measured from the lower edge of the rear riser surface (11.4,11.5) is determined by the following formula: Fi = t x Gi-1 / Wi-1    Where:

    i is the index for the step and i=I is the Index for the first, lowest step,

    t is the depth of the tread surface (19) of the staircase,

    G_i-1 is the vertical distance between the upper edge of the next-forward riser surface (11.3,11.4) and the axis of sight (A), and

    W_i-1 is the horizontal distance between the upper edge of the next-forward riser surface (11.3,11.4) and the eye point (AP).
12. Method according to claim 10 characterized in, that

    the vertical distance (G_i-1) is determined by the following formula: Gi-1 =(i-1) x h - H    Where:

    h is the height of the riser surfaces (11) of the staircase, and

    H is the vertical distance between the axis of sight (A) and the lower landing; and

    the horizontal distance (W_i-1) is determined by the following formula: Wi-1 =(i-2) x t + XA    Where:

    X_A is the horizontal distance between the upper edge of the riser surface of the first step and the eye point (AP).
13. Staircase with at least two riser surfaces (11.9,11.10,11.11) on which an image (10) is represented characterized in, that:

    The image (10) is divided into partial images (10.1,10.2,10.3) which are assigned to the riser surfaces (11.9-11.11) and which are represented on the riser surfaces (11.9-11.11) to which they are assigned; and

    Each partial image (10.2,10.3) is enlarged relative to the lowest partial image (10.1) corresponding to the horizontal distance of the riser surface(11.10,11.11) to which it is assigned from the lowest riser surface (11.9).
14. Staircase according to claim 13 characterized in, that the enlargement factor of a partial image (10.1,10.2,10.3) is equal to the quotient of the sum of the horizontal distance of the riser surface (11.9-11.11) to which it is assigned from the lowest riser surface (11.9) and the horizontal distance of the lowest riser surface (11.9) from a specified eye point (AP) lying in front of the staircase and the horizontal distance of the lowest riser surface (11.9) from the eye point (AP).
15. Staircase with at least two tread surfaces (19) on which an image (10) is represented characterized in, that:

    The image (10) is divided into partial images which are assigned to the tread surfaces (19) and which are represented on the tread surfaces (19) to which they are assigned; and

    Each partial image is enlarged relative to the topmost partial image corresponding to the vertical distance of the tread surface (19) to which it is assigned from the topmost tread surface (19).
16. Staircase according to claim 15 characterized in, that the enlargement factor of a partial image is equal to the quotient of the sum of the vertical distance of the tread surface (19) to which it is assigned from the topmost tread surface (19) and the vertical distance of the topmost tread surface (19) from a predefined eye point (AP) lying above the staircase and the vertical distance of the topmost tread surface (19) from the eye point (AP).
17. Staircase according to one of the claims 13 to 16 characterized in, that the staircase is an escalator.
18. Staircase according to one of the claims 13 to 16 characterized in, that the staircase lies in a grandstand of a sports stadium or a performance or exhibition venue.
19. Staircase according to one of the claims 13 to 18 characterized in, that the eye point (AP) is defined by the position of a camera.
20. Staircase according to one of the claims 13 to 19 characterized in, that it comprises at least one rear partial surface (11.4,11,5), which, from the point of view of the eye point (AP) is offset behind a forward partial surface (11.3,11.4) so that an area (20) of the rear partial surface (11.4,11.5) is concealed by the forward partial surface (11.3,11.4) and that this concealed area (20) of the rear partial surface (11.4,11.5) is not used for the representation of the partial image (10.3,10.4) assigned to the rear partial surface (11.4,11.5).
21. Staircase according claim 20 and according to claim 13 or 14 characterized in, that:

    The axis of sight (A) runs horizontally;

    Of the riser surfaces (11) at least one riser surface (11.4,11.5) from the point of view of the eye point (AP) lies behind this riser surface (11.2) on which the axis of sight (A) alights and thus on its lower edge has a strip-shaped area (20) which is concealed by the next forward riser surface (11.3,11.4); and

    The height (F_i) of the concealed area (20) measured from the lower edge of the rear riser surface (11.4,11.5) is determined by the following formula: Fi = t x Gi-1/W i-1    Where:

    i is the index for the step and i=1 is the index for the first, lowest step,

    t is the depth of the tread surface (19) of the staircase,

    G_i-1 is the vertical distance between the upper edge of the next-forward riser surface (11.3,11.4) and the axis of sight (A), and

    W_i-1 is the horizontal distance between the upper edge of the next-forward riser surface (11.3,11.4) and eye point (AP).
22. Staircase according to claim 21 characterized in, that:

    The vertical distance (G_i-1)) is determined by the following formula: Gi-1 = (i-1) x h - H    Where:

    h is the height of the riser surfaces (11) of the staircase, and

    H is the vertical distance between the axis of sight (A) and the lower landing; and

    the horizontal distance (W_i-1) is determined by the following formula: Wi-1 = (i-2) x t + XA    Where:

    X_A is the horizontal distance between the upper edge of the riser surface of the first step and the eye point (AP).

Images