Determining geometric boundary of mass, energy or force flow through channel having channel wall

Abstract

The invention relates to a computer-implemented method for determining a geometric boundary of a mass, energy or force flow through a channel (32) having a channel wall (33), in which-coordinates of first edge points of a first edge line (38) of a cross-sectional area of the channel (32) are received or present, the edge points being located on the channel wall (33),-coordinates of a second edge line (38) of the cross-sectional area of the channel (32) are determined using the first edge points, a first cross-sectional region is received or created as a subdivided surface region in which polygonal planar blocks of the subdivided surface region are arranged in a gap-free and non-overlapping manner, the first edge points being corner points of the blocks of the subdivided surface region, and the second edge points being corner points of the blocks of the subdivided surface region. The first edge points and all the further inner corner points of the blocks define the first cross-sectional area, determining the further cross-sectional area as a curved subdivision area of the aforementioned type by means of an iteration method, the positions of the edge points and the inner corner points varying during the iteration process, and-terminating the iteration when a specified termination criterion is satisfied, and outputting information about a minimum cross-sectional region for which the total area of all the blocks of the respective subdivided surface region is minimized with respect to the subdivided surface region resulting from the iteration.

Description

[0001] The invention relates to a computer-implemented method for determining geometric boundaries of a mass flow, energy flow or force flow through a channel having a channel wall. The invention also relates to a corresponding device for data processing.

[0002] In particular, the present invention relates to mass flows, such as gas and / or liquid flows and such as material-defined flows (e.g., electric currents), but also to force flows that occur, for example, when torque is transmitted by a shaft. In any case, there is specifically a channel outer wall, outside which there is no mass flow, energy flow or force flow. Typically, in the case of gas and / or liquid flows, there is no flow in the channel wall. The channel wall, which is usually composed of solid matter, defines the space of the channel available for flow. In contrast, in the case of the flow of charge carriers (which can be regarded as energy flow and also mass flow) in conductive materials and also in the case of force flow, the current or flux occurs in the entire material. In this case, the channel is not a space defined by a sleeve without solid matter, but a space filled with solid matter in general. In addition or in an alternative, this does not exclude the situation where the gaseous matter is the carrier of the flow, especially in the case of electric current. In order to transmit force or transmit torque, the channel is usually formed solidly by solid material, with the result that the channel wall is limited only by the surface or surface layer of the material. This does not exclude the actual situation that the channel for force transmission or torque transmission has a cavity. In all cases, the channel wall may be considered to be the outer sleeve of the channel, or in some cases the inner sleeve of the channel.

[0003] Force Flow and Mass Flow Commonly, a vector field can be specified at any time, which describes the intensity and direction of the flow or flux relative to a local area of ​​the channel. For example, in the case of mass flow, this is the vector field of the velocity of the flowing mass. Other vector fields describing the flow of a scalar physical parameter through the channel or fluxes corresponding to vector physical parameters and corresponding to the boundaries of the channel shape area (for example, in the case of the shaft for transmitting torque mentioned above) are also conceivable. The invention is also applicable to such other fluxes or flows.

[0004] For example, as specified on the Internet at the URL https: / / systemdesign.ch / wiki / Kraftfluss (retrieved on April 4, 2022), a force flow can be defined as "the path of the force and / or moment in its component from the point of attack (location of introduction) to the location where the force and / or moment is absorbed by the reaction force and / or reaction moment". Further, the following description of the term "force flow" from another source is quoted: When developing a correctly proportioned design, the designer is often faced with the problem of having to ensure optimal conduction of forces, torques and / or bending moments by the envisaged functional carrier. In order to describe the function of guiding forces and moments, it is popular to use the term "force flow". Corresponding definitions can also be provided for other fluxes of vector physical parameters.

[0005] Therefore, there is no mass flow or energy flow in force flow. However, the physical parameters are conducted through channels on a path or channels on multiple parallel paths corresponding to the underlying vector field. In this respect, the physical description is similar to the physical description of water flowing through a channel.

[0006] It follows from the above references to force flow that for applications in the corresponding technical field, the technician in the relevant field must know the geometry of the channel or, when constructing the channel, must have information about the influence of force flow due to the geometry. The corresponding statements apply to mass flow or energy flow. For example, when constructing a turbine (such as a gas turbine), for example, an attempt is made to quickly make fluid mechanical effects and parameters measurable by correlation with geometric parameters. The simulation of these flows is computationally intensive and therefore long-lasting. In this case, the position, shape and size of the minimum cross-sectional area of ​​the channel or channel section are used as geometric parameters. In the case of electric current and in the case of force flow, it is obvious that not only the geometry of the channel but also the transmission characteristics of the conductive material or the force transmission material need to be considered. In the case of gas and / or liquid flow, other influencing factors are also important for the description of the flow or for the construction of the channel, specifically the interaction of the mass flow with the channel wall.

[0007] As already mentioned, the substantial influencing parameter for describing the above-mentioned flux and flow is the minimum cross-sectional area that the flux or flow passes through in the channel or at the end of the channel. The minimum cross-sectional area of ​​the channel significantly contributes to the resistance to the flux or flow or the restriction of the limit of the flux or flow. In other words, in view of the minimum cross-sectional area, it is impossible to expect that the achievable flux or flow through the channel exceeds the maximum value corresponding to the minimum cross-sectional area in many cases. Therefore, the minimum cross-sectional area represents the geometric boundary of the mass flow, energy flow or force flow through the channel. Further, especially in the case of gas and / or liquid flow, the minimum cross-sectional area can be the necessary information about the type of flow (such as laminar flow or at least locally turbulent flow). The minimum cross-sectional area can also be referred to as the "narrowest cross section" (or "throat area").

[0008] If the channel extends in a straight line and has a constant cross section over its profile, the specification of the minimum cross-sectional area is trivial and can be calculated from any profile along the channel. A channel is usually defined only by the channel outer wall. However, it is not excluded that the channel also has a channel inner wall; for example, this actually occurs in the case of a pipe extending in the channel. In addition to a straight channel with a constant cross section, the calculation of the minimum cross-sectional area can also be easy in several other cases. However, the calculation of the minimum cross-sectional area may already be non-trivial for example for a pipe elbow having a special shape at its end in order to form a tight connection with another pipe piece.

[0009] Examples of channels to which the method according to the invention can be applied, in particular with the aid of the device according to the invention, are the channel between two blades of a blade ring in a turbine (e.g. a gas turbine, an aircraft engine or an axial pump), coolant channels or fuel channels in the cylinder block of an internal combustion engine of a drive motor, electrical wires made of a material such as copper, and blood vessels for transporting blood in the body of a human or animal.

[0010] The calculation of the minimum cross-sectional area of ​​the gap between two blades of a turbine is very complex. This applies in particular to the case where the invention calculates the actual minimum cross-sectional area resulting from the measurement of the gap between two respective blades for the mass flow. More generally, the calculation of the minimum cross-sectional area is complex and laborious in the case of irregular geometry of the passages. Irregular geometries are to be understood as meaning in particular geometries that cannot be described by or do not contain simple geometric elements, such as lines, cubes, squares, spheres, circles, cylinders and cones.

[0011] Not only in the case of blades of a blade ring, measured coordinates of one or more channel walls are preferably also input parameters for calculating the minimum cross-sectional area according to the invention. However, as an alternative or in addition, target coordinates can be used, which are derived, for example, from CAD construction data of the channel. In an extension of the computer-implemented method according to the invention, in particular the use of at least one coordinate measuring machine to determine the coordinates can therefore be part of the method, and the arrangement can include not only a device for determining the geometric boundaries of a mass flow, energy flow or force flow through a channel having a channel wall, but also at least one coordinate measuring machine for determining the coordinates.

[0012] The term "coordinate measuring machine" includes any type of machine that can be used to determine the coordinates of a workpiece. In one type of coordinate measuring machine, the coordinates are surface coordinates, i.e., the coordinates of points on the surface of the workpiece are determined. Another type of coordinate measuring machine is alternatively or additionally capable of determining the coordinates inside the workpiece. This type includes coordinate measuring machines that utilize invasive radiation that penetrates into the material of the workpiece and in particular measures the intensity of the radiation transmitted through the workpiece. Typically, the radiation is transmitted through the workpiece from different directions, and a computer-assisted reconstruction is performed on the scanned workpiece based on the results of the radiation transmission. This process is also known as computed tomography (CT). However, the term "coordinate measuring machine" also includes conventional coordinate measuring machines, such as machines with a gantry design or a gantry design, horizontal arm machines and articulated arm machines. The term "coordinate measuring machine" also covers machines that are not primarily designed as coordinate measuring machines, but are set to work like coordinate measuring machines. In particular, these machines have at least one measuring sensor for determining coordinates. For example, there are known robots, such as robot arms with rotary joints, on which sensors for capturing the surface of a workpiece (e.g., optical sensors) are fastened instead of tools, or there are known machine tools on which measuring sensors (e.g., tactile sensors) are fastened instead of machining tools. For example, there are also known hexapods on which sensors for capturing the surface of a workpiece (e.g., tactile sensors) are fastened instead of machining tools.

[0013] The term "coordinate measuring machine" also includes 3D scanners. For example, systems based on triangulation (such as laser scanners and projection sensors) are particularly advantageous here because they can generate many measuring points with 3D coordinates in a short time. The projection sensor projects a pattern (such as a stripe pattern) onto the surface area of ​​the measured object and uses at least one image capture unit (camera) to capture the image of the measured object and the projected pattern. The 3D coordinates of the surface points of the measured object can be determined by evaluating the image record. In order to completely capture the measured object or the surface of the measured object, only one measuring position is usually not enough, so the relative position of the 3D scanner relative to the measured object is usually changed repeatedly. This positioning can be done manually (in a handheld manner) or semi-automatically or automatically, for example by using a robot to guide the 3D scanner. The position change can also or additionally be achieved by moving the object relative to the 3D scanner, for example by a rotating table.

[0014] With regard to the invention, coordinate measuring machines having optical sensors, such as the above-mentioned projection sensors, cameras for creating one-dimensional and multi-dimensional images, and laser scanners are particularly advantageous.

[0015] In particular, a test plan may be defined or received in a known manner, according to which the coordinates of the channel, in particular the coordinates of the channel walls, are measured. The test plan may define which measurement points and / or measurement areas are measured.

[0016] Returning to determining the minimum cross-sectional area of ​​a passage, it is often not possible to determine the minimum cross-sectional area within a suitable time frame. For example, in the case of the above-mentioned gap between the blades of a turbine, the minimum cross-sectional area is not a planar area, because the opposing blades have surfaces that have a continuous circular curved profile over their extent in the radial direction of the turbine. Moreover, the passages formed between the blades of a turbine typically taper or expand in the flow direction. This also makes the calculation of the minimum cross-sectional area more difficult.

[0017] To determine the minimum cross-sectional area, individual distance measurements can be made near the theoretically expected minimum cross-sectional area, and then the individual distances are combined with weights by calculation to form the surface area. This approach cannot make accurate statements about the location, shape, or size of the geometric area compared to the area defined by the fluid machinery. Moreover, there are more non-measured ("blind") areas than measured areas. These differences hinder turbine designers from developing, operating, and maintaining turbines. Moreover, the minimum cross-sectional area, which typically has a curved range and is therefore a three-dimensional (3D) surface, has been approximated as a two-dimensional (2D) surface.

[0018] The problem addressed by the invention is to specify a method for determining the geometric boundaries of a mass flow, energy flow or force flow through a channel having a channel wall. Another problem addressed by the invention is to specify a corresponding device.

[0019] According to the invention, the geometric boundary is determined as the minimum cross-sectional area of ​​a channel or a channel section. Specifically, the position, shape and size of the minimum cross-sectional area of ​​a channel or a channel section can be determined simply and accurately. If a channel is mentioned below or in the claims, this can also be understood to refer to a section of the channel.

[0020] In order to model and / or describe the cross-sectional area of ​​a channel, it is proposed to use a tessellated area (i.e. a block-like area) whose polygonal plane blocks are arranged without gaps and without overlap. In this context, the literature also uses the term "tessellation", but it is often restricted to triangular blocks. Even if there are advantages in using only triangular blocks constituting a tessellated area, in particular with regard to a simple and unique mathematical and / or numerical description, the scope of the present invention does not exclude the use of other polygonal plane blocks additionally or exclusively as elements of a tessellated area. Therefore, it is also possible to describe a tessellated area in which polygonal blocks with different numbers of corners appear.

[0021] In particular, if a subset of corner points representing corner points of the same tile is also defined or uniquely determinable in each case, the tessellated area can be described exclusively and / or completely by the positions, in particular the coordinates of the corner points of the tile. In the case of exclusively triangular tiles, such a definition or determination is easily possible.

[0022] A mesh may also be referred to as the equivalent of a tessellated region. The corner points of the tessellated region correspond to the nodes of the mesh, and the straight edges of the tiles correspond to the straight line connections between the nodes of the mesh.

[0023] Once a tessellated region is known as a description / model of a cross-sectional area, the total area of ​​the tessellated region can be easily determined (as an approximation of the cross-sectional area) by adding the areas of all tiles. As the number of corners or tiles increases, the error of the approximation becomes smaller. Thus, with a sufficient number of corner points / tiles, the specification on the accuracy of the description can be met.

[0024] The geometry considered is a channel, and the edge points of the cross-sectional area are located on the channel wall of the channel. The channel wall can also be described as a tessellation area. The aforementioned description of possible embodiments of the tessellation area also applies to the channel wall, wherein the channel wall and the cross-sectional area can be described using the same type of tessellation area or different types of tessellation areas. However, it is not mandatory to describe the channel wall as a tessellation area. In particular, it is sufficient, for example, to specify only the multiple points on the channel wall by the three-dimensional coordinates of the multiple points on the channel wall, specifically in a suitable coordinate system. The definition of straight line connections between the block edges or points on the channel wall is not mandatory. However, in a specific embodiment, the channel wall is described as a tessellation area made of triangular plane blocks. In this specification, "a point on the channel wall" should be understood to mean that the point is part of the area that delimits the flow or flux in the channel. With respect to the channel wall, reference can also be made to the envelope surface.

[0025] It is also proposed that the method for determining geometric boundaries (describing cross-sectional areas as tessellated areas) be performed as a computer-implemented method. The method steps described below are advantageously performed in a computer-implemented manner, since many machine operations can be performed that allow for a fast and accurate determination of the minimum cross-sectional area.

[0026] The determination of the minimum cross-sectional area is based on information about the geometry of the channel, which, as described above, can optionally be a section of a longer channel. The geometry of the channel is specifically given by the geometry of one or more channel walls and is available to the computer or computer network that performs the method. Even if preferred, it is not mandatory to provide the computer or computer network with the coordinates of multiple points on the channel wall. For example, if the computer or computer network can use a geometric description of the channel wall, the computer or computer network can also independently determine the points on the channel wall. Specifically, it is also possible to describe the geometric description of the range of the channel wall in a vector graphics manner and / or by mathematical functions, which geometric descriptions can also specifically have a segmented definition, for example according to a polygon chain. However, in many cases, the geometric description of the channel wall is based on measurement results from measurements using at least one coordinate measuring machine. In these cases, it is preferred to provide the computer or computer network with the measured coordinates of multiple points on the channel wall.

[0027] Further, the determination of the minimum cross-sectional area is based on information about the geometry of the first edge line of the cross-sectional area of ​​the channel. If the channel has more than one channel wall, such as in the case of a net flow cross section between the inner channel wall and the outer channel wall, the determination of the minimum cross-sectional area is based on information about the geometry of all channel walls required for determining the minimum cross-sectional area.

[0028] Therefore, the computer-implemented method uses the first edge point of the first edge line of the cross-sectional area of ​​the passage as a starting point. Therefore, the coordinates of these first edge points are received or present in a computer or computer network. Specifically, the method may also include determining these coordinates based on information about the existence of the geometry of the first edge line and thus creating appropriate coordinates.

[0029] If at least one additional channel wall should be taken into account in the determination of the minimum cross-sectional area, a corresponding procedure exists for each additional channel wall, in which, for example, the coordinates of a first edge point on a first channel wall can also be received at the beginning of execution of the method and the coordinates of the first edge point on a second channel wall can be determined during execution of the method based on information about the geometry of the first edge line on the second channel wall.

[0030] Further, when executing the method, the first cross-sectional area is received or created as a tessellated area as described above, wherein the first cross-sectional area is bounded by first edge points of first edge lines. In other words, the first edge points are located on one or more first edge lines. As corner points, all first edge points belong to the tessellated area describing the first cross-sectional area. In particular, the first edge point group of the first edge lines contains all edge points of the tessellated area. Therefore, in this case, there are no additional corner points of the blocks at the edges of the tessellated area. However, in particular, multiple first edge points may be received or available at the beginning, and additional first edge points may be subsequently created or received additionally when executing the method.

[0031] It should be observed here that in order to perform the method, it is not necessary to know the route of the edge line from beginning to end. Instead, the situation that occurs in practice can be that the channel wall has a depression, opening or other gap, and when determining the minimum cross-sectional area, these depressions, openings or other gaps are advantageously still not taken into account. If necessary, the gap can be closed in the corresponding area of ​​the channel wall, for example, by interpolation. However, it is not necessary to close the gap in any case. For example, it may be that the edge line considered in the process of determining the minimum cross-sectional area by the method does not extend into the area of ​​the gap. However, if this is the case, then for example, the corresponding edge point of the edge line is defined to be very close to the gap, the opposite side of the gap and the two edge points are adjacent corner points of the same block, which may be enough. In its alternative or in addition, at least one additional edge point can be defined between the two edge points in an interpolation manner (for example, on the straight line connection between the two edge points). For example, this can be implemented when the distance between the two edge points exceeds a predetermined maximum value.

[0032] Since there is an infinite number of tessellation areas for each set of edge points, broadly speaking, any first cross-sectional area can be defined with the first edge points present (also referred to as a set of first edge points present) in order to start an optimization which continues until a minimum cross-sectional area is obtained. In this case, it is not necessary (although possible) to determine the associated minimum cross-sectional area for the set of first edge points. Rather, the method according to the invention should only allow the determination of the minimum cross-sectional area for a channel or channel segment, and therefore also for other desired edge lines or other sets of edge points.

[0033] Although this has been at least implicitly mentioned at the beginning and in the description of the proposed solution, it should be emphasized again that the cross-sectional area of ​​the channel is generally a three-dimensional (3D) surface, i.e. an area that does not only extend in a single plane in each case. The tessellation area of ​​the polygonal plane blocks arranged without gaps is suitable for describing a real curved 3D surface as a good approximation. Moreover, the total area of ​​the tessellation area can be easily calculated by summing the areas of the individual blocks. Further, describing the cross-sectional area as a tessellation area allows its shape to be changed in a simple manner by means of at least one corner point of a block, generally a plurality of corner points of the tessellation area, in particular all corner points, being displaced in space. Each corner point can be displaced continuously in space. In this case, it is necessary to observe the boundary conditions that will be discussed in detail for the corresponding type of corner point. The term "boundary condition" is understood in a mathematical sense and does not necessarily refer to the region boundary. Specifically, the type of corner point is an edge point, and in contrast, an inner corner point.

[0034] One boundary condition for edge points is that after spatial displacement (i.e. after their position has changed) they are still located on the channel wall, wherein, at least temporarily, this condition may also only approximately hold during the search for the minimum cross-sectional area. Possible boundary conditions for the displacement of inner corner points and also of edge points will be described below, which enable the detection of the minimum cross-sectional area in a time-saving manner. Otherwise, one boundary condition for the displacement of inner corner points may be that they do not become edge points and / or that they do not shift outside the channel wall.

[0035] It is also proposed to use the first cross-sectional area as the starting point for determining the minimized cross-sectional area by iteratively determining other cross-sectional areas as tessellation areas. In each iteration step, at least one corner point of the tessellation area is displaced until one of the other cross-sectional areas is obtained. In particular, once there is a changed cross-sectional area, the iteration step can be considered completed, for which the total area is calculated by summing the sizes of the areas of all blocks in the tessellation area. Naturally, the size of the area of ​​the individual blocks needs to be recalculated only when at least one corner point of the corresponding individual blocks is displaced compared to the previously valid cross-sectional area. However, if the specification for performing the iteration step is met, the iteration step can also be considered completed. For example, the specification can be that the spatial displacement should be calculated exactly according to the boundary conditions for all corner points or for a set of corner points that can be determined according to the specification (relative to the tessellation area that exists at the beginning of the iteration step). For example, the boundary condition is that the displacement of one or more corner points makes the total area of ​​the tessellation area smaller. The specific configuration of such boundary conditions will be discussed below. Thus, a decision may be made not to shift one or more corner points if displacement of a particular considered individual corner point or a particular considered group or subset of corner points does not result in a smaller overall area.

[0036] Further, it is proposed to terminate the iteration when a specified termination criterion is met. For example, the termination criterion can be that iterating one or more iteration steps does not obtain a cross-sectional area that is significantly smaller than the cross-sectional area previously obtained for the determined (so-called "other") cross-sectional area. For example, "significantly smaller" can be defined by a specified limit value. Regarding the method for finding the optimal value (minimum or maximum value), alternatives to this termination criterion are well known. For example, the termination criterion can use the rate of change or the gradient of change of the size of the cross-sectional area. For example, a so-called gradient method or a gradient descent method can be performed.

[0037] Since the intention is not to determine the minimum cross-sectional area only for a given edge line, but for a channel or a channel segment, not only the inner corner points but also the edge points of the tessellated area are displaced in space during the iteration.

[0038] Therefore, the following general content is proposed: A computer-implemented method for determining geometric boundaries of a mass flow, energy flow, or force flow through a channel having a channel wall, wherein

[0039] - receiving or providing the coordinates of a first edge point of a first edge line of the cross-sectional area of ​​the channel, wherein the edge point is located on the channel wall,

[0040] - using the first edge point, receiving or creating the first cross-sectional area as a tessellated area whose polygonal plane tiles are arranged without gaps and without overlap, the first edge point being a corner point of a tile of the tessellated area, and the first edge point and all further inner corner points of the tile defining the first cross-sectional area,

[0041] - determining further cross-sectional areas by an iterative method as tessellation areas of the aforementioned type,

[0042] - the positions of both edge points and inner corner points change during the iteration, and

[0043] - terminating the iteration when a specified termination criterion is met and outputting information on a minimum cross-sectional area for which, with respect to the tessellated area generated by the iteration, the total area of ​​all blocks of the corresponding tessellated area is minimized.

[0044] The coordinates of the edge points and the inner corner points can be related to any desired three-dimensional coordinate system, for example a Cartesian coordinate system with the origin located in the spatial region of the channel.

[0045] The information about the minimum cross-sectional area of ​​output may be different depending on the configuration of the method. For example, the size of the minimum cross-sectional area of ​​output may be different. In its alternative or in addition, for example, at least one edge line of the minimum cross-sectional area may be output. In addition, in its alternative or in addition, the three-dimensional coordinates of all inner corner points and all edge points may be output as the minimum cross-sectional area, for example, for the surface subdivision area, for the minimum cross-sectional area, the total area of ​​all blocks of the corresponding surface subdivision area is minimized with respect to the surface subdivision area in the iteration. The minimum cross-sectional area determined in the iteration process does not need to be the absolute minimum cross-sectional area. A possible reason for this has been found in the following fact: the minimum cross-sectional area is only roughly described by the identified surface subdivision area. Further, when the minimum cross-sectional area has not yet been determined, the iteration may have terminated according to the specified termination criteria. However, the determined minimum cross-sectional area may also be only a local minimum cross-sectional area, in which the size of the area does not represent the absolute minimum in the channel or channel section. This can be offset by performing the method again with different first edge lines in particular.

[0046] Preferably, the edge points are displaced in the iterative process in such a way that the corresponding edge points continue to be located on the channel wall in each case. By displacing the edge points so that they continue to be located on the channel wall, the geometry remains consistent with the channel wall and, on the other hand, it is possible to find the minimum cross-sectional area of ​​the channel in a simple manner.

[0047] As already mentioned, this can only be done approximately, at least temporarily, in particular for reasons related to the numerical implementation of the method and in particular for facilitating the calculation of the displacement of edge points. However, it is preferred that the edge points temporarily located next to the channel wall are displaced to the channel wall at least once a specified termination criterion is met or immediately thereafter. Preferably, the displacement to the channel wall occurs in each iteration step. Thus, in particular, preliminary new three-dimensional coordinates of a point on the channel wall can be determined in at least one iteration step for an edge point by means of the following: the respective edge point reaches a preliminary new position defined by the preliminary three-dimensional coordinates by being displaced from its previous position in a tangential plane to the channel wall in the previous position, wherein at a later stage (preferably within the same iteration step), if the preliminary new position is not located on the channel wall, there is a displacement of the respective edge point from the preliminary new position to the final new position on the channel wall. The tangential plane in contact with the channel wall at the previous position of the edge point represents a good approximation to the contour of the channel wall in the case of small displacements of the position of the edge point. At the same time, the displacement in the tangential plane ensures that the edge point is not displaced a considerable distance away from the channel wall, in particular not perpendicularly or approximately perpendicularly to the profile of the channel wall. However, the displacement in the tangential plane is only one option to ensure that the corresponding edge point is displaced approximately on the channel wall. As an alternative or in addition to this, this can be ensured, for example, by a boundary condition that the distance of the displaced edge point from the channel wall must not be greater than (e.g. not even temporarily) a specified maximum value.

[0048] Specifically, the new three-dimensional coordinates of the edge points and / or inner corner points can be determined in each iteration step by satisfying the following local conditions, namely, the sum of the areas of all blocks whose corners are defined by the corresponding corner points is minimized, while the three-dimensional coordinates of all other corner points remain unchanged.

[0049] In principle, such a local condition can be used in two different situations. First, according to the first situation, there may be no displacement of the corner points initially in the iteration step before the displacement of the corner points due to the fulfillment of the local condition is calculated for all corner points that may be displaced (i.e. for all corner points to which the local condition should be applied) in the iteration step. Then again, according to the second situation, the local condition can be used after at least one corner point has been displaced (in particular by using the local condition) in the iteration step. Thus, in the second situation, the process can be performed successively for the corner points, i.e. the process comprises the use of the local condition as well as the displacement of the corner points. It goes without saying that these two situations can be combined with each other. Thus, for example, before the displacement according to the local condition has been determined for the corner points in a local area of ​​the cross-sectional area, no displacement can be performed initially in this local area during the iteration step, and then exactly the same procedure can be performed for another local area or for individual corner points.

[0050] It is also possible to determine and / or perform a shift of the corner points according to the above-mentioned local conditions in a corresponding iteration step or in a part of an iteration step only with respect to the edge points or only with respect to the inner corner points.

[0051] As an alternative or in addition, different local conditions can be specifically defined for local areas with multiple corner points. For example, in this case, the local condition can be that the sum of the areas of all blocks whose corners are defined by the corner points in the local area is the smallest. Depending on the number of corner points in the local area, this can be achieved by determining the local minimum area by repeated shifting of individual corner points, that is, the sum of the areas of the blocks involved can be determined for different combinations of the positions of the corner points in the local area, and the minimum value of the sum of the areas can be determined in this way. Under the local conditions specified here, blocks that form corresponding local areas but not all have common corner points can be considered. However, these blocks preferably form a continuous area. It is also possible to apply one of the specified local conditions to edge points and another local condition to inner corner points.

[0052] Specifically, preliminary new three-dimensional coordinates of a point on the channel wall can be determined for an edge point in each iteration step by satisfying the local condition that the sum of the areas of all blocks whose corners are defined by the corresponding corner points is minimal while the three-dimensional coordinates of all other corner points remain unchanged, and by satisfying an additional displacement condition (which is also a boundary condition in a mathematical sense). The additional displacement condition can be that the corresponding edge point can reach its preliminary new position defined by the preliminary three-dimensional coordinates only by shifting from its previous position in a tangential plane to the channel wall at the previous position. Subsequently or at a later stage, if the preliminary new position is not located on the channel wall, there is a displacement of the corresponding edge point from the preliminary new position to its final new position on the channel wall with respect to the iteration step. The "tangential plane to the channel wall at the previous position" is a tangential plane that is in contact with the channel wall at least at the previous position and therefore at the edge point that has not yet been shifted. Attention has been drawn to the advantages of this type of displacement for edge points.

[0053] In addition, the scope of the present invention includes a device for data processing, which includes means for performing the method, in particular the method in one of the described configurations. The device may, for example, consist of a single computer or a computer network, or include the computer or the computer network. With regard to its operating method, the computer or at least one computer may in particular be an analog computer, a digital computer and / or a hybrid computer. In terms of size and design, it may be a smartphone, a personal digital assistant (PDA), a tablet computer, an embedded system (e.g. embedded in a control computer of a coordinate measuring machine), a single-board or multi-board computer, a personal computer (PC), a desktop computer, a workstation computer, a host or server integrated into a computer network, a thin client computer, a netbook, a notebook computer, a laptop computer, a mainframe computer or a supercomputer, wherein a part of the types described may be implemented by a single computer (such as a multi-board PC). In addition, the computer or at least one computer may have one or more central processing units (CPUs) and / or one or more computing cores per CPU. A graphics card or other dedicated card having a processor as part of a computer may also be a device for performing the method alone or in combination with other computers or processing units.

[0054] Furthermore, it should be noted that, although the computer is preferably prompted by a computer program to perform the method, the apparatus for performing the method may also comprise at least a hardware-implemented, preferably programmable arrangement (e.g. an arrangement of logic gates), such as an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device) or an FPGA (Field Programmable Gate Array).

[0055] Furthermore, the scope of the invention includes a computer program comprising instructions which, when executed by a computer, prompt said computer or, when executed by a computer network, prompt said computer network to perform the method, in particular in one of the described configurations.

[0056] Also included within the scope of the invention are data carrier signals and computer-readable media that transmit computer programs. The computer-readable medium comprises instructions that, when executed by a computer, prompt the computer or, when executed by a computer network, prompt the computer network to perform the method, in particular in one of the described configurations.

[0057] The aforementioned computer network or one of the aforementioned computer networks may be a local network or a non-local network, or a combination thereof. Specifically, the local area network may be a body area network (BAN), a wireless body area network (WBAN), a personal area network (PAN), a wireless personal area network (WPAN), a local area network (LAN), or a wireless LAN (WLAN). Specifically, the non-local area network may be a metropolitan area network (MAN), a wide area network (WAN), a global area network (GAN), a virtual private network (VPN), or a storage area network (SAN).

[0058] A computer-readable medium may also be referred to as a storage medium and may be, for example, a digital medium such as a compact disc (CD), a disk, a digital versatile disc (DVD), a hard drive, a memory card or a mass storage device, or may be an analog computer-readable medium such as a text (e.g., which is a printout of the program code), an image, an arrangement of images or an analog disk-shaped or disc-shaped data carrier.

[0059] The invention also relates to an arrangement having a device for data processing and having a coordinate measuring machine, which is configured to measure the coordinates of a channel wall as an input parameter for performing a computer-implemented method. In particular, the device for data processing can be at least partially integrated in the coordinate measuring machine. However, the device can also be implemented separately from the coordinate measuring machine.

[0060] Exemplary embodiments of the present invention will now be described with reference to the accompanying drawings. In the various figures of the accompanying drawings:

[0061] Figure 1 schematically shows an arrangement comprising a coordinate measuring machine and a data processing device for determining geometrical boundaries of a flow or flux,

[0062] Figure 2 A flow chart is shown which schematically represents in a simplified manner the procedure when determining the geometrical boundaries of a flow or flux through a channel,

[0063] Figure 3 shows a portion of the tessellated area of ​​the cross-sectional area that existed earlier, the tessellated area being represented by a triangular mesh of the edges of the tiles,

[0064] Figure 4 A portion of the tessellated area of ​​the cross-section area present at a later time is shown, with Figure 3 The tessellation area has been modified compared to

[0065] Figure 5 A portion of a turbine including two blades is schematically shown,

[0066] Figure 6An object is shown forming a channel having a channel wall extending discontinuously at one point,

[0067] Figure 7 Shows Figure 6 A magnified view of a discontinuity of an object, and

[0068] Figure 8 A blood vessel with multiple branches is shown.

[0069] Figure 1 An arrangement is shown having a coordinate measuring machine 1 and having a data processing device 5. Figure 1 In the figure, the coordinate measuring machine 1 is depicted as a gantry type coordinate measuring machine. However, this is only an example and the coordinate measuring machine may be of any type, for example also a coordinate measuring machine which uses invasive radiation such as x-ray radiation, a laser scanner or a projection sensor to perform the measurements. In contrast to the depiction, the coordinate measuring machine may also include a hand-guided sensor and / or a pattern projector. The types of coordinate measuring machines and sensors have already been mentioned above.

[0070] A workpiece 3 having a channel with irregularly shaped channel walls is located in a measuring region of a coordinate measuring machine 1 , in this example on a measuring table 2 . Figure 1 The data processing device 5 depicted in has been drawn as a desktop computer. Alternatively, for example, this can be any other type of data processing device, in particular also a device with a plurality of computers connected to each other via a remote data transmission network. The data processing device performs its functions in particular under the control of at least one computer program.

[0071] As indicated by the arrow, the data processing device 5 receives measurement results from the coordinate measuring machine 1 regarding the measurement of the workpiece 3. The measurement results contain the coordinates of the channel wall of the workpiece. These coordinates can, but do not necessarily, describe the shape of the entire channel wall. Instead, additional information may also be present or obtained, such as CAD planning data from the workpiece 3, and this additional information together with the measured coordinates of the channel wall describes the shape of the channel wall.

[0072] The data processing device 5 can also be part of the coordinate measuring machine 1 and in the process also implement functions for controlling the coordinate measuring machine 1 .

[0073] Alternatively or in addition thereto, a data processing device, such as the data processing device 5 , can, for example, start and / or trigger a program for measuring the workpiece 3 or any other measurement object when executing at least one computer program.

[0074] References below Figure 2 The procedure for a computer-implemented method for determining the geometric boundaries of a flow or flux through a channel is now described, specifically by or including determining a minimum cross-sectional area of ​​the channel.

[0075] In a first step S1, the coordinates of first edge points of a first edge line of the cross-sectional area of ​​the channel are received and / or determined, wherein these edge points are located on a channel wall of the channel whose minimum cross-sectional area is to be determined. If the channel has more than one channel wall, for example an inner channel wall and an outer channel wall, the coordinates of a first edge point of a further edge line of the cross-sectional area of ​​the channel may also be received and / or determined for a respective further channel wall in the first step S1.

[0076] In particular, a person may specify the first edge line completely or partially, for example by defining the coordinates of the edge line. In an alternative or in addition thereto, for example Figure 1 The data processing device 5 can automatically define the first edge line, for example, by means of the coordinates of the first edge point. Specifically, for this purpose, the geometry of the channel wall is completely or partially known (for example in a local area of ​​the first edge line).

[0077] Optionally, information about the geometry of one or more channel walls of the channel is received and / or determined in a further step S2 , which can be performed before, after and / or simultaneously with the first step S1 .

[0078] In order to carry out the further steps of the method, the required information about the geometry of the channel wall and the edge line of the first cross-sectional area is now available.

[0079] In another step S3 of the method, the first edge point is used to receive or create a first cross-sectional area as a tessellation area in which polygonal plane blocks are arranged without gaps and overlaps, the first edge point is a corner point of a block of the tessellation area, and the first edge point and all other inner corner points of the block define the first cross-sectional area.

[0080] At this point, it should be observed that it is possible, but not necessary, to initially receive and / or determine the coordinates of an edge line of the first cross-sectional area and thereby create the first cross-sectional area as a tessellated area. Instead, for example, it is also possible to determine and / or receive a data record describing the first cross-sectional area as a tessellated area. Since the tessellated area also has edge points, the points of the first edge line are also defined thereby. The schematic diagram of the procedure of the method in this case corresponds to Figure 2 However, in any case, the first cross-sectional area can be used as a tessellation area for the steps of the method after step S3. For example, as already mentioned above, knowing the three-dimensional coordinates of all corner points (inner corner points and edge points) of the tessellation area is sufficient to define the tessellation area.

[0081] If, at least for some of the tiles in the now existing tessellated area, the distances between mutually adjacent corner points are too large (and therefore if the edge lengths of the tiles are too long), the mesh corresponding to the tessellated area can now be refined in an optional step. For example, tiles that are too large are subdivided into a plurality of smaller tiles in the process. In particular, the maximum permissible edge length of a tile can also depend on the local curvature of the cross-sectional area. Therefore, tiles can also be subdivided or merged (i.e., one tile is created from a plurality of tiles or a smaller number of tiles is created) during and / or between the iterative determination of further cross-sectional areas.

[0082] As already mentioned, a triangle mesh corresponding to a tessellated area consisting only of planar triangle patches is an advantageous way of describing the first cross-sectional area and the further cross-sectional areas which are created when performing the method.

[0083] In a further step S4, in particular after step S3, a further cross-sectional area is determined as a tessellated area, wherein the further cross-sectional area is created by modifying a previously existing tessellated area. This is the first cross-sectional area when step S4 is performed for the first time. Step S4 is part of an iteration, in which, like the subsequent step S5, a check is performed as to whether the iteration should be terminated. Possible termination criteria have been discussed above. According to the invention, the positions of the edge points of the tessellated area and the positions of the inner corner points are usually modified simultaneously during the iteration.

[0084] If the termination criterion of the iteration is met, step S5 is followed by step S6, outputting information about the minimum cross-sectional area for which, with respect to the iterated tessellation areas (i.e., all tessellation areas determined in the iterative process), the total area of ​​all blocks of the corresponding tessellation area is minimized. Specifically, the size of the minimum cross-sectional area and / or the coordinates and / or the contours of the associated edge lines are output.

[0085] For example, as described below, another tessellation area can be determined in the above step S4 or in another embodiment of the method: one of the above local conditions is applied to each of the corner points of the existing tessellation area; preferably, the same local condition is applied to all corner points. This produces a displacement of the corresponding corner point. In an exemplary embodiment, in particular, the constraint that the displacement can occur exclusively on the corresponding tangential surface should be observed for the edge points. After the displacement of all corner points has been determined, the displacement is performed, that is, the displacement of each corner point does not depend on the displacement of other corner points. In order to speed up the calculation process, a device with a large number of processors operating in parallel (such as is the case with a graphics card) is suitable.

[0086] An exemplary embodiment of a procedure for finding the minimum cross-sectional area of ​​a channel is now described below with reference to the formulas. In doing so, with respect to the so-called stationary problem in discrete form, reference is made to the formulas and explanations in the paper "Constructing Triangular Meshes of Minimal Area" by Chen Wenyu, Cai Yiyu and Zheng Jianmin in "Computer-Aided Design & Applications" 5 (1-4), 2008, 508-51 (DOI: 10.3722 / cadaps.2008.508-518), specifically in Section 3.1 of the paper. This relates to formulas and explanations in the case of fixed specified or unchangeable edge lines. These formulas are extended to the case of changeable edge lines, which are located on the envelope surface defined by the channel wall in each case.

[0087] Next, P k Used to represent the point coordinates of a point P with index k. For example, a vector between two points is represented by an arrow on the sign of the two point coordinates D represents the set of triangles in the region, where each triangle consists of a corner point P with index k, l, m, for example k , P l , P m describe.

[0088] The surface area of ​​the region A to be minimized can be expressed as follows:

[0089]

[0090] Here, <k, l, m> represents a set of indices k, l, m. With respect to the sum symbol ∑, the entire expression t=<k, l, m>∈D means that it should be formed on all corner points of the set of triangles in region A. The symbol × represents the vector product of the vectors preceding and following it.

[0091] Now consider changing any desired interior point P a The change in surface area A when θ is 0.0447°; in the following equation, this is given by the surface area A relative to point P a The partial derivative of the change (displacement) is expressed as:

[0092]

[0093] Therefore, the displacement can be expressed by point P a The displacement of the components x, y, and z of . T represents the transposed vector. In the following, ND(a) represents the set of triangles in the region. These triangles are adjacent to the points P a, that is, the point that forms the corner of all these triangles. Inserting the right side of equation (1) into equation (2) yields:

[0094]

[0095] If all these derivatives are set to 0, then n equations with n variables are generated, where n is the number of interior points. Setting the derivatives to 0 corresponds to the local condition described above, i.e., the corners are determined by the corner points P a The sum of the areas of all defined tiles (triangles in this case) is minimized.

[0096] This solution provides the best mesh. However, these equations are nonlinear. It is difficult to solve such a nonlinear system. In case of a mesh with a large number of points, it is impossible to solve with reasonable expenditure. Therefore, a local mechanism is proposed and the solution is approximated iteratively. The above equations are reformulated as:

[0097]

[0098] In the formula,

[0099]

[0100] is a 3×3 matrix. Use (The above local conditions) produce the following situation:

[0101]

[0102] C -1 is the inverse matrix of C. The above equation cannot be considered as P a definite solution, since the right side of the equation also contains P a However, it provides a signal processing method to update point P a , as explained in the following publication: “A signal processing approach to fair surface design”, SIGGRAPH '95: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, September 1995, pp. 351-358 (https: / / dl.acm.org / doi / 10.1145 / 218380.218473), Gabriel Taubin, ed. That is, the new displacement point From the existing point P a and obtained from other corner points in the set ND(a) assigned to it (i.e., all its neighboring corner points),

[0103]

[0104] So far, the formulas and explanations have also been related to the case of fixed, specified or unchangeable edge lines. This is now extended to the case of variable edge lines, which are located on an envelope surface defined by the channel walls.

[0105] The above procedure is now also applied to the edge points. In doing so, the following constraint is taken into account: the edge points must always remain at least approximately on the envelope surface, ie at the edge of the channel.

[0106] For this purpose, the envelope surface at the edge point P is used e The fact that the tangent plane at approximates the envelope surface in a small neighborhood ε. One can assume that for sufficiently well-shaped surfaces, each iteration step is small enough that this approximation is sufficient.

[0107] Instead of the three degrees of freedom that appear in equation (2), this still only involves two degrees of freedom, specifically, P e The envelope surface is tangential to the two degrees of freedom of the plane (where the plane is spanned by the two directions t1 and t2):

[0108]

[0109] Thus, the above procedure can be similarly applied. However, It is then projected onto the envelope surface so as to satisfy the above constraints. Figure 3 and Figure 4 And the triangle mesh is now used to show, for example, the above based Figure 2 Describes how the corner points of the tessellated area are displaced during the iteration process. The triangle meshes both show the edge outline of the tessellated area made of flat triangle blocks. However, the two figures only show a portion of the overall tessellated area or a portion of the overall cross-sectional area of ​​the channel. Only the displacement of two corner points (the edge point and the inner corner point) is shown. Figure 3 Shown Figure 4 The state at a previous time. In this case, earlier and later can refer both to a single iteration step and to time in subsequent iteration steps.

[0110] exist Figure 3 and Figure 4 In each of the , only some of the corner points are marked by reference numerals, specifically P followed by a number in each case. In this case, P1, P2, P3 and P4 denote edge points, P5, P6 and P7 denote inner corner points. In addition, two Figure 3 and Figure 4 Two corresponding arrows are depicted in each; these arrows indicate the displacement of one of the corner points. Figure 3 The downward pointing arrow starting from edge point P2 in the image correspondingly generates edge point P2 shifted downward to Figure 4 Further, the upward pointing arrow at the inner corner point P5 generates the position where the inner corner point P5 is shifted upward to Figure 4 The position where the shifted corner point P5' is located.

[0111] As explained above and previously in general terms based on the formula, the displacement of the edge point P2 occurs in the tangential plane of the envelope surface or channel wall, which is Figure 3 and Figure 4 However, since the displacement is in each case based on minimization of the total area of ​​the local block, the corner points of the triangular block are the planes of the edge points P2' that are approximately perpendicular to Figure 4 The tangent plane is the tangent plane that touches the envelope surface at the non-displaced edge point P2.

[0112] Regarding the displacement of the inner corner point P5, Figure 3 and Figure 4 It is obvious from the above that the total area of ​​the triangular block whose corner point is the inner corner point P5 has become smaller. The shifted corner point P5' no longer forms a local low point. However, since no other condition applies to the displacement of the inner corner point P5 except minimizing the total area in its local area (specifically minimizing the total area through all triangles whose corner point is the point P5), the displacement can in principle be implemented in any direction, not just in the plane as in the case of the corner point.

[0113] Figure 3 and Figure 4 The two arrows pointing in opposite directions upward and downward in FIG. 1 only relate to specific exemplary embodiments and specific cases. As mentioned, in any case, in the case of an inner corner point, a displacement can be implemented in any desired direction.

[0114] Figure 5 Two blades 11, 13 extend approximately in radial direction from a section 12, 14 of the hub of the impeller to a housing 16, wherein when the impeller rotates, Figure 5 The ends of the blades 11, 13 depicted at the top of the impeller may still move from left to right along the housing 16, so there is a corresponding small gap between the blades 11, 13 and the housing 16. The blades 11, 13 extend only approximately in the radial direction, because they have a curved profile along their range from the hub of the impeller to the housing 16.

[0115] Further, Figure 5 Two circumferential dotted lines and two tessellation areas 20, 21 consisting of triangles are depicted. The dotted lines each represent the outline of a first edge line 18, 19. The edge line 19 may be Figure 5The further right side of the tessellation region 21 is identified and the tessellation region 21 resulting therefrom after iterative calculation of the further tessellation region is depicted as if they were completely drawn. The leaves at the edge line 19 and the right edge of the tessellation region 21 have been removed from Figure 5 In contrast, the edge line 18 identifiable further to the left and the resulting tessellation area 20 are partially hidden by the blade 13 .

[0116] The method according to the invention for calculating the minimized cross-sectional area starts, for example, from a first edge line 18 of the passage between the blades 11, 13. Not depicted is a first tessellation area associated with this first edge line 18. Due to the iterative determination of further tessellation areas in the manner described above, the area of ​​the tessellation area 20 emerges as an approximation of the minimum cross-sectional area.

[0117] Figure 6 and Figure 7 The object 31 depicted in the figure forms a channel 32 having a channel wall 33. The channel 32 is depicted as being cut open so as to expose its interior. The channel wall 33 comprises a wall region 34 in which the channel wall 33 no longer has a continuously curved profile connected to an adjacent region. For example, a hole (e.g. a bore), a dent, a protrusion, an inlet or an outlet may be located on the wall region 34. The case of an outlet may also be referred to as a branch or bifurcation; the case of an inlet may also be referred to as an inflow. However, in all these cases it is advantageous to adopt a profile of the channel wall 33 when performing the method according to the invention, which profile has a continuously curved profile with the adjacent regions in the wall region 34. In particular, discontinuities such as in the wall region 34 may produce an unfavorable solution for the minimum cross-sectional area. For example, in the case of a dent, the minimum cross-sectional area may be located at the dent, even if in the case of a (adopted) continuously curved profile, the minimum cross-sectional area is located at a different position of the channel 32. In the case of a protrusion, inlet or outlet, the minimum cross-sectional area is located in the section with the hole, indentation, protrusion, inlet or outlet, even in the case of a continuously curved profile, and the minimum cross-sectional area can be found, for example, in different sections of the channel 32.

[0118] The above explanations for the discontinuous profile of the channel wall not only affect Figure 6 When considering flow or flux, the non-continuous profile of the channel wall is often troublesome in terms of finding the minimum cross-sectional area, which is why a continuous profile is then taken. If previously reference was made to a continuous curved profile of the channel wall, this involves Figure 6and a large number of other cases. However, this does not exclude that the channel wall can also have a plane area (i.e., an area extending in a plane) or, more generally, can have a profile (i.e., a circumferential edge line) that has at least one section with a straight line extent. Holes, indentations, protrusions, inlets or outlets can be located in this straight line section. In this case, it is advantageously assumed that the channel wall extends straight there (i.e., in a straight line), as in at least one adjacent wall area.

[0119] Further, in Figure 6 and Figure 7 A tessellation area 35 formed exclusively of triangles can be identified in FIG. 3 ; after carrying out the method according to the invention, this tessellation area is determined as an approximation of the minimum cross-sectional area of ​​the channel 32 . Figure 6 Also shown is a first edge line 38 , starting from which the tessellation region 35 is determined by iteratively determining further tessellation regions.

[0120] Figure 6 and Figure 7 The example of shows that if the edge of the minimum cross-sectional area is located in the region of the opening of the channel wall, then the minimum cross-sectional area can also be determined as a tessellated area. For example, the channel wall at the opening can be enlarged to form a closed channel wall. However, this is not necessary in many cases, because the edge of a single block can almost close the opening. For example, an additional constraint that the edge point of the tessellated area must not be located in the opening can be applicable in this case.

[0121] Figure 8 Another example of an object having a channel 42 is shown, specifically a blood vessel 41 depicted as being partially cut open. Figure 6 and Figure 7 The channel wall 43 is identified in a manner corresponding to the illustration of FIG. The smallest cross-sectional area is located at the constriction 46 of the blood vessel, which is approximated as a tessellation area 45 in the manner according to the invention.

[0122] List of Reference Numerals

[0123] 1 Coordinate measuring machine

[0124] 2 Measuring table

[0125] 3 Workpiece

[0126] 5 Data processing device

[0127] 11, 13 blades

[0128] 12, 14 Impeller hub area

[0129] 16 Housing

[0130] 18, 19 First edge line

[0131] 20, 21 Surface subdivision area

[0132] 31 Objects

[0133] 32 channels

[0134] 33 Channel wall

[0135] 34 Wall Area

[0136] 35 Subdivision area of ​​the surface with the minimum cross section

[0137] 38 First edge line

[0138] 41 Blood vessels

[0139] 42 channels

[0140] 43 Channel wall

[0141] 45 Subdivision area of ​​the surface with the minimum cross section

[0142] 46 Contraction

[0143] P Corner point

Claims

1. A computer-implemented method for determining geometric boundaries of a mass flow, energy flow or force flow through a channel (32; 42) having a channel wall (33; 43), wherein: - receiving or storing the coordinates of first edge points of a first edge line (38) of the cross-sectional area of ​​the channel (32; 42), wherein these edge points are located on the channel wall (33; 43), - using these first edge points, receiving or creating a first cross-sectional area as a tessellated area whose polygonal plane tiles are arranged without gaps and without overlap, the first edge points being corner points (P) of the tiles of the tessellated area and the first edge points and all further inner corner points (P) of the tiles defining the first cross-sectional area, - determining further cross-sectional areas by an iterative method as tessellation areas of the aforementioned type, - the positions of the edge points and the inner corner points (P) are changed during this iteration, and - terminating the iteration when a specified termination criterion is met and outputting information on a minimum cross-sectional area for which, with respect to the tessellated area generated by the iteration, the total area of ​​all blocks of the corresponding tessellated area is minimized.

2. The method of claim 1, wherein: The edge points are displaced during this iteration in such a way that the corresponding edge point in each case continues to lie on the channel wall (33; 43).

3. The method of claim 2, wherein: In each iterative step, new three-dimensional coordinates of a point on the channel wall (33; 43) are determined for an edge point by satisfying the local condition that the sum of the areas of all blocks whose corners are defined by the corresponding edge points and / or whose corners are defined by the corner points (P) in the local area is minimized while the three-dimensional coordinates of all other corner points (P) remain unchanged.

4. The method according to any one of claims 1 to 3, wherein: By satisfying the local condition that the sum of the areas of all blocks whose corners are defined by the corresponding edge points and / or whose corners are defined by the corner points (P) in the local area is minimized while the three-dimensional coordinates of all other corner points (P) remain unchanged, and by satisfying the additional displacement condition that the corresponding edge point can reach its preliminary new position defined by the preliminary three-dimensional coordinates only by shifting from its previous position in a tangential plane on the channel wall (33; 43) at the previous position, preliminary new three-dimensional coordinates of the point on the channel wall (33; 43) are determined for the edge point in each iterative step, and if the preliminary new position is not located on the channel wall (33; 43), this is followed by the displacement of the corresponding edge point from the preliminary new position to its final new position on the channel wall (33; 43) with respect to the iterative step.

5. The method according to any one of claims 1 to 4, wherein: In each iterative step, new three-dimensional coordinates of these internal corner points (P) are determined by satisfying the local conditions that the sum of the areas of all blocks whose corners are defined by the corresponding corner point and / or whose corners are defined by the corner point (P) in the local area is minimized while the three-dimensional coordinates of all other corner points (P) remain unchanged.

6. The method according to any one of claims 1 to 5, wherein: The information output about the minimum cross-sectional area includes the size of the minimum cross-sectional area and / or at least one edge line of the minimum cross-sectional area and / or the three-dimensional coordinates of a point of the minimum cross-sectional area.

7. The method according to any one of claims 1 to 6, wherein: The coordinates of the channel wall (33; 43) are measured using at least one coordinate measuring machine as input parameters for performing the computer-implemented method.

8. A device for data processing, the device comprising means for executing the method as claimed in any one of claims 1 to 7.

9. A computer program comprising instructions which, when executed by a computer, prompt the computer or, when executed by a computer network, prompt the computer network to perform the method as claimed in any one of claims 1 to 7.

10. A data carrier signal transmitting a computer program as claimed in claim 9.

11. A computer readable medium comprising instructions which, when executed by a computer, prompt the computer or, when executed by a computer network, prompt the computer network to perform the method of any one of claims 1 to 7.

12. An arrangement having a device as claimed in claim 8 and having a coordinate measuring machine (1) which is configured to measure the coordinates of the channel wall (33; 43) as input parameters for performing the computer-implemented method.

Images