Issue #5/2017

Triangulation Grids and Hierarchical Structures of The Models in Calculation of Led Modules

**V.V.Baynev**Triangulation Grids and Hierarchical Structures of The Models in Calculation of Led Modules

The calculation of the optical system of a light device determines not only its technical properties, but also the consumer ones. The review of the most prominent software products for lighting design is given.

Теги: calculation of led modules lighting design расчет светодиодных модулей светотехническое проектирование

INTRODUCTION

The use of light devices with a high coefficient of efficiency makes it possible to significantly increase the efficiency of lighting equipment for mass use and to reduce their energy consumption. Therefore, the design of light devices (LD) is an important and urgent task for the modern lighting industry. The development of the technology of creating light devices is largely determined by the state and development of methods for their lighting design. The results of the calculation largely determine the shape and dimensions of the optical system and the entire LD, as well as its lighting parameters associated with the device application conditions.

The solution of the sequence of direct problems of calculating the LD lies at the heart of the lighting design, i. e. finding the LD light distribution with the known parameters of the optical system and the light source. Various methods for solving the direct LD calculation problem are known, based on the method of elementary mappings, balance of flows and numerical-ray methods [1].

The optical system calculation is the main stage in the development of a light device, since it determines not only the technical properties, but also the consumer ones of the device under development. The optical calculation leads to determination of the geometric characteristics of the optical system and radiation sources, as well as of their parameters that ensure the given photometric characteristics of the light device [2]. When optical calculation is performed, the transmission of light rays in systems consisting of lenses, reflectors, etc. is modeled [3].

1. METHODS AND MEANS FOR CALCULATING AND DESIGNING LIGHTING SYSTEMS

The practice of using different lighting devices indicates the need for flexible methods and means for their design. Numerical and iterative methods are used to calculate the reflecting (refracting) surfaces of a free form, allowing optimizing the shape of the refractive surfaces based on the conditions for the formation of given light distribution. In most cases, the optics calculation is a time-consuming, lengthy and very responsible process. If the optics calculation is performed incorrectly or with errors, it will only become clear after all the other design and construction stages have been completed, when all the planned time and material resources have already been spent. Errors can also occur during the operation of such devices, which is fraught with serious consequences, including in terms of personal safety. Furthermore the effectiveness of existing methods is still not high enough to meet practical needs. Therefore, the problem of optics calculation for the formation of a given lighting still plays a large role [4].

The use of computing technology and the use of specialized software can relieve the engineers from time-consuming calculations, multivariate analysis and a large amount of graphic work. Such automated systems for calculating and modeling of lighting systems using modern software significantly expand the possibilities of modern lighting technology. Modern computer computing technologies allow expanding the possibilities for modeling and researching optical systems significantly, while creating a user-friendly interface.

Currently, the following most famous software products are used in lighting design and production.

DIALux is a professional package for working with lighting, which calculates light characteristics such as brightness, lightness, glossiness, natural light ratio, etc., allowing calculating daylight and shadows when planning lighting, taking into account the geographical location of the building, weather conditions and shadows from surrounding buildings and other objects. DIALux also simulates various light scenes in the rooms.

Light-in-Night Road software product is designed for calculating street lighting, for designing outdoor lighting for off-city highways, street network of cities and rural settlements and related infrastructure. The program allows carrying out lighting calculations for three classes of objects: straight-line sections of roads and streets, typical sections of roads and areas of arbitrary configuration. It calculates the distribution of illumination and brightness of the road surface, normalized values of the average level and uniformity of these characteristics, regulating indicators of blinding the driver by light devices, etc.

However, the analysis of the above mentioned software has shown their task to be mainly in the design of lighting, and they do not deal with calculation and modeling of light-redistributing devices.

For the design of lighting systems, several programs based on different principles of work are used [5]. In some programs, sequence of relative positions of the constituent elements is indicated to represent and analyze the operation of the optical system, and the calculation of the rays is performed sequentially. The other use the global coordinate system and inconsistent calculation of the rays to analyze the operation of the system. This approach is usually applied for the design and analysis of lighting systems.

Currently, foreign software packages such as Zemax, TracePro, Light Tools, OSLO, ASAP, etc. are widely used for the development of optical systems. They have a wide range of functions, including modeling the propagation of light from the sources to radiation receivers.

One Zemax feature is the ability to analyze a consistent and inconsistent calculation of the rays, the ability to calculate designs from lenses, mirrors, diffraction gratings, light filters and other optical elements. LightTools program builds models of lighting systems, where the effects of refraction, reflection, scattering, etc. are taken into account in the calculation of rays. The lighting analysis uses direct ray tracing, which simulates the propagation of light through the model, and a reverse tracer showing the lighting source from the receiver point.

In the design of lighting optical systems, TracePro software is widely used for the calculation of rays and photometric analysis, apparently, due to its low cost. It has a three-dimensional solid-state visualization, the ability to model optical processes based on models created in CAD systems such as SolidWorks, COMPASS. This also significantly facilitates the research process and, importantly, reduces costs for the developer [6].

Photopia (LTI Optics) provides computer modeling of luminaires and their photometric analysis. It can be integrated as a module in SolidWorks, and also allows you to import files into AutoCAD, Pro/Engineer. Furthermore, the program has a database of light sources and materials.

However, many software systems have significant disadvantages: they are sometimes not built to perform highly specialized operations, or require very thorough study of models. Not the least role for their wide promotion in Russia is the cost, which can amount to hundreds of thousands of dollars. Furthermore, there is now an urgent need to reduce the dependence of domestic production on foreign software and the development of proprietary software products.

In connection with the increased need of the Russian lighting industry in computer facilities for research and design of lighting devices, the creation of own software and mathematical tools in the form of a specialized system with the possibilities of geometric modeling has been started. Let’s consider the features of construction of the mathematical model underlying LightModeling software package, and its operational principles as illustrated by the modeling of LED module structure and its light distribution for a street light.

2. MATHEMATICAL MODEL DESCRIPTION

Hierarchical structures in the light devices geometry modeling

When solving a wide range of problems, complex objects are often represented as a collection of simpler ones, which in turn are also disintegrated into smaller components. This process is carried out until the required degree of detail is achieved with the representation of the object in the form of a tree (hierarchical) structure. This approach is very convenient and optimal in the calculation and design of many technical systems, which can be considered as a LD. In this regard, it was decided to consider the LD also in the form of a hierarchical structure. In this case, the LD directly acts as the root element of the tree, where a casing, an optical system, a light source, a protective glass, a suspension assembly and electrics are placed in the next level of the hierarchy (Fig. 1). Each of these parts, in turn, can be presented in more detail. For example, an optical system can be presented in the form of a set of reflector, lens and diffuser.

The elements in this structure are logic nodes. Descending nodes inherit the values of the properties and parameters of the parent nodes. Therefore, if you hide any node, then all of its descendants will also disappear. Similarly, if the descending node does not explicitly specify the type of material, then it is inherited from the parent.

Also, each parent node specifies a geometric basis for the descending nodes. All coordinates are relative. By moving, rotating or scaling any node in space (for example, a light source), its components (bulb, cap) will also move, rotate and scale therewith, forming one indivisible entity.

Logic nodes geometry

To calculate the absolute node coordinates, the following affine transformations are used:

• moving to a vector of

;

• turn around the X axis by an angle of rx

;

• turn around the Y axis by an angle of ry

;

• turn around the Z axis by an angle of rz

;

• scaling along the axes with the coefficients of

;

The coordinates transformation order of points can be carried out in any sequence, but the most common order is: moving, turning around the Z, Y, X axes, scaling. To specify a different order, creating several nested nodes and applying the desired type of transformation to each one in the required sequence, starting with the top-level node, is enough.

Thus, the final expression for converting the relative coordinates to absolute ones according to the given basis of the parent node has the following form

Logical nodes at lower levels of abstraction shall be represented in the form of real objects, for example, reflecting surfaces, light-emitting elements, and heat-conducting plates. The geometry of such nodes is modeled with the help of triangulation grids.

Triangulation grids for light devices geometric modeling

The triangulation grid as such consists of vertices and faces. The vertices define the position of points in space; the faces connect the three given vertices by a planar triangle. Figure 2 shows an example of a LED model with a surface represented as a triangulation grid.

In lighting calculations, there is a problem of modeling smooth surfaces, such as: paraboloids, spheres, cylinders, since in most cases such forms have optical systems that specify the required light distribution [7]. However, if the triangulation grid is assumed to be plane for the purposes of ray tracing, when the rays will be reflected by beams (Fig. 3). In this case, the result of the calculation of the light distribution will not correspond to reality: there will be bursts and dips on the surface of the photometric body where an equal portion should be obtained. Only a significant increase in the density of the triangulation (i. e., an increase in the number of faces per unit area) can partially relieve this undesirable effect.

Hence, the third component of the triangulation grid, the edge, was introduced. It links two vertices and indicates adjacent faces the way to calculate the normal vectors at the associated vertices. For that end, each edge specifies either a sharpening, or a smooth transition between adjacent faces. In the first case (Fig. 4a) the normal vectors at both vertices will be perpendicular to the planes of the corresponding faces. In the second case (Fig. 4b), the normal vectors at these vertices for each face will coincide and shall be calculated as the normalized arithmetic mean of the vectors perpendicular to the faces

.

In the case of smooth transition for these faces, the direction of the normal vector will depend on the location of the point on the triangle surface. This vector is calculated by the following formula

,

where are normal vectors at the corresponding vertices of the ABC triangle, α and β are the barycentric coordinates of the point on the triangle surface.

Fig. 5 shows two variants of torus surfaces defined by the same set of vertices and faces of triangulation grids and differing only in the type of concentric and perpendicular edges.

Thus, the application of this expanded method of specifying a triangulation grid with the use of edges makes it possible to greatly simplify the smooth surfaces approximation process without any increase in the density of the grid as such and without manually specifying the normal vectors.

Resulting model creation

Many LD have the same elements (e. g., LEDs). In order to avoid creating and storing the same triangulation grids for each model node, the grid was mapped based on the node: each node points to a grid which geometry it uses. This principle of modeling is shown schematically in Fig. 6. Now it is enough to simulate one or several basic forms (details), create and arrange logical nodes in space and bind these forms to the nodes. As a result, a model consisting of the same elements is obtained. When you adjust the shape of one part, the forms of the other will synchronously change. The practical application of such scheme is demonstrated by an example of LED module (Fig. 7).

However, when ray tracing is required, it is necessary to denormalize such structure by duplicating nodes and constructing one global triangulation grid. Thus, the presented basic methods for constructing and organizing geometric models are quite applicable to modeling of the LD structural elements. This greatly facilitates the process of calculating, studying and analyzing the devices under development.

3. PRACTICAL IMPLEMENTATION OF THE LD MODELING TASK

The described models are the basis for the developed software package, used for LED optics and devices modeling. The calculation of LED secondary optics is one of the most complex problems in lighting engineering. This package, according to the known LED light distribution and the required light distribution of the device, allows you to simulate the geometry of the lens with a radiating surface providing a comfortable visual perception and easily reproduced by modern production methods.

The following parameters are used as the initial data for the calculation: light intensity curve (LIC is a function describing the dependence of the LED light intensity from the direction of observation in the selected plane, e. g., in the horizontal plane, and it is a cross section of the light distribution by this plane) of LED, the standard (required) LIC of the device, refractive index of the optics material, lens overall dimensions [8].

Fig. 8 shows an example of calculating the light distribution of a single LED module, where the photometric body is given. The color scale, containing information about the minimum and maximum values of the intensity of light, helps to approximately assess the strength of light in a particular direction. When studying and analyzing the obtained data on light distribution, the designer tries to select such parameters of the optical system model in order to obtain the required characteristics of the light device. Fig. 9–12, respectively, show the LD module model for the LD, the model of the LED street light as such, the process of ray tracing from the LED module, the software work window, where the LED and LED module models are reflected, the simplified model of the luminaire, the ray tracing process and the photometric body obtained for a broad light intensity curve.

CONCLUSION

In modern lighting engineering, calculation and modeling of lighting characteristics of light-emitting modules and light devices is an urgent task. The developed program complex allows considerably simplifying the process of designing optical LED systems and improving their quality. In this software package, the light device as a complex product is viewed in the form of a hierarchical structure of parent and descending nodes, which geometry is modeled, using triangulation grids. To smooth the surface of the optical element and the photometric body, an edge was introduced as an additional element of the triangulation grid. This triangulation grid assignment makes it possible to substantially simplify the process of smooth surfaces approximation. Also, the formation of the resulting model was realized in the developed software using basic forms and logic tree, thus ensuring synchronism of changing the forms of the same type elements. Using this software package, we simulated LED secondary optics by developing surface models, ray tracing for a given type of surface with obtaining a photometric body.

The use of light devices with a high coefficient of efficiency makes it possible to significantly increase the efficiency of lighting equipment for mass use and to reduce their energy consumption. Therefore, the design of light devices (LD) is an important and urgent task for the modern lighting industry. The development of the technology of creating light devices is largely determined by the state and development of methods for their lighting design. The results of the calculation largely determine the shape and dimensions of the optical system and the entire LD, as well as its lighting parameters associated with the device application conditions.

The solution of the sequence of direct problems of calculating the LD lies at the heart of the lighting design, i. e. finding the LD light distribution with the known parameters of the optical system and the light source. Various methods for solving the direct LD calculation problem are known, based on the method of elementary mappings, balance of flows and numerical-ray methods [1].

The optical system calculation is the main stage in the development of a light device, since it determines not only the technical properties, but also the consumer ones of the device under development. The optical calculation leads to determination of the geometric characteristics of the optical system and radiation sources, as well as of their parameters that ensure the given photometric characteristics of the light device [2]. When optical calculation is performed, the transmission of light rays in systems consisting of lenses, reflectors, etc. is modeled [3].

1. METHODS AND MEANS FOR CALCULATING AND DESIGNING LIGHTING SYSTEMS

The practice of using different lighting devices indicates the need for flexible methods and means for their design. Numerical and iterative methods are used to calculate the reflecting (refracting) surfaces of a free form, allowing optimizing the shape of the refractive surfaces based on the conditions for the formation of given light distribution. In most cases, the optics calculation is a time-consuming, lengthy and very responsible process. If the optics calculation is performed incorrectly or with errors, it will only become clear after all the other design and construction stages have been completed, when all the planned time and material resources have already been spent. Errors can also occur during the operation of such devices, which is fraught with serious consequences, including in terms of personal safety. Furthermore the effectiveness of existing methods is still not high enough to meet practical needs. Therefore, the problem of optics calculation for the formation of a given lighting still plays a large role [4].

The use of computing technology and the use of specialized software can relieve the engineers from time-consuming calculations, multivariate analysis and a large amount of graphic work. Such automated systems for calculating and modeling of lighting systems using modern software significantly expand the possibilities of modern lighting technology. Modern computer computing technologies allow expanding the possibilities for modeling and researching optical systems significantly, while creating a user-friendly interface.

Currently, the following most famous software products are used in lighting design and production.

DIALux is a professional package for working with lighting, which calculates light characteristics such as brightness, lightness, glossiness, natural light ratio, etc., allowing calculating daylight and shadows when planning lighting, taking into account the geographical location of the building, weather conditions and shadows from surrounding buildings and other objects. DIALux also simulates various light scenes in the rooms.

Light-in-Night Road software product is designed for calculating street lighting, for designing outdoor lighting for off-city highways, street network of cities and rural settlements and related infrastructure. The program allows carrying out lighting calculations for three classes of objects: straight-line sections of roads and streets, typical sections of roads and areas of arbitrary configuration. It calculates the distribution of illumination and brightness of the road surface, normalized values of the average level and uniformity of these characteristics, regulating indicators of blinding the driver by light devices, etc.

However, the analysis of the above mentioned software has shown their task to be mainly in the design of lighting, and they do not deal with calculation and modeling of light-redistributing devices.

For the design of lighting systems, several programs based on different principles of work are used [5]. In some programs, sequence of relative positions of the constituent elements is indicated to represent and analyze the operation of the optical system, and the calculation of the rays is performed sequentially. The other use the global coordinate system and inconsistent calculation of the rays to analyze the operation of the system. This approach is usually applied for the design and analysis of lighting systems.

Currently, foreign software packages such as Zemax, TracePro, Light Tools, OSLO, ASAP, etc. are widely used for the development of optical systems. They have a wide range of functions, including modeling the propagation of light from the sources to radiation receivers.

One Zemax feature is the ability to analyze a consistent and inconsistent calculation of the rays, the ability to calculate designs from lenses, mirrors, diffraction gratings, light filters and other optical elements. LightTools program builds models of lighting systems, where the effects of refraction, reflection, scattering, etc. are taken into account in the calculation of rays. The lighting analysis uses direct ray tracing, which simulates the propagation of light through the model, and a reverse tracer showing the lighting source from the receiver point.

In the design of lighting optical systems, TracePro software is widely used for the calculation of rays and photometric analysis, apparently, due to its low cost. It has a three-dimensional solid-state visualization, the ability to model optical processes based on models created in CAD systems such as SolidWorks, COMPASS. This also significantly facilitates the research process and, importantly, reduces costs for the developer [6].

Photopia (LTI Optics) provides computer modeling of luminaires and their photometric analysis. It can be integrated as a module in SolidWorks, and also allows you to import files into AutoCAD, Pro/Engineer. Furthermore, the program has a database of light sources and materials.

However, many software systems have significant disadvantages: they are sometimes not built to perform highly specialized operations, or require very thorough study of models. Not the least role for their wide promotion in Russia is the cost, which can amount to hundreds of thousands of dollars. Furthermore, there is now an urgent need to reduce the dependence of domestic production on foreign software and the development of proprietary software products.

In connection with the increased need of the Russian lighting industry in computer facilities for research and design of lighting devices, the creation of own software and mathematical tools in the form of a specialized system with the possibilities of geometric modeling has been started. Let’s consider the features of construction of the mathematical model underlying LightModeling software package, and its operational principles as illustrated by the modeling of LED module structure and its light distribution for a street light.

2. MATHEMATICAL MODEL DESCRIPTION

Hierarchical structures in the light devices geometry modeling

When solving a wide range of problems, complex objects are often represented as a collection of simpler ones, which in turn are also disintegrated into smaller components. This process is carried out until the required degree of detail is achieved with the representation of the object in the form of a tree (hierarchical) structure. This approach is very convenient and optimal in the calculation and design of many technical systems, which can be considered as a LD. In this regard, it was decided to consider the LD also in the form of a hierarchical structure. In this case, the LD directly acts as the root element of the tree, where a casing, an optical system, a light source, a protective glass, a suspension assembly and electrics are placed in the next level of the hierarchy (Fig. 1). Each of these parts, in turn, can be presented in more detail. For example, an optical system can be presented in the form of a set of reflector, lens and diffuser.

The elements in this structure are logic nodes. Descending nodes inherit the values of the properties and parameters of the parent nodes. Therefore, if you hide any node, then all of its descendants will also disappear. Similarly, if the descending node does not explicitly specify the type of material, then it is inherited from the parent.

Also, each parent node specifies a geometric basis for the descending nodes. All coordinates are relative. By moving, rotating or scaling any node in space (for example, a light source), its components (bulb, cap) will also move, rotate and scale therewith, forming one indivisible entity.

Logic nodes geometry

To calculate the absolute node coordinates, the following affine transformations are used:

• moving to a vector of

;

• turn around the X axis by an angle of rx

;

• turn around the Y axis by an angle of ry

;

• turn around the Z axis by an angle of rz

;

• scaling along the axes with the coefficients of

;

The coordinates transformation order of points can be carried out in any sequence, but the most common order is: moving, turning around the Z, Y, X axes, scaling. To specify a different order, creating several nested nodes and applying the desired type of transformation to each one in the required sequence, starting with the top-level node, is enough.

Thus, the final expression for converting the relative coordinates to absolute ones according to the given basis of the parent node has the following form

Logical nodes at lower levels of abstraction shall be represented in the form of real objects, for example, reflecting surfaces, light-emitting elements, and heat-conducting plates. The geometry of such nodes is modeled with the help of triangulation grids.

Triangulation grids for light devices geometric modeling

The triangulation grid as such consists of vertices and faces. The vertices define the position of points in space; the faces connect the three given vertices by a planar triangle. Figure 2 shows an example of a LED model with a surface represented as a triangulation grid.

In lighting calculations, there is a problem of modeling smooth surfaces, such as: paraboloids, spheres, cylinders, since in most cases such forms have optical systems that specify the required light distribution [7]. However, if the triangulation grid is assumed to be plane for the purposes of ray tracing, when the rays will be reflected by beams (Fig. 3). In this case, the result of the calculation of the light distribution will not correspond to reality: there will be bursts and dips on the surface of the photometric body where an equal portion should be obtained. Only a significant increase in the density of the triangulation (i. e., an increase in the number of faces per unit area) can partially relieve this undesirable effect.

Hence, the third component of the triangulation grid, the edge, was introduced. It links two vertices and indicates adjacent faces the way to calculate the normal vectors at the associated vertices. For that end, each edge specifies either a sharpening, or a smooth transition between adjacent faces. In the first case (Fig. 4a) the normal vectors at both vertices will be perpendicular to the planes of the corresponding faces. In the second case (Fig. 4b), the normal vectors at these vertices for each face will coincide and shall be calculated as the normalized arithmetic mean of the vectors perpendicular to the faces

.

In the case of smooth transition for these faces, the direction of the normal vector will depend on the location of the point on the triangle surface. This vector is calculated by the following formula

,

where are normal vectors at the corresponding vertices of the ABC triangle, α and β are the barycentric coordinates of the point on the triangle surface.

Fig. 5 shows two variants of torus surfaces defined by the same set of vertices and faces of triangulation grids and differing only in the type of concentric and perpendicular edges.

Thus, the application of this expanded method of specifying a triangulation grid with the use of edges makes it possible to greatly simplify the smooth surfaces approximation process without any increase in the density of the grid as such and without manually specifying the normal vectors.

Resulting model creation

Many LD have the same elements (e. g., LEDs). In order to avoid creating and storing the same triangulation grids for each model node, the grid was mapped based on the node: each node points to a grid which geometry it uses. This principle of modeling is shown schematically in Fig. 6. Now it is enough to simulate one or several basic forms (details), create and arrange logical nodes in space and bind these forms to the nodes. As a result, a model consisting of the same elements is obtained. When you adjust the shape of one part, the forms of the other will synchronously change. The practical application of such scheme is demonstrated by an example of LED module (Fig. 7).

However, when ray tracing is required, it is necessary to denormalize such structure by duplicating nodes and constructing one global triangulation grid. Thus, the presented basic methods for constructing and organizing geometric models are quite applicable to modeling of the LD structural elements. This greatly facilitates the process of calculating, studying and analyzing the devices under development.

3. PRACTICAL IMPLEMENTATION OF THE LD MODELING TASK

The described models are the basis for the developed software package, used for LED optics and devices modeling. The calculation of LED secondary optics is one of the most complex problems in lighting engineering. This package, according to the known LED light distribution and the required light distribution of the device, allows you to simulate the geometry of the lens with a radiating surface providing a comfortable visual perception and easily reproduced by modern production methods.

The following parameters are used as the initial data for the calculation: light intensity curve (LIC is a function describing the dependence of the LED light intensity from the direction of observation in the selected plane, e. g., in the horizontal plane, and it is a cross section of the light distribution by this plane) of LED, the standard (required) LIC of the device, refractive index of the optics material, lens overall dimensions [8].

Fig. 8 shows an example of calculating the light distribution of a single LED module, where the photometric body is given. The color scale, containing information about the minimum and maximum values of the intensity of light, helps to approximately assess the strength of light in a particular direction. When studying and analyzing the obtained data on light distribution, the designer tries to select such parameters of the optical system model in order to obtain the required characteristics of the light device. Fig. 9–12, respectively, show the LD module model for the LD, the model of the LED street light as such, the process of ray tracing from the LED module, the software work window, where the LED and LED module models are reflected, the simplified model of the luminaire, the ray tracing process and the photometric body obtained for a broad light intensity curve.

CONCLUSION

In modern lighting engineering, calculation and modeling of lighting characteristics of light-emitting modules and light devices is an urgent task. The developed program complex allows considerably simplifying the process of designing optical LED systems and improving their quality. In this software package, the light device as a complex product is viewed in the form of a hierarchical structure of parent and descending nodes, which geometry is modeled, using triangulation grids. To smooth the surface of the optical element and the photometric body, an edge was introduced as an additional element of the triangulation grid. This triangulation grid assignment makes it possible to substantially simplify the process of smooth surfaces approximation. Also, the formation of the resulting model was realized in the developed software using basic forms and logic tree, thus ensuring synchronism of changing the forms of the same type elements. Using this software package, we simulated LED secondary optics by developing surface models, ray tracing for a given type of surface with obtaining a photometric body.

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