System and method for visualizing 3D fields with associated variations

Abstract

The present disclosure provides a method and system for rendering 3D data fields with variations. The method includes receiving a 3D representation of a physical object or process, discretized into points defined by a surface mesh or point cloud, values of a main field at a set of points in the 3D representation, and values of a variation field associated with the main field for at least a subset of the set of points. A combined visualization of the main field values and the variation field values is generated and overlaid on the 3D representation, with the overlay configured to spatially correlate the variation field values with the main field values. The combined visualization is then displayed via an output interface. The method can generate dynamic pulsating visualizations or static overlays for both scalar and vector fields, and can be applied in various display environments, such as virtual reality and augmented reality interfaces.

Description

Docket No. 202417635SYSTEM AND METHOD FOR VISUALIZING 3D FIELDS WITH ASSOCIATED VARIATIONSTECHNICAL FIELD

[0001] The present disclosure relates to visualization of three-dimensional data fields, and more particularly to a system and method for visualizing a main field with associated variations (e.g., uncertainties) on a three-dimensional representation of a physical object or process.BACKGROUND

[0002] Three-dimensional (3D) data visualization plays an important role in various fields, including engineering, scientific research, and industrial applications. As technology advances, the ability to generate and analyze complex 3D data sets has become increasingly important for understanding physical phenomena, optimizing designs, and making informed decisions.

[0003] In many applications, 3D data fields represent physical properties or measurements associated with objects or processes. These fields can be scalar, containing a single value at each point in space, or vector, containing multiple values at each point. Examples of such fields include temperature distributions, stress fields, fluid flow velocities, magnetic fields, etc. However, real-world data often comes with inherent variations, such as uncertainties. These uncertainties may arise from measurement errors, computational approximations, or natural variability in the underlying phenomena, among other factors. Understanding and visualizing these variations alongside the primary data can be valuable for assessing the reliability of results and making robust decisions based on the data.

[0004] Traditional visualization techniques for 3D data fields typically focus on representing the main field values using color maps, contour plots, etc. While these methods are effective for displaying the primary data, they often struggle to incorporate additional information about uncertainties or variations associated with the field values. Existing approaches to visualization of variations of 3D fields have limitations. Some methods rely on separate visualizations for the main field and its associated uncertainties, requiring users to toggle between multiple views to correlate contextual information. Others may use simple statistical summaries, e.g., maximum and minimumDocket No. 202417635 variation, that fail to capture the spatial distribution of uncertainties across 3D objects or processes.

[0005] For example, in one-dimensional (ID) charts, error bars may be added to a line to represent uncertainty. For two-dimensional (2D) maps of scalar fields, a third dimension could potentially be utilized to display uncertainty values. However, for 3D scalar or vector fields, effective methods for visualizing associated uncertainties remain an open problem.SUMMARY

[0006] Aspects of the present disclosure provide methods, systems, and computer program products that can address and overcome one or more of the above-described technical challenges. In particular, the present disclosure addresses the challenge of providing a rendering system and method that can effectively visualize both primary field values and their associated variations simultaneously in a 3D representation, while offering flexibility to adapt to different types of data and user requirements.

[0007] According to one aspect of the present disclosure, a method for rendering 3D data fields with variations is provided. The method includes receiving, via an input interface: a 3D representation of a physical object or process, discretized into points defined by a surface mesh or point cloud; values of a main field at a set of points in the 3D representation; and values of a variation field associated with the main field for at least a subset of the set of points. The method also includes generating, via one or more processors, a combined visualization of the main field values and the variation field values overlaid the 3D representation, the overlay configured to spatially correlate the variation field values with the main field values. Additionally, the method includes displaying, via an output interface, the combined visualization.

[0008] According to another aspect of the present disclosure, a computer program product including a non-transitory computer-readable medium storing instructions is provided. When executed by one or more processors, the instructions cause the one or more processors to perform the method for rendering 3D data fields with variations as described above.

[0009] According to yet another aspect of the present disclosure, a rendering system is provided. The rendering system includes an input interface configured to receive: a 3D representation of a physical object or process, discretized into points defined by a surface mesh or point cloud; values ofDocket No. 202417635 a main field at a set of points in the 3D representation; and values of a variation field associated with the main field for at least a subset of the set of points. The rendering system also includes one or more processors and memory storing instructions executable by the one or more processors to generate a combined visualization of the main field values and the variation field values overlaid the 3D representation, the overlay configured to spatially correlate the variation field values with the main field values. Additionally, the rendering system includes an output interface configured to display the combined visualization.

[0010] Additional technical features and benefits may be realized through the techniques of the present disclosure. Embodiments and aspects of the disclosure are described in detail herein and are considered a part of the claimed subject matter. For a better understanding, refer to the detailed description and to the drawings.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The foregoing and other aspects of the present disclosure are best understood from the following detailed description when read in connection with the accompanying drawings. To easily identify the discussion of any element or act, the most significant digit or digits in a reference number refer to the figure number in which the element or act is first introduced.

[0012] FIG. 1 illustrates a block diagram of a rendering system for visualizing 3D fields with variations, according to aspects of the present disclosure.

[0013] FIG. 2 depicts two snapshots capturing a dynamic pulsating 3D visualization of a scalar field on a circuit board, according to an example embodiment.

[0014] FIG. 3 shows a static visualization of a scalar field on a circuit board with orthogonal segments representing variation, according to an example embodiment.

[0015] FIG. 4 illustrates a static visualization of a scalar field on a circuit board using color saturation to represent variation, according to an example embodiment.

[0016] FIG. 5 depicts two snapshots capturing a dynamic pulsating visualization of a vector field on a ball surface, according to an example embodiment.Docket No. 202417635DETAILED DESCRIPTION

[0017] The following description sets forth exemplary aspects of the present disclosure. It should be recognized, however, that such description is not intended as a limitation on the scope of the present disclosure. Rather, the description also encompasses combinations and modifications to those exemplary aspects described herein.

[0018] As the complexity of data and the need for accurate decision-making increase, there is a growing demand for more sophisticated visualization techniques that can effectively communicate both the main field values and their associated variations in a single, intuitive representation. Addressing these challenges in the design of 3D field visualization systems is desirable for creating tools that are not only technically accurate but also practically useful in real- world scenarios. Such techniques would be valuable across a wide range of applications, from product design and manufacturing to environmental modeling and beyond.

[0019] The methodology proposed in this disclosure is directed to a rendering system and method for visualizing 3D data fields that can generate combined visualizations of main field values and variation field values overlaid on 3D representations of physical objects or processes. The inputs to the rendering system include a 3D representation of a physical object or process, values of a main field (a scalar or a vector field) at a set of points in the 3D representation, and values of a variation field associated with the main field for at least a subset of the set of points. Based on this input, a processor may generate a combined visualization that spatially correlates the variation field values with the main field values. The combined visualization may then be displayed via an output interface.

[0020] Unlike existing methods that display main field data and variation / uncertainty information separately, the proposed methodology combines both into a single, spatially correlated visualization. This integration can allow users to immediately perceive the relationship between main field values and their associated variations without needing to combine multiple visualizations or toggle between different views. This can improve the efficiency of data interpretation. By overlaying the variation field values directly onto the 3D representation of the physical object or process, the methodology can provide context that was often lost in previous solutions. Users can now see exactly where on the object or within the process space variations occur, leading to more informed decision-making and analysis.Docket No. 202417635

[0021] The proposed methodology can work with 3D representations discretized into points, which may be defined, for example, by a point cloud or a surface mesh. The 3D representations can range from simple geometries to complex, high-resolution scans of physical objects or detailed simulation results of processes. By maintaining the 3D nature of variation data in the combined visualization, the methodology can preserve important spatial relationships that might be lost in 2D projections or statistical summaries. This can be particularly valuable for complex geometries or processes where the spatial distribution of variations is critical.

[0022] In some embodiments, the combined visualization may comprise a dynamic pulsating 3D visualization. The dynamic pulsating visualization may alternate a visual characteristic associated with points or patches on the 3D representation in a range defined by a sum of the main field and variation field (main field + variation field) values. For scalar fields, the visual characteristic may be defined by color or by texture or pattern density. For vector fields, the visual characteristic may be defined by vector glyphs with alternating length and / or orientation. A dynamic pulsating visualization according to the disclosed embodiments can provide information not only about the magnitude of the variation but also the entire range of values that that the variable “main field + variation field” may assume. The range of values of the variable may lie between the main failed value and the maximum variation field value in either direction from the main field value. This can be particularly informative in situations where the main field value is not centrally positioned in the range of the variation values.

[0023] In other embodiments, the combined visualization may comprise a static overlay of the main field and variation field values. For scalar fields, this may include generating a 3D color map representing the main field values with orthogonal segments or color properties representing the variation field values. For vector fields, the main field may be represented by vector glyphs with the variation field represented by visual characteristics of the surface or the vector glyphs. A static visualization can be particularly useful when a snapshot view of the data is required, or when comparing multiple states or configurations side by side.

[0024] Embodiments of the proposed methodology may be applicable across various industries and applications. By way of example, the combined visualizations may be used to simulate operating conditions and assess uncertainties for industrial assets, or to determine regions of high uncertainty and recommend design or operational or maintenance changes.Docket No. 202417635

[0025] Embodiments of the proposed methodology may be particularly suitable in the context of an industrial metaverse, where the combined visualization may be rendered via virtual or augmented reality interfaces, enabling real-time overlay of 3D field data and associated uncertainties on digital twins or physical industrial assets. This may enhance remote monitoring, predictive maintenance, and collaborative decision-making in complex industrial environments. Alternately, the combined visualization may be rendered via a standard computer screen for a more traditional computing visualization.

[0026] Before undertaking the description of specific embodiments, some terms that have been used in the present description and claims are defined:

[0027] The term "object" refers to any physical entity that can be represented in three dimensions. This can include, but is not limited to, industrial assets such as machinery, equipment, or components thereof; manufactured products or prototypes; and so on.

[0028] The term "process" encompasses any dynamic system or phenomenon that can be represented in three dimensions and evolves over time or space. This can include, but is not limited to, fluid flows, heat transfer, chemical reactions, or electromagnetic field propagation. For instance, a "process" could be the airflow around an aircraft wing, the temperature distribution in a furnace, or the stress distribution in a bridge under load.

[0029] The term "main field" refers to the primary set of data values associated with points in a 3D representation. This can be a scalar field, where each point has a single value (e.g., temperature, pressure), or a vector field, where each point has multiple values representing components of the vector (e.g., velocity, force). For example, in a thermal analysis of an engine, the main field could be the temperature distribution across the engine components. In a structural analysis, the main field may represent stress or strain values.

[0030] The term "variation field" encompasses the uncertainty, deviation, or variability associated with the main field values. This may be derived, for example, from comparing multiple simulation results, real-world measurements, or a combination of both. For instance, in a structural analysis, the variation field might represent the range of stress values at each point due to manufacturing tolerances or different loading conditions.Docket No. 202417635

[0031] The term "overlay" refers to the visual superimposition of the variation field information onto the main field visualization. This creates a combined representation where both sets of data are spatially correlated and simultaneously visible.

[0032] The phrase "dynamic pulsating visualization" refers to an animated representation where visual characteristics of the display elements change over time to represent the range of possible values in the main field plus variation field. This can create a pulsing or throbbing effect that intuitively conveys the extent of variation at different points in the 3D space.

[0033] The term "visual characteristic" refers to any perceivable attribute of a graphical element used in the visualization. This can include color, which is the spectral composition of light emitted or reflected by the element; pattern, which is a repeating graphical design; texture, which is the surface quality of the graphical element; or thickness, which is the perceived width or depth of lines or surfaces in the visualization.

[0034] The term "property of a color" refers to specific attributes that define or modify a color's appearance. This can include saturation, which is the intensity or purity of the color; brightness, which is the perceived luminance of the color; or hue, which is the dominant wavelength of the color.

[0035] The term "vector glyph" refers to a graphical symbol used to represent both magnitude and direction of a vector quantity in a visualization. Common examples include arrows, cones, ellipsoids, etc. whose length and orientation represent the vector's magnitude and direction, respectively.

[0036] Turning now to FIG. 1, a rendering system 100 in accordance with one or more embodiments is shown. The rendering system 100 may include an input interface 102, a 3D field overlayer / visualizer 104, and an output interface 110.

[0037] The input interface 102 can include software and / or hardware components that receive and process incoming data. The software components may run, for example, on a PC or on a server or cloud infrastructure. The hardware components may include one or types of input devices (e.g., keyboard, mouse, touchscreen, etc.), dedicated data acquisition cards or network interface controllers, among others.

[0038] The input interface 102 may be configured to receive various inputs, including a 3DDocket No. 202417635 representation 112 of a physical object or process. The 3D representation 112 may be discretized into points. In some embodiments, the 3D representation 112 may include a point cloud, which may be produced, for example, by scanning a physical object. In other embodiments, the 3D representation 112 may include a 3D surface mesh, i.e., a 3D model (e.g., derived from a CAD file) that uses polygon faces to cover a surface, where points may be defined by vortices of the 3D surface mesh.

[0039] The input interface 102 may also receive values of a main field 114 at a set of points in the 3D representation 112. The main field could be a scalar field (e.g., temperature) or a vector field (e.g., stress). The main field values 114 may be obtained, for example, using simulation and / or real-world experimental data. Additionally, the input interface 102 may receive values of a variation field 116 associated with the main field 114 for at least a subset of the set of points. In some cases, the variation field 116 may be provided for all points in the 3D representation 112, while in other cases, it may be provided for only a subset of points, such as locations where sensors are present or where variations are of particular interest. The variation field value for a given point may be specified, for example, as a range. In some cases, the range may define a maximum deviation from the main field value at a given point, which can be in a positive and / or negative direction with respect to the main field value. The variation field values 116 may be obtained through various methods.

[0040] In some embodiments, the variation field values 116 may be computed using uncertainty quantification methods. These methods may include, for example, Monte Carlo simulations, polynomial chaos expansion, or Bayesian inference techniques, among others. Uncertainty quantification methods often define variation values in the form of a probability distribution. This can be particularly useful for complex systems where analytical solutions are not feasible.

[0041] In other embodiments, the variation field values 116 may be determined by comparing and subtracting multiple simulation results. This approach can capture variations arising from different model parameters, initial conditions, or numerical methods. This approach can be particularly useful when exploring the sensitivity of the main field to various factors in the simulation setup.

[0042] In yet other embodiments, the variation field values 116 may be determined by comparing and subtracting experimental data or scans. This approach can account for real-world variability and measurement uncertainties. This approach can be valuable for validating simulation results and capturing variations that may not be accounted for in theoretical models.Docket No. 202417635

[0043] In yet other embodiments, the variation field values 116 may be obtained by comparing and subtracting experimental data or scans with digital models, which may be geometrical, or physics related. This approach may allow for the quantification of discrepancies between theoretical predictions and real- world observations. This can highlight areas where the digital model may need refinement or where physical phenomena not captured by the model are significant. Geometrical comparisons can identify variations in shape or dimensions, while physics-related comparisons can reveal differences in field values or behaviors.

[0044] The 3D field overlayer I visualizer 104 may process the received input data to generate a combined visualization. The 3D field overlayer / visualizer 104 may include one or more processors 106, which may include various processing units such as central processing units (CPUs), graphics processing units (GPUs), or other specialized processors. The processor(s) 106 may execute instructions stored in a memory 108 to perform this processing. The processor(s) 106 may be configured to generate a combined visualization of the main field values 114 and the variation field values 116 overlaid on the 3D representation 112. This combined visualization may spatially correlate the variation field values 116 with the main field values 114, providing a comprehensive view of both the primary data and its associated variations in a single, integrated representation.

[0045] In some embodiments, the processor(s) may be configured to determine points on the 3D representation 112 on which the variation field values 116 are to be overlaid based on a user- specified point selection 118 received via the input interface 102. The point selection 118 may be specified in various ways. For example, the point selection 118 may be based on a spatial discretization factor, which may specify a density or spacing of points at which to display the variation field values 116. This approach may be useful for reducing visual clutter in areas where the variation field 116 is relatively uniform. Alternatively, the point selection 118 may be based on a selected region or component on the 3D representation 112. This may allow users to focus on areas of particular interest or concern. For instance, in a thermal analysis of an engine, a user may choose to display variation field values 116 only on critical components or in areas prone to overheating. In some cases, the point selection 118 may combine both spatial discretization and region selection approaches. For example, a user may specify a higher density of points in a selected (e.g., critical) region, while using a lower density in other areas of the 3D representation 112.

[0046] In some embodiments, the processor(s) 106 may be configured to generate differentDocket No. 202417635 visualization options based on the nature of the main field 114. In some cases, the processor(s) 106 may automatically determine whether the main field 114 is a scalar field or a vector field. For scalar fields, where each point has a single value, the processor(s) 106 may generate options such as color maps or pattern densities to represent the main field values 114. For vector fields, where each point has multiple values (typically up to 3 values per point, representing the components of the vector), the processor(s) 106 may generate options using vector glyphs, such as arrows or cones, to represent both magnitude and direction of the field values.

[0047] The input interface 102 may also be configured to receive a visualization mode selection 120. The visualization mode selection 120 may determine how the main field values 114 and variation field values 116 will be visually represented in the combined visualization 122. The available visualization modes may depend on whether the main field 114 is a scalar field or a vector field.

[0048] For scalar fields, the visualization mode selection 120 may include options such as color mapping, where the main field values 114 are represented by colors and the variation field values 116 are represented by properties of those colors (e.g., saturation or brightness). Another option may be to use orthogonal segments to represent the variation field values 116, with the length of each segment proportional to the magnitude of the variation. For vector fields, the visualization mode selection 120 may include options such as using vector glyphs (e.g., arrows or cones) to represent the main field values 114, with the variation field values 116 represented by visual characteristics of the glyphs or the surface at the corresponding points.

[0049] In some embodiments, the visualization mode selection 120 may also specify whether to generate a static or dynamic visualization. For dynamic visualizations, the mode selection 120 may include parameters such as the cycle speed or frequency of color or vector glyph alternation to represent the range of the variable "main field + variation field".

[0050] The point selection 118 and visualization mode selection 120 may be processed by the processor(s) 106 to generate the combined visualization. For example, the processor(s) 106 may apply the selected point density or region to filter the variation field values 116, and then apply the chosen visualization mode to create the visual representation of both the main field values 114 and the filtered variation field values 116.Docket No. 202417635

[0051] The output interface 110 may be configured to display the combined visualization 122 generated by the processor(s) 106 through various means. In embodiments, the output interface 110 may comprise a virtual reality (VR) interface or augmented reality (AR) interface, which may include various types of head-mounted displays (headsets). For example, when using a VR interface, the combined visualization 122 may be displayed together with a photorealistic rendering of the physical object or process. A photorealistic rendering is an image rendering that is based on simulation of the behavior of light using techniques such as ray tracing (e.g., using tools such as Nvidia Omniverse®, among others). For example, the combined visualization 122 may be superimposed on or displayed next to the photorealistic rendering of the physical object or process. This approach may allow users to interact with and analyze the data in an immersive 3D environment, potentially improving spatial understanding and data interpretation. When using an AR interface, the combined visualization 122 may be overlaid directly on the physical object or process being displayed. The overlay of digital information onto the real world may enable real-time analysis and decision-making in situ, which may be particularly valuable for maintenance, troubleshooting, or quality control applications. In other embodiments, the output interface 110 may include a standard computer screen configured for scientific computing visualizations.

[0052] The output interface 110 may include both hardware and software components. Hardware components may include display devices, graphics cards, or specialized AR / VR equipment. Software components may include rendering engines, graphics libraries, or AR / VR development kits that enable the creation and display of the combined visualization 122 in the appropriate format for the chosen display method.

[0053] Referring to FIG. 2, a combined visualization of main field and variation field values on a 3D representation of a circuit board is shown, according to an example embodiment. The raised sections may represent different components of the circuit board. The generated combined visualization 200 in this case includes a dynamic pulsating 3D visualization where a variable, namely main field + variation field, for a given point or patch on the 3D representation is represented by alternating a visual characteristic associated with the point or patch. The alternation may occur within a range defined by the range of values that the variable "main field + variable field" takes.

[0054] In the example shown in FIG. 2, the main field is a scalar field representing temperature. The visual characteristic used to represent the variable "main field + variation field" may be definedDocket No. 202417635 by color. The dynamic 3D color map generated by the 3D field overlayer / visualizer 104 may represent the values of the variable "main field + variation field" at different points on the 3D surface 202 of the circuit board. The upper and lower snapshots in FIG. 2 illustrate two different states of the dynamic visualization for a region identified as 204. The region 204 may be defined, for example, by a user-selected area or component of the circuit board in the 3D representation. The color of this region may alternate between different values within the range defined by the main field value plus or minus the variation field value at that location. This alternation creates a pulsating effect that visually represents the range of possible values at each point.

[0055] The dynamic pulsating visualization technique not only conveys the magnitude of the variation but also illustrates the full spectrum of possible values that the combined variable "main field + variation field" can take. This visualization method can be particularly valuable in scenarios where the main field value is not centrally positioned within the range of variation values. In such cases, a static representation might fail to accurately convey the asymmetry of the variation or the potential for extreme values in one direction. For example, if a temperature field has a nominal value of 100°C (main field value) but can vary between 90°C and 120°C, a static visualization might not necessarily communicate this asymmetric range. By employing a dynamic pulsating visualization, users can observe the full range of potential values over time. This temporal dimension allows for a more intuitive understanding of the field’s variability and potential extremes. In the temperature example above, users would see the visualization pulsate between 90°C and 120°C, clearly showing that the variation leans more towards higher temperatures than lower temperatures in relation to the main field value.

[0056] In some embodiments, the timing of the dynamic pulsating visualization may be based on a probability distribution of the values taken by the variable "main field + variation field". For example, if the variation follows a normal or Gaussian distribution, the visualization may spend more time displaying colors near the mean value and less time at the extremes. This probabilistic approach to color duration may provide users with an intuitive understanding of not only the range of possible values but also their likelihood.

[0057] While color is used in this example, in other cases, the visual characteristic may be defined by the density of a pattern or texture applied to the 3D surface. The texture or pattern density may increase or decrease to represent higher or lower values of the variable, creating a similar pulsatingDocket No. 202417635 effect. This approach can be effective in monochrome display environments.

[0058] In some embodiments, the combined visualization may incorporate adjustable pulsation frequencies to emphasize different levels of variation intensity. For instance, areas with higher variation may pulse more rapidly, while areas with lower variation may pulse more slowly. This frequency-based approach can provide an additional dimension of visualization, allowing users to quickly identify regions of high variability without relying solely on color or other visual cues.

[0059] Referring now to FIG. 3, a combined visualization 300 of main field and variation field values on a 3D representation of a circuit board is shown, according to another example embodiment. In this case, the generated combined visualization 300 includes a static overlay of the main field values and the variation field values on the 3D representation. The raised sections may represent different components of the circuit board, similar to the representation shown in FIG. 2.

[0060] For a scalar main field such as temperature, the combined visualization 300 may comprise a 3D color map on a surface 302 of the circuit board, where the colors represent the main field values. The variation field values may be represented by segments orthogonal to the 3D surface 302, such as segments 304a, 304b, 304c. The length of these segments may be proportional to the magnitude of the variation field at the corresponding points. The orthogonal segment representation may provide a clear and quantifiable indication of variation magnitude,

[0061] For example, segment 304a may indicate a region of high temperature (e.g., represented by a red color on the surface 302) but with low variation (represented by a short orthogonal segment). Conversely, segment 304b may indicate a region with low temperature (e.g., represented by a blue color on the surface 302) but high variation (represented by a long orthogonal segment). Users can thereby quickly identify both, areas where the main field values are extreme, as well as areas where the variation is significant, providing valuable insights for design or operational decisions.

[0062] In some cases, to avoid visual clutter, the segments indicating variation values may be generated not for all points but for only a subset of the points. For example, a spatial discretization factor (e.g., spacing or density of the points) may be specified by the user through the input interface 102, e.g., via point selection 118. This approach may allow for a clearer visualization while still providing a comprehensive understanding of the variation across the 3D representation.Docket No. 202417635

[0063] In a variant of the illustrated embodiment, the segments may extend through the 3D surface 302 in opposite directions, such that the length of a segment in each direction is proportional to a mathematical deviation from the main field in each direction. This bidirectional representation may be particularly useful when the variation is not symmetrical around the main field value, allowing users to visualize both positive and negative deviations in the relation to the main field value simultaneously.

[0064] Referring now to FIG. 4, a combined visualization 400 of main field and variation field values on a 3D representation of a circuit board is shown, according to another example embodiment. In this case, the generated combined visualization 400 includes a static overlay of the main field values and the variation field values on the 3D representation. The raised sections may represent different components of the circuit board, similar to the representations in FIG. 2 and 3.

[0065] For a scalar main field such as temperature, the combined visualization 400 may comprise a 3D color map on a surface 402 of the circuit board, where the colors represent the main field values. The variation field values may be represented by a property associated with those colors. In the example shown in FIG. 4, the property is color saturation. For example, areas with higher variation may be represented by higher color saturation, while areas with lower variation may be represented by lower color saturation. This approach may allow users to quickly identify regions of high variability while still maintaining a clear view of the main field values. This is illustrated for a selected region 404 of the 3D representation. The region 404 may be selected by the user through the input interface 102, e.g., via point selection 118.

[0066] Referring to FIG. 5, a dynamic pulsating visualization 500 for a vector main field on a 3D representation of a ball is shown, according to an example embodiment. The dynamic pulsating visualization 500 is captured in FIG. 5 by two snapshots. The snapshots show a 3D representation of a ball, which may represent a physical object.

[0067] In this case, the main field is a vector field, and the visual characteristic is defined by vector glyphs, whose length and / or orientation alternates in a range defined by the values of the variable "main field + variation field". Specifically, in the shown example, the main field is a deformation force on the surface of the ball. The combined visualization 500 comprises a 3D map representing the main field values by arrows (e.g., 504a, 504b, 504c), whose length and / or orientation alternate in aDocket No. 202417635 range defined by the range in which the variable "main field + variation field" takes values. The length of each arrow may represent the magnitude of the main field vector at that point, while the orientation of the arrow may represent the direction of the main field vector. The variation field may be represented by the range of lengths and / or orientations that each arrow cycles through over time.

[0068] The left and right snapshots may show two different states of the variable "main field + variation field". For example, the arrows shown at 504a, 504b, 504c may have different magnitudes and potentially different orientations between the left and right snapshots. This alternation may create a dynamic pulsating effect, visually representing the range of possible values for both magnitude and direction of the vector field at each point.

[0069] Similar to the embodiment of FIG. 2, the dynamic pulsating visualization 500 not only conveys the magnitude of the variation but also illustrates the full spectrum of possible values that the combined variable "main field + variation field" can take. In some embodiments, the timing of the dynamic pulsating visualization 500 may be based on a probability distribution of the values taken by the variable "main field + variation field". Also, in some embodiments, the frequency or speed of the pulsation may be adjusted to emphasize different aspects of the variation. For example, areas with higher variation may pulse more rapidly, while areas with lower variation may pulse more slowly.

[0070] In other embodiments, not specifically shown in the drawings, a static visualization may be generated for a vector field and its associated variations. In this case, the main field values may again be represented by vector glyphs, while variations may be captured via visual characteristics of the vector glyphs or of the surface on the 3D representation. For instance, in some embodiments, a 3D map may be generated where the main field values are represented by vector glyphs of defined length and orientation. The variation field values may then be represented by a visual characteristic of a surface of the 3D representation at points corresponding to the vector glyphs. This visual characteristic may include color, texture, or opacity of the surface. Alternatively, a 3D map may be generated where the main field values are represented by vector glyphs of defined length and orientation, wherein the variation field values may be represented by a visual characteristic of the vector glyphs themselves. For example, the thickness or color of each arrow may indicate the magnitude of variation at that point. In still other embodiments, the main field values may be represented by vector glyphs colored based on the magnitude of the main field, while the variation field values may be represented by a property associated with the colors of corresponding vectorDocket No. 202417635 glyphs, such as saturation or brightness.

[0071] In some aspects, the proposed methodology may be applied to analyze and optimize industrial assets. For example, the combined visualization 122 may be used to identify regions of high uncertainty in an industrial asset. The processors(s) 106 may analyze the combined visualization 122 to detect areas where the variation field values 116 exceed a predetermined threshold. Based on the identified regions of high uncertainty, the processor(s) 106 may determine recommended design changes, operational adjustments, or maintenance activities for the industrial asset. These recommendations may be output via the output interface 110, potentially in the form of a report or interactive visualization.

[0072] The proposed methodology have many other engineering and industrial applications. For example, in the field of aerospace engineering, the combined visualization may be used to analyze stress distributions or aerodynamic properties of aircraft components, allowing engineers to identify areas of high variability that may require additional testing or design modifications. In the automotive industry, the system may be employed to visualize and analyze crash test simulation results, helping designers optimize vehicle safety features by focusing on areas with high uncertainty in impact response. In the realm of environmental science, the rendering system may be utilized to visualize climate models or pollution dispersion patterns. The ability to represent both the main field values and variation field values simultaneously may allow researchers to identify regions where climate predictions are most uncertain, potentially guiding the allocation of resources for additional data collection or model refinement. In the oil and gas industry, the combined visualization may be applied to seismic data analysis. By representing both the main seismic response and the associated uncertainty, geologists and engineers may more accurately assess the potential risks and rewards of drilling in specific locations.

[0073] These diverse applications demonstrate the versatility of the proposed methodology in addressing complex visualization challenges across multiple domains where understanding both primary data and its associated variations is valuable for informed decision-making.

[0074] The embodiments of the present disclosure may be implemented with any combination of hardware and software. In addition, the embodiments of the present disclosure may be included in an article of manufacture (e.g., one or more computer program products) having, for example, a nonDocket No. 202417635 transitory computer-readable storage medium. The computer readable storage medium has embodied therein, for instance, computer readable program instructions for providing and facilitating the mechanisms of the embodiments of the present disclosure. The article of manufacture can be included as part of a computer system or sold separately.

[0075] The computer readable storage medium can include a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network.

[0076] The system and processes of the figures are not exclusive. Other systems, processes and menus may be derived in accordance with the principles of the disclosure to accomplish the same objectives. Although this disclosure has been described with reference to particular embodiments, it is to be understood that the embodiments and variations shown and described herein are for illustration purposes only. Modifications to the current design may be implemented by those skilled in the art, without departing from the scope of the appended claims.

Claims

Docket No. 202417635CLAIMS1. A method for rendering 3D data fields with variations, comprising: receiving, via an input interface: a 3D representation of a physical object or process, discretized into points defined by a surface mesh or point cloud, values of a main field at a set of points in the 3D representation, and values of a variation field associated with the main field for at least a subset of the set of points; generating, via one or more processors, a combined visualization of the main field values and the variation field values overlaid the 3D representation, the overlay configured to spatially correlate the variation field values with the main field values; and displaying, via an output interface, the combined visualization.

2. The method according to claim 1, wherein the generating the combined visualization comprises generating a dynamic pulsating 3D visualization in which a variable, namely main field + variation field, for given point or patch on the 3D representation, is represented by alternating a visual characteristic associated with the point or patch in a range defined by the range in which said variable takes values.

3. The method according to claim 2, wherein the main field is a scalar field, and wherein the wherein the visual characteristic is defined by a color, and / or by a density of a pattern or texture.

4. The method according to claim 2 wherein the main field is a vector field, are wherein the visual characteristic is defined by a vector glyph whose length and / or orientation alternates in a range defined by the range in which said variable takes values.

5. The method according to any of claims 2 to 4, comprising timing the dynamic pulsating visualization based on a probability distribution of the values taken by the variable main field + variation field.Docket No. 2024176356. The method according to claim 1, wherein generating the combined visualization comprises generating a static overlay of the main field values and the variation field values on the 3D representation.

7. The method according to claim 6, wherein the main field is a scalar field, and wherein generating the combined visualization comprises one of: generating a 3D color map representing the main field values and segments orthogonal to a surface of the 3D representation surface representing the variation field values, wherein a length of each segment is proportional to a magnitude of the corresponding variation field value, or generating a 3D color map representing the main field values, and wherein the variation field values are represented by a property associated with those colors.

8. The method according to claim 6, wherein the main field is a vector field, and wherein generating the combined visualization comprises one of: generating a 3D map representing the main field values by vector glyphs of defined length and orientation and representing the variation field values by a visual characteristic of a surface of the 3D representation at points corresponding to the vector glyphs, or generating a 3D map representing the main field values by vector glyphs of defined length and orientation and representing the variation field values by a visual characteristic of the vector glyphs, or generating a 3D map representing the main field values by vector glyphs colored based on a magnitude of the main field and representing the variation field values by a property associated with the colors of corresponding vector glyphs.

9. The method according to any of claims 1 to 7, comprising determining, via the one or more processors, points on the 3D representation on which the variation field values are overlaid based on a specified spatial discretization factor, and / or based on a selected region or component on the 3D representation.Docket No. 20241763510. The method according to any of claims 1 to 9, comprising generating visualization options via the one or more processors by determining whether the main field is a scalar field or a vector field.

11. The method according to any of claims 1 to 10, comprising displaying the combined visualization via a virtual reality interface in which the combined visualization of the main field values and the variation field values are displayed together with a photorealistic rendering of the physical object or process.

12. The method according to any of claims 1 to 10, comprising displaying the combined visualization via an augmented reality interface in which the combined visualization of the main field values and the variation field values are displayed over the physical object or process.

13. The method according to any of claims 1 to 12, wherein the object is an industrial asset, and wherein the method further comprises: analyzing, via the one or more processors, the combined visualization to identify regions of high uncertainty in the industrial asset; determining, based on the identified regions of high uncertainty, recommended design or operational or maintenance changes for the industrial asset; and outputting, via the output interface, the recommended design or operational or maintenance changes.

14. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform the method according to any of claims 1 to 13.Docket No. 20241763515. A rendering system, comprising: an input interface configured to receive: a 3D representation of a physical object or process, discretized into points defined by a surface mesh or point cloud, values of a main field at a set of points in the 3D representation, and values of a variation field associated with the main field for at least a subset of the set of points; one or more processors; memory storing instructions executable by the one or more processors to generate a combined visualization of the main field values and the variation field values overlaid the 3D representation, the overlay configured to spatially correlate the variation field values with the main field values; and an output interface configured to display the combined visualization.

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