Patent Application
20140132619
Developers have proposed various graphics applications which simulate the application of paint to a canvas to produce artwork. There remains an ongoing effort to make these graphics applications more realistic and versatile. A developer will also typically attempt to create painting-related effects in a technically sound manner, to thereby ensure that the effects can be executed on various commercially-available user devices in an efficient and user-friendly manner.
A graphics system is described herein for simulating the interaction of differing media. In operation, the graphics system determines, for each affected position: (a) a type of new medium that a user seeks to add to a simulated canvas; (b) a type of existing medium (if any) that has already been applied to the simulated canvas; and (c) a media interaction behavior that governs the application of the new medium, based on at least factors (a) and (b). The graphics system then applies the new medium to the simulated canvas, if possible, based on the media interaction behavior that has been determined.
In one case, the new medium is a watercolor medium and the existing medium is a hydrophobic (water-repellent) medium, such as an oil medium. In that case, according to one non-limiting implementation, the media interaction behavior specifies that the watercolor medium cannot be applied over the top of the hydrophobic medium. However, in one implementation, the graphics system may simulate the tunneling of the watercolor medium beneath the hydrophobic medium within a flow layer of the simulated canvas.
According to another illustrative aspect, the graphics system can utilize a media adhesion matrix to determine the media interaction behavior. That matrix can be extensible in nature. For instance, a developer or end-user can add new media types and/or new media interaction behaviors to the table, and/or can change existing specified media interaction behaviors.
According to another illustrative aspect, the graphics system may employ various provisions to improve the efficiency of its simulation operation.
The above approach can be manifested in various types of systems, components, methods, computer readable storage media, data structures, articles of manufacture, and so on.
This Summary is provided to introduce a selection of concepts in a simplified form; these concepts are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.
The same numbers are used throughout the disclosure and figures to reference like components and features. Series 100 numbers refer to features originally found in
This disclosure is organized as follows. Section A describes an illustrative graphics system for simulating the interaction of two or more different kinds of media on a simulated canvas. Section B describes illustrative methods which explain the operation of the graphics system of Section A. Section C describes illustrative computing functionality that can be used to implement any aspect of the features described in Sections A and B. Section D provides illustrative details regarding one way of simulating the flow of a watercolor medium within a three-layer model.
As a preliminary matter, some of the figures describe concepts in the context of one or more structural components, variously referred to as functionality, modules, features, elements, etc. The various components shown in the figures can be implemented in any manner by any physical and tangible mechanisms, for instance, by software, hardware (e.g., chip-implemented logic functionality), firmware, etc., and/or any combination thereof. In one case, the illustrated separation of various components in the figures into distinct units may reflect the use of corresponding distinct physical and tangible components in an actual implementation. Alternatively, or in addition, any single component illustrated in the figures may be implemented by plural actual physical components. Alternatively, or in addition, the depiction of any two or more separate components in the figures may reflect different functions performed by a single actual physical component.
Other figures describe the concepts in flowchart form. In this form, certain operations are described as constituting distinct blocks performed in a certain order. Such implementations are illustrative and non-limiting. Certain blocks described herein can be grouped together and performed in a single operation, certain blocks can be broken apart into plural component blocks, and certain blocks can be performed in an order that differs from that which is illustrated herein (including a parallel manner of performing the blocks). The blocks shown in the flowcharts can be implemented in any manner by any physical and tangible mechanisms, for instance, by software, hardware (e.g., chip-implemented logic functionality), firmware, etc., and/or any combination thereof.
As to terminology, the phrase “configured to” encompasses any way that any kind of physical and tangible functionality can be constructed to perform an identified operation. The functionality can be configured to perform an operation using, for instance, software, hardware (e.g., chip-implemented logic functionality), firmware, etc., and/or any combination thereof.
The term “logic” encompasses any physical and tangible functionality for performing a task. For instance, each operation illustrated in the flowcharts corresponds to a logic component for performing that operation. An operation can be performed using, for instance, software, hardware (e.g., chip-implemented logic functionality), firmware, etc., and/or any combination thereof. When implemented by a computing system, a logic component represents an electrical component that is a physical part of the computing system, however implemented.
The phrase “means for” in the claims, if used, is intended to invoke the provisions of 35 U.S.C. §112, sixth paragraph. No other language, other than this specific phrase, is intended to invoke the provisions of that portion of the statute.
The following explanation may identify one or more features as “optional.” This type of statement is not to be interpreted as an exhaustive indication of features that may be considered optional; that is, other features can be considered as optional, although not expressly identified in the text. Finally, the terms “exemplary” or “illustrative” refer to one implementation among potentially many implementations
A. Illustrative Graphics System
Without limitation, the types of media that may be applied to the simulated canvas include a watercolor medium, an oil medium, a graphite medium, a pastel medium, a crayon-type medium, and so on. However, to facilitate explanation, each of these media types will be loosely referred to below as a form of simulated paint. For example, even crayon is referred to as a type of paint in the interest of simplifying the terminology used herein.
The graphics system 100 may also store a media adhesion matrix table 106 in the data store 104. The adhesion matrix table 106 specifies the media interaction behavior that is produced when applying a stroke of new paint over a stroke of existing paint. That is, the stroke of existing paint corresponds to paint of any type that the user has previously applied to the simulated canvas. The stroke of new paint corresponds to paint of any type that the user wishes to apply, at least in part, over the stroke of existing paint. To repeat, the word “paint” encompasses any type of media.
The adhesion matrix table 200 specifies, without limitation, four different types of new paint (oil, watercolor, pastel, and graphite) and four illustrative types of existing paint (oil, watercolor, pastel, and graphite). The adhesion matrix table 200 also specifies three different types of behavior (“apply over,” “non-apply,” and “mixing”). However, each adhesion matrix table is fully extensible in nature. This means that a user can add new kinds of paint to a table, and/or change any behavior specified in the table.
Starting with
According to one manner of behavior, the new paint stroke 310 will have the end result of completely masking the appearance of any existing paint that lies underneath the new paint stroke 310. According to another manner of behavior, the new paint stroke 310 is translucent. The new paint stroke 310 may therefore modify the appearance of the existing paint. For example, the new paint stroke 310 may produce a sheen or glaze over the existing paint. Still other “apply-over” behaviors are possible.
The graphics system 100 can achieve the non-apply behavior in different ways. In one case, the graphics system 100 can prevent application of the new paint to the existing paint, without simulating the flow of the new paint over the existing paint. In another case, the graphics system 100 can simulate a physical phenomenon in which a quantity of new paint that is deposited on an existing paint stroke will be shed from the surface of the existing paint stroke. The shedding process may deposit the new paint at the perimeter of the existing paint stroke. The shedding process itself can be simulated in any level of detail. For example, suppose that the existing paint exhibits simulated three-dimensional ridges produced by the bristles of the brush. The graphics system 100 can simulate the flow of new paint along channels created by the ridges in the existing paint. This flow will depend on the simulated orientation of the canvas with respect to the direction gravity, among other factors.
The graphics system 100 can produce the mixing behavior in different ways. In one case, the graphics system 100 can produce a new color for application to the mixing regions (502, 504) that is a combination of the pigment of the existing paint and the pigment in the new paint. In addition, the graphics system 100 can combine other simulated physical properties of the existing paint and new paint, such as the viscosities of the paints, etc.
Returning to
Another table (not shown) can specify the effect of adding a stroke of new paint to existing paint when the existing paint is dry (instead of wet, which is the assumption of
Other tables (not shown) can be applied for different kinds of tools that are used to apply the paint. For example,
Still other tables are possible for different input scenarios. Factors that may affect the media interaction behavior include, but are not limited to: the type of paint being applied to the simulated canvas; the type of paint that already exists on the simulated canvas; the state of the paint(s) (e.g., whether the paints are wet or dry, etc.); the orientation of the simulated canvas with respect to the direction of gravity; the simulated temperature, humidity, etc. under which the paint(s) are applied; the tool(s) used to apply the paint(s); the curing process(es) (if any) which are applied to the paint(s); the additives (if any) which are added to the paint(s), and so on. Also, the type(s) of paint can take into account different possible chemical and/or mechanical properties of the paints. Generally, one or more adhesion matrix tables may specify behaviors for any combinations of the factors described above, treating the factors as input information to a behavior look-up process.
In another case, a table can define the media interaction behavior when a new paint stroke is added to an area of the simulated canvas having two or more existing layers of paint. In yet another case, any behavior specified in any table can be a composite of two or more component behaviors described above. For example, a behavior may specify that new paint will partially shed away from existing paint, but may also partially adhere to the existing paint.
Returning to
Known techniques can be used to implement the logic components 108 and 110. For example, without limitation, the graphics system 100 can employ the tool modeling functionality described in common-assigned U.S. patent application Ser. No. 12/756,190, filed Aug. 8, 2010, entitled “Simulating Painting,” and naming the inventors of Baxter, III et al. In addition, or alternatively, the graphics system 100 can use the technology described in Chu, et al., “Real Time Painting with an Expressive Virtual Chinese Brush,” IEEE Computer Graphics and Applications, 2004, pp. 76-85.
A logic component 112 assesses the media interaction behavior that will govern the application of new paint to the digital canvas. The logic component 112 executes this task by performing a test for each position of the simulated canvas that is affected by the new paint stroke. For example, the logic component 112 can perform a test for each position encompassed by the footprint determined by the logic component 110. Here, the term “affected position” has broad connotation. In one case, the simulated canvas includes an array of elements. A position may correspond to a particular element in the array, or, more precisely, a representative position of that element in the array. The elements may correspond to pixels, or may have sizes larger than pixels, or sizes smaller than pixels.
In one case, the test may comprise, for each affected position: (a) determining the type of new paint to be applied at that position; (b) determining the type of existing paint that is already applied at that position (if any); and (c) determining the interaction rule that governs the application of the new paint to the existing paint. As explained above, the logic component 112 can take into consideration any number of additional factors in making an adhesion-related assessment.
A logic component 114 applies, at each affected position, the new paint to the surface of the simulated canvas, as per the interaction behavior determined by the logic component 112. In some cases, this operation involves adding the new paint over the top of the existing paint. In other cases, this operation involves prohibiting the addition of the new paint over the top of the existing paint. In other cases, this operation involves mixing the new paint with the existing paint. As explained above, these behaviors can be implemented in different ways to mimic different physical interaction phenomena. And as said, the graphics system 100 can accommodate additional behaviors.
A logic component 116 simulates the effects that are produced by adding the new paint to the existing paint. In some cases, the effects manifest themselves in gradual fashion over a period of time following the application of the new paint to the simulated canvas. For example, consider the scenario in which the user adds a watercolor paint to the surface of the simulated canvas. As will be explained in detail below, the watercolor paint will seep into a flow layer of the canvas. The watercolor paint will then laterally disperse in the flow layer through its simulated fibers. As the watercolor paint dries, the pigments in the paint will move to a fixture layer of the canvas. The logic component 116 simulates this dynamic behavior.
Consider, for example, the particular scenario shown in
However, the watercolor paint seeps into the flow layer and continues to disperse in all directions. In one implementation, the logic component 116 also simulates the tunneling of the watercolor paint beneath the existing oil paint stroke 604. For example, at time t2 the watercolor paint has dispersed to define a first perimeter, and at time t3 the watercolor paint has dispersed to define a second perimeter, larger than the first perimeter. Note that, at time t3, part of the watercolor paint has completely tunneled under the existing oil paint stroke 604 in the flow layer, and has emerged on the “other side” of the oil paint stroke 604. Hence, pigments that have been deposited in the fixture layer will be visible on the other side of the oil paint stroke 604.
The logic component 116 can produce yet other simulation effects. For example, assume that a new oil paint stroke is added to an existing oil paint stroke, and that the existing oil paint stroke is still wet. The logic component 116 can simulate the mixing of pigments in the new and existing paints. (In some cases, the wet paint from the simulated canvas may also move to the brush of the tool, where it mixes with the paint on the brush.)
As a result of its simulation, the logic component 116 can produce an updated image of the simulated canvas in a data store 118. This image is referred to herein as canvas image information. The canvas image information captures the appearance of the simulated canvas at a particular point in time.
The logic component 116 can also store state information in a data store 120 that represents, at a particular time, the state of the simulation produced by the logic component 116. For example, assume that, at the particular time, the watercolor paint is still flowing within the flow layer of the simulated canvas. The logic component 116 can store state information pertaining to this intermediate non-stable state.
Finally, a logic component 122 renders a depiction of the simulated canvas based on the canvas image information. The logic component 122 can then present that depiction to the user using any output mechanism, such as a display device, a printer, and so on. The rendering operation performed by the logic component 122 can take into account such factors as scaling effects, zoom level, panning effects, shadow effects, and so on. The logic component 122 can, in addition, or alternatively, send the canvas image information to a storage device for archiving.
The user can also remove paint that was previously added to the canvas. In one approach, the user accomplishes this objective using an eraser tool. In one implementation, the graphics system 100 performs an erasure operation by removing all layers of media that lie beneath the path of the eraser tool as it traverses the simulated canvas. For example, if a particular part of the simulated canvas includes oil paint applied on top of watercolor paint, the graphics system 100 will remove all paint from the designated part.
The logic component 116 can respond to an erasure command in various scenario-specific ways. Consider, for example, the scenario in which a user removes paint from an area of the canvas that is next to wet watercolor paint. In this case, the logic component 116 can simulate the dispersion of watercolor paint back into the region that has been erased. The user can prevent this effect by: (a) waiting until the watercolor paint has dried before executing an erasure operation; or (b) accelerating the drying process in an artificial manner, e.g., by activating a “dry” command or the like.
In another implementation, the graphics system 100 can provide media-specific eraser tools. For example, the user can employ an oil eraser tool which will have the effect of removing oil paint, but not graphite media, and so on. The user can employ a watercolor eraser tool that will remove watercolor paint, but not oil paint, and so on.
In addition, or alternatively, a user can instruct the graphics system 100 to “undo” one or more previous brush strokes. In one implementation, the graphics system 100 supports the undo functionality by storing the state of the simulated canvas prior to the application of each brush stroke. In some scenarios, all media applied to the simulated canvas has reached a stable state at the time that a user applies a new brush stroke. In other scenarios, some paint remains in transition at the time that the user applies the new stroke. For example, watercolor paint may be dispersing within the flow layer at the time that a user seeks to apply a new paint stroke to the canvas. The graphics system 100 is expected to store more state information for the latter case compared to the former. This is because, in the latter case, it may be appropriate for the graphics system 100 to store state information pertaining to the movement of watercolor paint in plural layers of the simulated canvas.
More generally,
In other cases, the graphics system 100 stores a time-stamped record of each stroke (and other actions) that a user makes to create an artwork. If the user wishes to return to a particular point in time, the graphics system 100 can then erase the entire simulated canvas and re-apply all of the brush strokes to the canvas up to the designated point in time.
The graphics system 100 described with reference to
Starting with
The effectors 704 simulate the manner in which each of the tools may interact with the surface of the simulated canvas to deposit paint on the canvas. A single tool can invoke different effectors depending on how it is used. For example, consider a brush tool. A user can manipulate the brush tool such that it drags across the surface of the simulated canvas. This action invokes a first effector which models, at each instance of time, the footprint of the brush as it moves across the canvas. A user can alternatively flick the same brush towards the canvas, without touching the canvas. This action invokes second effectors, each of which models a drop of paint produced by the flicking motion.
The graphics system 100 can invoke one of the simulators 706 to simulate the effect that paint has when applied to the canvas. Each simulator may implement the logic component 116 of
A rendering mechanism 710, which implements the logic component 122 of
In one case, the machine functionality 802 can be implemented by any kind of standalone user device. Without limitation, illustrative types of user devices include: a personal computer, a laptop or netbook-type computer, a tablet-type computer, a mobile telephone device (e.g., a smartphone device), a game console device, a portable game-playing device, a portable music-playing device, a book reader device, a device having a tabletop or wall interaction/display surface, and so on.
In another case, at least some aspects of the machine functionality 802 can be implemented by remote computer functionality. The remote computer functionality can be provided at a single site, or may be distributed over plural sites. For example at least some aspects of the machine functionality 802 can be implemented by remote server computer equipment, data stores, and so on. For instance, the remote equipment may correspond to cloud computing resources or the like. A user can access this equipment using a user device, via any type of network, such as a wide area network (e.g., the Internet), a local area network, point-to-point links, and so on.
However implemented, the machine functionality 802 can include one or more input mechanisms 804. The input mechanisms 804 can include, but are not limited to, any of: touchscreen input mechanisms, stylus-type input mechanisms, gesture input mechanisms (including the Kinect® device provided by Microsoft Corporation of Redmond, Wash., or other motion-sensing device), key input mechanisms, mouse device input mechanisms, voice input mechanisms, tabletop or wall-mounted input mechanisms, and so on. The machine functionality 802 can also include one or more output mechanisms 806. The output mechanisms 806 can include, but are not limited to, any of: display devices, printer devices, three-dimensional modeling devices (for creating three-dimensional models of artwork), storage devices, and so on. In some cases, the machine functionality 802 can perform interpolation on the canvas image information to increase its resolution for output to certain devices, such as a high-resolution printer.
The machine functionality 802 can also include any type or combination of types of processing resources 808. For example, the machine functionality 802 can employ a combination of one or more central processing units (CPUs) 810 and one or more graphical processing units (GPUs) 812. The machine functionality 802 can devote certain processing tasks to the CPUs 810 and other more computation-intensive tasks to the GPUs 812. For example, the machine functionality 802 can use the CPUs 810 to execute at least parts of the logic component 108 of
The machine functionality 802 includes various memory and data storage resources 814. The CPUs 810 and GPUs 812 can interact with these resources 814 in any manner. In one implementation, for example, the GPUs 812 interact with a set of textures 816. One or more of the textures store constant information used by the simulation operation, such as information defining the grain patterns of the simulated canvas, and so on. In some cases, the machine functionality 802 can store a small tile of such constant information, and the graphics system 100 can duplicate this tile over the entire simulation space. One or more other textures store state information associated with the simulation operation. The following description will clarify the nature of the state information that is stored by the simulation operation (for the case in which watercolor paint is applied to the simulated canvas).
In one mode of operation, the GPUs 812 can perform their functions by leveraging a ping-pong type of buffer. That is, the GPUs 812 can read input information from a first buffer memory. After performing computations using that input information, the GPUs can send processed information to a second buffer memory. The second buffer memory may then provide input information to a next round of computations.
The machine functionality 802 also includes component coupling resources 818. These component coupling resources 818 can include bus infrastructure of any type. For example, the component coupling resources 818 can include communication mechanisms for transferring information between the CPUs 810 and the GPUs 812.
The remainder of this section describes techniques by which the graphics system 100 can simulate the movement of watercolor through a canvas. To begin with,
The graphics system 100 represents the appearance of the watercolor paint during the drying process by combining the pigments in the surface layer 902, the flow layer 904, and the fixture layer 906. But when the watercolor paint has fully dried, the fixture layer 906 holds all of the pigments 920 deposited by the watercolor paint. In one implementation, the graphics system 100 can represent the pigment colors in each layer in cyan/magenta/yellow (CMY) color space, which is a subtractive color space. The graphics system 100 can also combine the colors from different layers in the CMY color space.
However, the graphics system 100 can represent the color of each image element in the final canvas image information in an additive color space, such as the red/green/blue (RGB) color space. More specifically, the graphics system 100 can represent the color using color information (e.g., that defines the RGB color) together with concentration information (e.g., that describes the concentration of the RGB color). The graphics system 100 can adopt this manner of expressing color to accommodate the depiction of light-colored paints on dark backgrounds, in addition to the more common use of paints of varying colors on light-colored backgrounds.
More specifically, a position x 1002 identifies an element within a lattice in a D2Q9 lattice model. In the streaming phase, the LBE technique simulates the movement of particles in nine discrete directions with respect to x, defined by vectors (e0, e1, e2, e8).
Different known techniques can be used to implement the LBE equation. In one approach, the graphics system 100 can apply the mathematical equations set forth in Section D below. Those equations, in turn, are based on the modeling described in Chu, et al., “MoXi: Real-time Ink Dispersion in Absorbent Paper,” ACM Transactions on Graphics, Vol. 24, Issue 3, July 2005, pp. 504-511.
In the first pass, a logic component 1208 simulates the flow of watercolor from the surface layer 902 into the flow layer 904 (pertaining to the absorption operation 914). A logic component 1210 then executes the first phase of the LBE technique (corresponding to the flow operation 916). That is, this process simulates the streaming aspects of the LBE technique. The logic component 1210 can store the results of its processing as a texture. That texture forms an input to the next pass of the processing performed by the simulation logic 1202.
In the second pass, a logic component 1212 performs the second phase of the LBE technique (also corresponding to the flow operation 916). That is, this process simulates collision of fluid particles that arrive at the same element. A logic component 1214 simulates the evaporation of water in the flow layer 904 and the movement of pigments from the flow layer 904 to the fixture layer 906 (corresponding to the fixation operation 918). A logic component 1216 renders the output of the second pass to the canvas image information. The resultant colors produced in this process represent a combination of the pigments in the three layers (902, 904, 906).
In executing the above-described process, the simulation logic 1202 maintains various kinds of state information. For each element of the surface layer 902, the simulation logic 1202 stores water concentration information, glue concentration information, color information, and color concentration information (α). The simulation logic 1202 can represent the color information in CMY space. For each element in the flow layer 904, the simulation logic 1202 stores LBE particle distribution information for the nine vectors identified above, glue concentration information, color-related information (CMYα), and a blocking factor (κ) (to be described in Section D). For each element of the fixture layer 906, the simulation logic 1202 stores color-related information (CMYα) associated with the pigments that have come to rest in this layer 906.
A logic component 1218 defines a bounding box of elements for which the above-described two-pass processing is to be performed. The logic component 1218 can update this bounding box after each iteration of the processing, e.g., to take account for the movement of watercolor paint, the application of new paint strokes, and so on. The logic component 1218 can repeat its processing until all of the elements in the bounding box have dried. The logic component 1218 creates a new bounding box when (and if) the user later applies another paint stroke. The logic component 1218 also initiates the two-pass iterative processing with respect to the elements in the new bounding box.
Another logic component 1220 can make various adjustments to the two-pass process to make it more efficient. For example, the logic component 1220 can determine whether the machine functionality 802 has failed to meet a threshold level of performance when executing the two-pass processing. If so, the logic component 1220 can decrease the frequency at which the processing is performed and the canvas image information is updated. Alternatively, or in addition, the logic component 1220 can coarsen the granularity of elements for which analysis is performed, e.g., by increasing the size of the elements shown in
The simulation logic 1202 can adopt other measures to make the two-pass processing more efficient. In one case, the simulation logic 1202 can store an instance of first information for each element in the flow layer 904. That instance of the first information expresses the particle density associated with that element. Each instance of the first information has a first size, such as 16 bits in one non-limiting example. The simulation logic 1202 can then store an instance of second information for each of the nine directions (ei) shown in
According to another provision, the simulation logic 1202 can use stencil buffer functionality to define the portion of the simulation space for which the above-described two-pass processing is performed. For example, the simulation logic 1202 need not perform processing for sections of the simulation space in which all of the elements are dry. The simulation logic 1202 can use the stencil buffer functionality to mask out the regions for which updating is not required. In other cases, the simulation logic 1202 can demarcate different regions of the simulation space and perform the two-pass processing for these regions at different respective update rates.
Still other techniques can be employed for accelerating the processing performed by the simulation logic 1202.
B. Illustrative Processes
In block 1302, the graphics system 100 receives an input action from a user. In block 1304, the graphics system 100 determines a manner in which a user is applying a simulated tool. For example, the graphics system 100 determines whether the user has manipulated the tool to deposit a new medium on the surface layer of the simulated canvas. In block 1306, the graphics system 100 determines, for each position of the simulated canvas affected by the application of the new medium: (1) the type of new medium that the user is attempting to add to the simulated canvas; (2) the type of existing medium already applied to the simulated canvas (if any); and (3) the media interaction behavior that governs the manner in which the new medium is applied to the existing medium, if possible. Representative types of behaviors described in Section A include: (a) “apply over,” in which the graphics system 100 adds the new medium over the existing medium; (b) “non-apply,” in which the graphics system 100 prohibits the application of the new medium over the existing medium; and (c) “mixing,” in which the graphics system 100 mixes the new medium with the existing medium.
In block 1308, the graphics system 100 applies the new medium to the simulated canvas, if possible, in accordance with the media mixing behavior determined in block 1306. In block 1310, the graphics system 100 simulates the effects of adding the new medium to the existing medium, to produce canvas image information. In one case, block 1310 may correspond to the three-layer watercolor processing described above. In block 1312, the graphics system 100 renders a depiction of the simulated canvas to the user based on the canvas image information, or outputs the canvas image information to some other output device.
C. Representative Computing Functionality
The computing functionality 1400 can include volatile and non-volatile memory, such as RAM 1402 and ROM 1404, as well as one or more processing devices (e.g., one or more CPUs 1406, one or more GPUs 1408, etc.). The computing functionality 1400 also optionally includes various media devices 1410, such as a hard disk module, an optical disk module, and so forth. The computing functionality 1400 can perform various operations identified above when the processing devices (1406, 1408) execute instructions that are maintained by memory (e.g., RAM 1402, ROM 1404, or elsewhere).
More generally, instructions and other information can be stored on any computer readable medium 1412, including, but not limited to, static memory storage devices, magnetic storage devices, optical storage devices, and so on. The term computer readable medium also encompasses plural storage devices. In many cases, the computer readable medium 1412 represents some form of physical and tangible entity. The term computer readable medium also encompasses propagated signals, e.g., transmitted or received via physical conduit and/or air or other wireless medium, etc. However, the specific terms “computer readable storage medium” and “computer readable medium device” expressly exclude propagated signals per se, while including all other forms of computer readable media.
The computing functionality 1400 also includes an input/output module 1414 for receiving input information from various input mechanisms 1416, and for providing output information to various output mechanisms. One particular output mechanism may include a presentation device 1418 and an associated graphical user interface (GUI) 1420. The computing functionality 1400 can also include one or more network interfaces 1422 for exchanging data with other devices via one or more communication conduits 1424. One or more communication buses 1426 communicatively couple the above-described components together.
The communication conduit(s) 1424 can be implemented in any manner, e.g., by a local area network, a wide area network (e.g., the Internet), etc., or any combination thereof. The communication conduit(s) 1424 can include any combination of hardwired links, wireless links, routers, gateway functionality, name servers, etc., governed by any protocol or combination of protocols.
Alternatively, or in addition, any of the functions described in the preceding sections can be performed, at least in part, by one or more hardware logic components. For example, without limitation, the computing functionality can be implemented using one or more of: Field-programmable Gate Arrays (FPGAs); Application-specific Integrated Circuits (ASICs); Application-specific Standard Products (ASSPs); System-on-a-chip systems (SOCs); Complex Programmable Logic Devices (CPLDs), etc.
D. Appendix: Illustrative Modeling of Watercolor Movement
The graphics system 100 can simulate the movement of watercolor paint using different mathematical models. Without limitation, for instance, the graphics system 100 can apply the mathematical modeling described in the above-referenced Chu, et al. paper, “MoXi: Real-time Ink Dispersion in Absorbent Paper.” This Section describes illustrative modeling equations set forth in that paper, with cross reference back to the concepts set forth with respect to
In one implementation, the graphics system 100 can model the flow of water φ from the surface layer 902 to the flow layer 904 by repetitively applying the equation: φ=clamp(s, 0, π−ρ). In this equation, s represents the quantity of water on the surface layer 902, ρ is the fluid density in the flow layer 904 (defined below), and π corresponds to the capacity of the simulated fibers in the canvas. The clamping function returns the clamped value of s, with respect to a minimum value of 0 and a maximum value of π−ρ. The movement of water to the flow layer 904 changes the values of s and ρ for a next calculation of flow φ.
The graphics system 100 can then use the LBE technique to simulate the flow of water in the flow layer 904. The following equation expresses both the streaming and collision phases of the LBE technique:
f
i(x+eiΔt,t+Δt)=(1−ω)fi(x,t)+wfieq(x,t).
In this equation, ω corresponds to a relaxation parameter (which is related to the viscosity of the fluid), Δt refers to the time interval between successive computations using the equation, and fieq(x,t) refers to an equilibrium distribution function. In one implementation, the equilibrium distribution function may be expressed by:
In this equation, ρ corresponds to the fluid density and u corresponds to velocity, which are respectively defined as:
Further, the symbol ρ0 corresponds to average fluid density, c corresponds to Δx/Δt (where Δx identifies a distance between two closest-neighboring elements in the lattice), wi are constants that reflect the geometry of the lattice, ψ is a weight defined by ψ=smoothstep(0,δ,ρ) (where δ is a user-selected parameter, and the smoothstep operation implements cubic Hermite interpolation).
In one implementation, the streaming step can be more specifically expressed by:
f
i(x,t+1)=τi(x)fk(x,t)+(1−τi(x))fi(x−ei,t).
In this expression, fk refers to a particle distribution function associated with a direction that is opposite to the direction of fi. The symbol τi refers to a factor that operates in the above equation to block the flow of particles in a particular direction i. That is, each element in the lattice is associated with a blocking factor κ. The symbol τi refers to the average of two blocking factors associated with two respective neighboring elements, with respect to the direction i. The blocking factor κ of each element itself represents the accumulated effect of plural factors which impede the flow of fluid. Those factors may include, but are not limited to, the grain of the paper, the variable amount of alum added to the paper, the variable concentration of glue in the flow layer 904, and so forth. Dispersion of fluid in the fibers is also affected by a pinning factor which creates temporary blockages.
Additional equations express the movement of pigments in the water. For example, assume that the symbol ps expresses the concentration of pigments in the surface layer 902, pf expresses the concentration of pigments in the flow layer 904, and px expresses the concentration of pigments in the fixture layer 906. The graphics system 100 can simulate the movement of pigments from the surface layer 902 to the flow layer 904 according to the equation: pf←(pfρ+psφ)/(ρ+φ). The graphics system 100 can simulate the movement of pigments within the flow layer 904 itself as an advection process. And the graphics system 100 can simulate the movement of pigments from the flow layer 904 to the fixture layer 906 to achieve behavior in which: (1) the flow of pigments decreases as the paint dries out; and (2) the flow of pigments decreases with an increase in glue concentration. As noted above, the graphics system 100 treats the pigments as stable in the fixation layer 906 when the paint completely dries out.
In closing, the description may have described various concepts in the context of illustrative challenges or problems. This manner of explanation does not constitute an admission that others have appreciated and/or articulated the challenges or problems in the manner specified herein. Further, the claimed subject matter is not limited to implementations that solve any or all of the noted challenges/problems.
Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.
