Conflict Resolution of Boolean Operations by Integration in Real-Time Collaborative CAD Systems

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1 Conflict Resolution of Boolean Operations by Integration in Real-Time Collaborative CAD Systems Yang Zheng, Haifeng Shen, Steven Xia, and Chengzheng Sun School of Computer Engineering, Nanyang Technological University, Block N4, Nanyang Avenue, Singapore {zhen0042, ashfshen, stevenxia, Abstract. Boolean operations are widely used in CAD applications to construct complex objects out of primitive ones. Conflict resolution of Boolean operations is a special and challenging issue in real-time collaborative CAD systems, which allow a group of geographically dispersed users to jointly perform design tasks over computer networks. In this paper, we contribute a novel conflict resolution technique that can retain the effects of individual conflicting Boolean operations by integrating them. This technique, named as CRIBO (Conflict Resolution by Integration for Boolean Operations), is in a sharp contrast to other ones that either desert the effects of some operations or keep the effects of different operations in different versions of the design. It is particularly good for collaborative CAD applications, where integration of different mindsets is a main source of creation and innovation. This technique lays a good foundation for resolving conflicting operations in design-oriented collaborative applications that require collective wisdom and stimulus of creation. Keywords: CAD, Boolean operation, conflict resolution, real-time collaborative system, creative design. 1 Introduction Computer Aided Design (CAD) is the use of a wide range of computer-based tools to assist engineers, architects and other design professionals in their design activities. In general, a CAD system is used to design, develop and optimize products, which can be goods used by end consumers or intermediate goods used in other products. It is also extensively used in the design of tools and machinery used in the manufacturing of components as well as in the drafting and design of all types of buildings, from small residential types (e.g., houses) to large commercial and industrial structures (e.g., hospitals and factories). Collaboration has been increasingly needed in the CAD community since early 1990s. As design tasks are getting more and more complex, designers have to work together more and more often as a team rather than individually. With the help of computer networks and online collaboration tools, it is possible to effectively fill up communication gaps among geographically dispersed designers and to significantly R. Meersman, Z. Tari et al. (Eds.): OTM 2007, Part I, LNCS 4803, pp , Springer-Verlag Berlin Heidelberg 2007

2 Conflict Resolution of Boolean Operations 239 reduce the time in both the design and the implementation phase in a product development cycle. CAD designers/draftsmen may use a real-time collaborative CAD system to clarify doubts quickly without leaving their desktops. Designers and the project leader can track bugs and discuss changes in front of computers instead of face-to-face. Engineers from different streams or departments can collaborate to work around a conflicting situation. Furthermore, a collaborative CAD system can be used to interactively demonstrate its main features to customers, or to train or get feedback from customers. Before the advent of real-time collaborative CAD systems, collaboration is mainly facilitated by various online chatting applications such as ICQ [2] and MSN [10]. However, this kind of collaboration could hardly meet the specific needs of technical discussions, in which verbal communication is not enough to express designers ideas clearly and to represent graphical features accurately. Some designers use applicationsharing systems such as Microsoft NetMeeting [11] to share their CAD applications for real-time collaboration. These systems, however, do not support concurrent work and are not responsive in Wide Area Networking (WAN) environments. To meet specific requirements in the CAD community, a few real-time collaborative CAD systems have been developed, which allow designers to manipulate the same design documents at the same time. To achieve high responsiveness in a networking environment, shared documents are usually replicated at each collaborating site so that editing operations can be performed at local sites immediately and then propagated to remote sites. Consistency maintenance is a fundamental issue in these real-time collaborative CAD systems, especially in the presence of conflicting operations. In a distributed environment, users may concurrently issue operations that semantically or syntactically conflict with each other. For example, two move operations may conflict with each other when two users concurrently try to move a particular object to different positions. Several strategies have been proposed to solve conflicting operations. One of those strategies is to adopt a conflict prevention strategy based on pessimistic concurrency control mechanisms such as locking and turn-taking. In these systems, a user has to gain the ownership of the target objects before she/he can edit it, thus preventing other users from generating conflicting operations on the same object. For example, the TOBACO system [8] adopts a floor control mechanism; the Cooperative ARCADE system [13] uses a locking mechanism. This means that at any moment in time, only one active user (i.e., the one who holds the floor/lock on the particular objects) is allowed to perform her/his design. This could significantly degrade the system s responsiveness and furthermore make a design process tedious. Another alternative conflict resolution approach is by means of serialization, which ensures that the effect of executing a group of concurrent operations be the same as if these operations were executed in the same order at all sites. If there is any conflict among concurrent operations, only the effect of the last operation (based on the total ordering) will be kept. This approach was mostly used in early collaborative systems such as GroupDesign [4] and LICRA [3]. However, as a design process is usually complex, it is undesirable to keep the effect of only one operation while destroying the effects of others.

3 240 Y. Zheng et al. A more advanced conflict resolution technique is Multi-Versioning (MV) [9, 14]. The MV technique preserves all users work by keeping multiple versions of shared artifacts. Such a strategy provides better feedback to the users, helps the users to better understand the nature of the conflicts, and to better adjust and coordinate their actions in the face of conflicts. However, MV is not suitable for design-oriented collaborative systems because keeping conflicting operations in different versions of shared objects does not help designers analyze conflicts as a whole or make use of conflicts to stimulate creative design. In this paper, we contribute a novel technique to resolve conflicting Boolean operations. The technique, named as CRIBO (Conflict Resolution by Integration for Boolean Operations), is able to retain the effects of individual conflicting Boolean operations and integrate them as a whole. Compared with previous conflict resolution techniques that either desert the effects of some conflicting operations or keep the effects of different operations in different versions of the design, CRIBO provides designers with a more comprehensive and straightforward view of the conflict. This is particularly good for design-oriented applications as integration of different mindsets is a main source of creation and innovation. The rest of this paper is organized as follows. In Section 2, conflicting Boolean operations are introduced and their special characteristics are analyzed. Section 3 then explains how to resolve conflicting Boolean operations using CRIBO in detail. This includes selecting proper techniques to support CRIBO and specifying rules on how to determine the results for a group of conflicting Boolean operations. In Section 4, we discuss how to use CRIBO to better support collaborative design scenarios that involve Boolean operations and other typical CAD operations. Finally, major contributions of this paper and the future work are summarized in Section 5. 2 Conflicting Boolean Operations Consistency maintenance in the presence of conflicting operations is a challenging issue in collaborative systems. Conflicts are domain-specific and application-specific. Our investigation reveals that operations in the CAD domain have several special characteristics that raise challenging but interesting issues in the face of conflicts. For example, the process of performing a particular CAD operation takes relatively longer time, as users have to interact with the system to specify parameters and select options. In addition, a CAD operation may involve a considerable number of objects, which significantly increases the possibility that concurrent operations have common target objects and may consequently lead to potential conflicts. This paper takes Boolean operations, a representative category of CAD operations, as an example to illustrate the characteristics of conflicting CAD operations and to devise an effective conflict resolution technique for CAD operations. 2.1 Boolean Operations Nowadays, most off-the-shelf CAD systems (e.g., AutoCAD [1] and OneSpace Modeling [12]) are object-based, in which geometrical objects such as rectangles,

4 Conflict Resolution of Boolean Operations 241 circles, polygons and 3D solids can be created and modified. In these systems, complex artificial objects can be constructed out of primitive ones using Boolean operations. In this paper, Boolean operations refer to the three primitive ones Union, Subtract and Intersect, which are supported by most CAD systems. The Union operation, denoted as, is used to join two or more objects into one based on the total geometry of all. The Subtract operation, denoted as, is used to subtract one or more objects from another to create an object based on the remaining geometry. The Intersect operation, denoted as, is used to create a single object from two or more objects based on the intersected geometry. For the good of presentation, we express a Boolean operation with its target objects and its operator. That is, operation O = A B is to Union two objects A and B; operation O = A - B is to Subtract object B from A; and operation O = A B is to Intersect two objects A and B. Figure 1 illustrates the three primitive Boolean operations and their effects 1. Fig. 1. Primitive Boolean operations and their effects 2.2 Conflicting Boolean Operations A Boolean operation has several target objects. In a real-time collaborative CAD environment, when different designers concurrently issue their own Boolean operations, it is possible that those Boolean operations have common target objects. To illustrate this, let s look at a collaborative design scenario. Assume two designers are working together to mold a cubical diamond (marked as D in Figure 2 (a)). To get a desirable shape, a cylinder (marked as C in Figure 2 (a)) and a box (marked as B in Figure 2 (a)) are created. All the three objects are 3D solids. Suppose the two 1 It should be pointed out that there is a specific geometrical relationship between objects A and B and they are actually overlapping with each other. However, this geometrical relationship is not revealed explicitly in Figure1. This is done on purpose so that readers can get a clear idea about the effects of Boolean operations.

5 242 Y. Zheng et al. Fig. 2. Conflicting Boolean operations and their individual effects designers concurrently issue Boolean operations that target at D, C and B. The first designer s operation is O 1 = D C, whereas the second designer s operation is O 2 = D B. Definition 1 Conflicting Boolean operations. Two Boolean operations O 1 and O 2 2 conflict with each other, denoted as O 1 O 2, if and only if O 1 O 2 (i.e., they are concurrent) 3 and Target (O 1 ) Target (O 2 ) null; or there exists another concurrent operation O x, such that O O 1 x and O O x 2. Here, Target (O) denotes the set of objects targeted by a Boolean operation O. 2 In this paper, we suppose O 1 and O 2 are always generated at the same document state. 3 Two operations are concurrent if they are generated without any knowledge of each other. For the formal definition of concurrent operations, readers may refer to [6, 14].

6 Conflict Resolution of Boolean Operations 243 For example, in Figure 2, O O because O O 2 and Target (O 1 ) Target (O 2 ) = {D} null. 3 Resolving Conflicting Boolean Operations by Integration 3.1 Resolving Conflicting Boolean Operations In the face of conflicting Boolean operations, it is important to preserve operations intentions using appropriate techniques to resolve the conflicts. This implies several requirements. First, after resolving the conflicts, only one version that has the effects of all the operations should be produced. This allows designers to analyze the conflicts as a whole and to make use of the conflicts to stimulate design innovation. Second, for an arbitrary group of conflicting Boolean operations, rules should exist to precisely determine the effects of the operations. These rules should be independent of the execution order of those Boolean operations so that consistency can be maintained [14]. Third, the produced effects should be understandable to users so that they can assess the situation, react accordingly and make use of the effects in a collaborative design environment. We propose an innovative conflict resolution technique, which can retain the effects of individual conflicting Boolean operations by integrating them. The biggest challenge here is how to achieve the integration. To explain our solution, we will first introduce some notations. First, given a Boolean operation O, its effect, denoted as E (O), is the geometrical effect when O is successfully performed. Second, given a group of conflicting Boolean operations O 1, O 2,..., O n, their Integrated Effect is denoted as IE ( O1 O 2... On ), where operator is union, subtract or intersect. In a collaborative environment, IE ( O1 O 2... On ) defines the effect after those operations are successfully performed. Third, given a Boolean operation expression whose targeting objects are A 1, A 2,..., A m, its effect is denoted as A A A, where operator is union, subtract or intersect. It should 1 2 m be pointed out that the definitions of E and IE are defined at the operation level whereas is defined at the object level. Therefore, from users point of view, an E or IE expression can always be mapped to an object expression with the format of A1 A2 Am, which provides a more straightforward way to understand the effects of an E or IE expression. We have investigated possible techniques to integrate a group of conflicting Boolean operations. The results revealed that the most appropriate one is to use Union to integrate those operations. For the example in Figure 2, after integrating O 1 and O 2 using Union, the result is ( D C) ( D B) (as shown in Figure 3). The advantages of selecting Union to resolve conflicting Boolean operations are as follows. First, a single version can be obtained from the N individual versions that are created by a group of conflicting Boolean operations O 1, O 2,..., O n. Based on the semantics of Union, all individual operations effects (i.e., E (O 1 ), E (O 2 ),, E (O n ))

7 244 Y. Zheng et al. Fig. 3. The obtained effect after integrating O 1 and O 2 will be interpreted in the produced version and reflected to designers. It should be pointed out that, on some occasions, the effects of the produced version could also be achieved through a serializable execution (to be explained in Section 3.3). However, compared with the serialized one in which the resultant effects can be expected, our approach produces totally unexpected effects, which could well be the source of creative design (to be explained in Section 4). Second, by using Union, the produced version will be consistent at different sites. This is because the Union operator conforms to the Commutative Law (i.e., O 1 O 2 = O 2 O 1 ) and the Associative Law (i.e., (O 1 O 2 ) O 3 = O 1 (O 2 O 3 )). Therefore, given an arbitrary group of conflicting Boolean operations O 1, O 2,..., O n, no matter in which order the operations are executed at a particular site, the obtained geometrical effect is always the same as IE (O 1 O 2 O n ). Third, as Union is an operator that belongs to the CAD community, it is relatively easy for users to understand the produced result as it is natural for them to analyze it using their knowledge about the operator. 3.2 Rules According to our solution, given a group of conflicting Boolean operations O 1, O 2,, O n, the effect of the produced version is IE (O 1 O 2, O n ). As mentioned in the previous section, Union conforms to both the Commutative Law and the Associative Law. As a result, it can be drawn that O 1 O 2 O n = (O 1 O 2, O n-1 ) O n, which means that the effect of Unioning N objects is equal to that of Unioning one object with the other N - 1 objects. Assuming that there are two operations O i and O j, where 1<= i < j <= n, if we can correctly determine IE (O i O j ), then we can correctly determine IE (O 1 O 2 O n ). Therefore, we only need to focus on how to draw rules to determine IE (O i O j ). We first start from the simplest scenario, in which each of the two conflicting Boolean operations targets at only two objects and one of the two objects is targeted by both operations, e.g., Target (O 1 ) = {A, B} and Target (O 2 ) = {B, C}, and Target (O 1 ) Target (O 2 ) = {B}. All possible results of IE (O 1 O 2 ) are listed in Table 1.

8 Conflict Resolution of Boolean Operations 245 O 1 O 2 Table 1. The effects of resolving conflicting Boolean operations B C BmC B - C C - B A B B (AmC) BmC (A B)m(B - C) (A B)m(C - B) A B A B A B C A B A B C A - B (A - B)m(B C) A B C (A - B)m(B - C) (AC) - B B - A (B - A)m(B C) BmC (B - A)m(B - C) (B - A)m(C - B) The rules between two arbitrary conflicting Boolean operations start from the above table and in the end four rules are drawn. In the following part of this section, we will first introduce the four rules and then make an analysis on them. For the good of presentation, we first define complex object sets A, B, C, D and E as operands in conflicting Boolean operations. These object sets are A = A... A, B = B... B, C = C... C, 1 K 1 L 1 M D = D... D, and E = E... E 1 N 1 P where A k (1 k K ), B l (1 l L ), C m (1 m M ), D n (1 n N ) and E p (1 p P) are primitive objects that are the smallest units and not required to be further split in the given Boolean operations. For Boolean operators Union ( ), Intersect ( ), Subtract ( ), we categorize Union and Intersect as positive operators since these two operators conform to the Commutative Law, whereas Subtract is considered as negative operator as it dose not conform to the Commutative Law. Given two conflicting Boolean operations O i and O j, where Oi = A B and Oj = B C, based on Table 1, the effect of integrating O i and O j is A B C. If the two conflicting Boolean operations are O i and O j, where Oi = A B and Oj = B C, the effect of integrating O i and O j is ( A C) B. Based on these two results, we can derive Rule 1 as follows. Rule 1. Conflicting Boolean operations with the same positive operators. Given two conflicting Boolean operations O i and O j, where operator is either Union or Intersect, if O i = A B and O = B C, then the effect of integrating O j i and O j is B ( A C). Rule 2. Conflicting Boolean operations with different positive operators. Given two conflicting Boolean operations O i and O j, where Oi = A B and Oj = B C, the effect of integrating O i and O j is A B, which is the same as E (O i ).

9 246 Y. Zheng et al. Rule 3. Conflicting Boolean Operations with Union and Subtract. Given two conflicting Boolean operations O i and O j, where O = A B, i O = C B D B ( B j S1 S2 S1 BS2 = null, BS1 BS2 = B ) 4, the effect of integrating O i and O j is A B ( C D). Rule 4. Conflicting Boolean Operations with Intersect and Subtract. Given two conflicting Boolean operations O i and O j, where O = D C i X1 E C X 2 ( CX1 CX2 = null, CX1 CX 2 = C ), and Oj = A B or Oj = A CY1 B CY2 ( CY1 CY2 = null, CY1 CY2 = C ), then the effect of integrating O i and O j is E (O i ) E (O j ). 3.3 Rules Analysis In the face of an arbitrary group of conflicting Boolean operations, the four rules can preserve individual operations effects and integrate them as a whole. From designers perspective, the integrated effect is not a premeditated one and thus is new to them. In a collaborative design environment, this new effect could be a great stimulus to design innovation. That is, in a design process, when conflicting Boolean operations are generated, it is usually because there is no obvious or pre-defined solution to those commonly targeted objects (Otherwise, the designers would not target at the same objects and instead, would perform operations on their own objects). In this case, it is vital that a designer has a comprehensive and yet easy-to-understand way to learn other designers ideas, which is provided by applying CRIBO. As a result, a designer can easily analyze other designers ideas and thus achieve design efficiency. It should be pointed out that the integrated effect may also be achieved in a singleuser design environment. To Rule 1, Rule 2 and the Rule 3, a target object appears once and only once in the rule expression, which means that the resulted effect could be achieved by sequentially performing a set of Boolean operations on the target objects. Nevertheless, efficiency can be significantly increased by achieving parallel computing in a collaborative design environment as individual operations are performed at different sites. 4 Significance of the CRIBO Technique in Supporting Creative Design The conflict resolution technique CRIBO distinguishes itself from other techniques in that it can retain the effects of individual conflicting operations by integrating them. This characteristic could significantly benefit a design process, where integration of different mindsets is a main source of creation and innovation. In this section, we 4 i.e., B s1 and B s2 are disjoint subsets of B, and all the elements of B belong to either B s1 or B s2 but not both.

10 Conflict Resolution of Boolean Operations 247 provide concrete examples to show how CRIBO is applied to support collaborative designs that involve Boolean operations and other typical CAD operations. 4.1 Obtain Hard-to-Achieve Effects As mentioned in previous sections, Boolean operations have been widely used in design representation, analysis and manufacturing. In these domains, the inherent complexities of geometrical configuration require strong capability from the CAD tools for the purpose of complex modeling. These applications, with specific requirements in their respective domains [5, 15], require comprehensive and complex modeling functionalities. As a result, the three basic Boolean operations are not enough, and more complex and domain-specific Boolean operations are required. Our investigation on the complex Boolean operations, however, reveals that those operations are all based on the three basic Boolean operations and therefore can be achieved with a proper combination of the basic Boolean operations. However, it is non-trivial to implement complex Boolean operations by combining basic Boolean operations in single-user design environment. For example, the Combine operation is a widely-used complex Boolean operation [16]. As shown in Figure 4, the Combine operation is like the Union operation but removes the portions in common (e.g., the geometrically overlapping part), i.e., Combine (A, B) = (A B) U (B A). It is obvious that the Combine operation cannot be achieved by sequentially executing Boolean operations as it requires a pair of A and B. For example, to achieve this operation in AutoCAD, designers have to make a copy of both A and B, locate them at exactly the same position, perform A B and B A respectively, and in the end union them together. Fig. 4. The Combine operation Such a process is tedious and undesirable in a design session. However, this could be easily solved in a collaborative design environment by purposely generating conflicting Boolean operations and using our conflict resolution strategy to achieve the desired effects. For example, given two users in a real-time collaborative design session, one user performs A B and the other performs B A concurrently. Under the well-defined rules of our conflict resolution strategy (actually based on Rule 4),

11 248 Y. Zheng et al. we can immediately get the geometry of the required result (i.e., (A B) U (B A)), which significantly saves design efforts and simplifies the design process. 4.2 Stimulate Design Innovation Another significant contribution of our conflict resolution strategy is that it can not only resolve conflicts, but also provide new effects based on the conflicting operations. We believe that these effects could dramatically stimulate design innovation and in the long run could significantly benefit the design of collaborative systems. To the best of our knowledge, previous conflict resolution strategies in the CAD community consider a design process as purely a technical process, in which conflicts are usually regarded as being abnormal and should be avoided as soon as possible. However, a collaborative design process is not as simple as this and other factors, especially social factors between different designers (who are usually from different domains) should also be taken into account. As argued in [7], a collaborative design process is mostly a socio-technical process, in which conflicts must be systematically and explicitly dealt with as a resource to drive design innovations. For example, consider a collaborative design scenario in Figure 5. Three users are trying to get creative shapes based on the three primitive ones, which are represented as A, B and C. At a particular time, they concurrently issue their own Boolean operations as O 1 = A B, O 2 = A C and O 3 = B C. Three effects are achieved as A B, A C and B C, but none has obvious meanings. However, these operations conflict with each other and as a result, the underlying collaborative system unions the three effects into a new one, which resembles a simple model of an airscrew. This example demonstrates that a collaborative CAD system can not only resolve conflicts, but also achieve new effects based on conflicting operations. More importantly, these new effects are not randomly generated, but are based on welldefined rules. This ensures that the effects have relationships with all the individual effects and thus could very likely stimulate designers ideas. 4.3 Applying CRIBO to Other CAD Operations As proved in previous sections, CRIBO can resolve conflicting Boolean operations by integration and provide new effects to stimulate design innovation. Our investigation shows that this technique lays a good foundation for resolving other conflicting operations in design-oriented collaborative applications. The key to achieving this, however, is to select the most appropriate approach to integrate those conflicting operations. Such a selection is non-trivial because the integration depends on several aspects, such as the conflicting operations semantics and their working environments. In the following section, we will explain how to find out the appropriate approaches to resolving conflicts that involve other typical CAD operations, including the rotate operation and the color operation.

12 Conflict Resolution of Boolean Operations Apply CRIBO to the Rotate Operation Rotate is a typical CAD operation, which allows users to rotate an object around a specified point based on a particular angle value. In a real-time collaborative design environment, two rotate operations may conflict with each other if they concurrently target at the same object but attempt to rotate it in different directions. Fig. 5. Achieve the effects of an airscrew by resolving conflicts Let s look at a simple but interesting scenario. Suppose two designers are collaborating to design the layout of a living room. At a time, they are to determine where to arrange the bed, as shown in Figure 6 (a). Both designers have their own arrangement criteria. The first designer wants the bed to be near the window so that it can gain more sunshine whereas the second designer wants it to be opposite to the door to avoid noise at the corridor. As a result, they concurrently issue their own rotate operations and locate the bed according to their preferences, as shown in Figure 6 (b) and (c), respectively. Obviously, the two designers intentions can coexist (as they are based on different criteria) and therefore should both be reflected in the design. However, previous collaborative design systems would consider them as a conflict as they rotate the same objects to different positions and directions. As a result, designers may receive messages about the conflicts, communicate to explain their intentions to each other and then try to find another solution to satisfy both criteria. This tedious process could be effectively shortened by using CRIBO. For example, suppose a rotate operation is represented as Rotate (object, base-point, rotate-angle).

13 250 Y. Zheng et al. In the face of two conflicting rotate operations, we can integrate both operations effects into one, in which the centroid of the object is the mid-point of the two basepoints and the new direction is an average of the rotate-angles. Based on this rule, we can determine the arrangement of the bed by integrating both designers operations. As shown in Figure 6 (d), the bed is located at a position that is opposite to the door and not far from the window, which could satisfy both designers intentions Apply CRIBO to Color Operation Color is a vastly-used CAD operation. It can fill a graphic object based on user specified colors or texture patterns. In a real-time collaborative design environment, two color operations may conflict with each other if they concurrently target at the same object but fills it with different colors. Fig. 6. Resolve conflicting rotate operations using CRIBO To explicitly explain this scenario, let s look at an example. Suppose three designers are in a real-time design process to determine which colors should be filled in to an object A, whose original color is black. For the good of presentation, we assume a color operation is represented as Color (object, old-color, new-color). Suppose the designers concurrently issue three color operations O 1, O 2 and O 3. These operations are O 1 = color (A, black, red), O 2 = color (A, black, green) and O 3 = color (A, black, blue). Obviously, the three operations conflict with each other as they are trying to change the same object (i.e., A) to different colors.

14 Conflict Resolution of Boolean Operations 251 This conflict can be resolved using CRIBO by integrating the three colors into another based on classical color storage scheme in graphic design. That is, for three operations O 1, O 2 and O 3, suppose O 1 s new color is represented as an RGB triple <R 1, G 1, B 1 >, O 2 s is represented as <R 2, G 2, B 2 > and O 3 s is represented as <R 3, G 3, B 3 >. Then the mixture of O 1, O 2 and O 3 s new colors is equal to <(R 1 +R 2 +R 3 ) mod 256, (G 1 +G 2 +G 3 ) mod 256, (B 1 +B 2 +B 3 ) mod 256>. Based on this rule, the integration of O 1, O 2 and O 3 in this scenario is filling the object A with the color of white, which is new to all the three designers. Furthermore, the white color is not the only possible new color achievable using CRIBO. As shown in Table 2, we can altogether obtain eight colors from the three original colors. To the best of our knowledge, existing conflict resolution strategies can at most achieve the first four color effects (i.e., black, red, green and blue). However, CRIBO can obtain not only these four colors but also four more colors (i.e., yellow, purple, cyan and white) that could not directly be achieved by using any other strategies. We believe that these new effects could greatly provide designers with collective wisdom and stimulus of creation, especially in those complex design scenarios. It should be pointed out that the aim of using CRIBO is to provide designers with several options to resolve a conflict rather than to produce a specific result. By using CRIBO, designers are able to have all the possible results (e.g., the eight resultant colors in Table 2). After negotiation and discussion, they can inform the underlying collaborative design systems about the selected effects. Such an approach ensures that designers ideas are correctly realized in the design process and prevent potential disputes and conflicts from happening 5 Conclusion Table 2. Differnt color effects achieved by integration Color Integrated operations 1. Black ( no operation integrated ) 2. Red (O 1 ) 3. Green (O 2 ) 4. Blue (O 3 ) 5. Yellow (O 1, O 2 ) 6. Purple (O 1, O 3 ) 7. Cyan (O 2, O 3 ) 8. White (O 1, O 2, O 3 ) Real-time collaborative CAD systems allow a group of users to view and edit the same design document at the same time from geographically dispersed sites connected by networks. With several members working on a project collaboratively and concurrently, it is possible to shorten design cycle, improve design quality and reduce design cost. As those collaborative CAD systems adopt a replicated architecture to achieve quick local responsiveness, consistency maintenance is a fundamental issue, especially in the face of conflicting operations. This article contributes a novel technique CRIBO to resolve conflicting Boolean operations. CRIBO distinguishes itself from previous ones in that it can retain the

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