A Methodology for automatic retrieval of similarly shaped machinable components Mark Ascher - Dept of ECE

Motivation Retrieval of similarly shaped components can: –Add functionality to existing CAD databases –allow for the reuse of process plans which can both speed up and reduce the cost of development. Challenges Retrieval of similarly shaped components has many challenges: –Multiple interpretations –Interacting features –Topological differences do not guarantee component dissimilarity –Graph matching solution is computationally intensive

Contributions Retrieval of sub pieces to cover a component –Use of Maximal Feature Sub-graphs to divide a component Use of type abstraction hierarchies to guide similarity search –Feature and interaction Histogram based –Ability to abstract Features and Interactions of machinable components –Ability to determine distances of features and interactions based on objective criterion

Related Work Shape Based Similarity Retrieval (Eakins) –Two dimensional parts –retrieved complete components Volumetric Reasoning (Lee et al) and Planar Reasoning (Cohn et al) –Groundwork for symbolic volumetric reasoning –Does not address part matching Content Retrieval From Images Based on Knowledge of Shape (Hsu et al) –Worked with medical images –Presented the Type Abstraction Hierarchy Concept

Related Work 3D Model Shape Based Similarity Retrieval (Osada et al, Regli et al) –Uses D2 Distance measures –Works well for simple models Feature Based Model Retrieval (Regli et al) –Retrieves complete models –Feature interaction representation too simplistic –No method for indexing

Related Work Group Technology –Goal is to group components by similar machining processes for improved factory flow –Similar machining processes does not guarantee shape similarity

Query Evaluator User Interface System Overview Query In B-Rep Feature Extractor Query Relaxation Spatial Logic Component Database Geometric Modeler Query Answer Spatial Logic Block Handler

Component Representation In the Database Data Represented in Three Layers –Raw B-Rep Component (Representation Layer) –Graph of Maximal Features and Interactions (Knowledge Layer) –Histograms of Features and Abstracted Interactions (Semantic Layer) Interactions Encoded at Multiple Abstraction Levels –Interaction Matrix –Set of Face Pairs –Abstracted Interaction

Interactions Interactions Represented as an nxm matrix where: –n is the number of faces in feature 1(f1) –m is the number of faces in feature 2 (f2) –Entries are in the set { +, -, s, i} + indicates that f1 lies in the positive half space of f2 - indicates that f1 lies in the negative half space of f2 s indicates they lie on the same plane I indicates that the features interact R 5,2

Interactions Continued If only orthonormal features are considered –Results in 6x6 interaction Matrices –The near diagonal data points contain the pertinent data –The number of unique columns is reduced to 5 ordered types that are physically valid The following notation indicates (same, opposite) face (-,+) No Interaction (-,s) indicates a shared face with no internally shared points (-,-) indicates a face that is interior to both faces of the other feature (s,-) indicates a shared face with internally shared points (+,-) indicates a face that is not interior to one face of the other feature –The following Combinations are invalid: (+,+) can not be outside both faces parallel to the face of interest (s,s) can not be the same as two faces which bound a feature (+,s) and (s,+) can not be same as one face and outside the other

(+,-)(-,s)(+,-) Interactions Continued (-,-) 1 30 (s, -) 2

Interactions Continued Pairs of parallel Faces are compared Resulting in 7 Feasible Unordered face-pair Combinations: (s,-) Face 1Face 2Relation of faces to other Feature (s,-) (-,s) (+,-) (-,-) (+,-) (-,s) Both Faces Shared One Face Shared Other Inside One face shared, Other Outside Opp Not Possible Both Faces Inside One Face Inside, Other Outside Both Outside One Face Shared, Other Outside D B A C F G E Type

Interactions Continued Inverse Relations Exist for some Face-pair Types. (s,-) Face 1Face 2 (s,-) (+,-) (-,-) (+,-) (-,s) Inverse Interaction D E B F C A G D B A C F G E Type E D C B A F G

Interactions Continued Several Face-pair types indicate a family of interactions. -s Face 1Face 2Interaction Family -+ +s Intrusion Face Pass Through E G F Type ---+Improper InteractionC

Show All Interactions Here

Interactions Continued Each Interaction can be represented by three Face-pairs

Query Evaluator User Interface System Overview Query In B-Rep Feature Extractor Query Relaxation Component Database Geometric Modeler Query Answer Block Handler Spatial Logic

The Spatial Logic Utilizes Knowledge encoded in the interactions to: –Reduce Computations to determine Interactions –Determine Closest Matches from Candidate Pool –Guide Query Relaxation –Invalidate Non-Maximal Features Spatial Logic Applied in One Dimension 3D Accomplished by combining 1D results 3D Uses Facts About Maximal Features to: –Reduce Number of Reasoned Interactions –Guide Quantitative Interaction Determination

One Dimensional Examples First Interaction P1 to P2 Face Pair F Logic (1,1) Second Interaction P1 to P3 Face Pair A Logic (3,3) Inferred Interaction P2 to P3 Face Pair A Logic (1,1) New Face Pair Completely Determined –Qualitative Interaction in this dimension known –No Quantitative Computation Required

One Dimensional Examples First Interaction P1 to P2 Face Pair F Logic (1,3) Second Interaction P1 to P3 Face Pair A Logic (3,3) Inferred Interaction P2 to P3 Face Pair A,B,C Logic (1,y) New Face Pair Incompletely Determined –One face determinable –Quantitative Computation Required for One Face

One Dimensional Examples First Interaction P1 to P2 Face Pair F Logic (1,3) Second Interaction P1 to P3 Face Pair F Logic (3,1) Inferred Interaction P2 to P3 Face Pair C, G None Logic (3,z) New Face Pair Incompletely Determined –One face determinable –Interaction Existence In-determinable –Quantitative Computation Required for One Face

One Dimensional Examples First Interaction P1 to P2 Face Pair F Logic (1,1) Second Interaction P1 to P3 Face Pair F Logic (1,1) Inferred Interaction P2 to P3 Face Pair Undeterminable Logic (U) New Face Pair Undeterminable –Not enough information to make any determination –Existence of an interaction unknown –Quantitative Computation Required for both Faces

Inferencing Table Value yN303yN303yNN303y 11NUx3 3x33 N3x33 123yzy2y33z3233N3z yyzy1yy3z313yN3z313y 21Nzyz3 2y23 303y y11 1y21 2y3031 3y 30NNNN333y2y3 31Nzyz3 1y13 y1yyy y1 y2y3 331y11 1y11 1yy1 yy x – -1,0,1,2,3, y – 1,2,3, z – -1,0,1, N – no interaction, U - unknown

Spatial Logic Continued Maximal Features Reduce the Possible Results –No maximal feature can be subsumed by any other single feature –No maximal feature can have an entire face end in the interior of another feature. –No maximal feature shall subsume any other maximal feature –Intersecting Maximal feature must share at least one point interior to a face

Example Logic Application 3 Dimensions Interaction 1 PI-2a B,E,B [(2,1), (2,3), (2,1)] Interaction 2 II-2 B, E, C [(2,1), (3,2) (3,1)] (2,y)(3,1) (3,y) Implies Improper [(2,1), (3,1), (3,1)]OKB, C, CIB-1 [(2,1), (3,1), (3,2)]OKB, C, EII-2 [(2,1), (3,1), (3,3)]OKB, C, FII-1 (Inverse) [(2,2), (3,1), (3,1)]OKD, C, CIB-2 [(2,2), (3,1), (3,2)]Maximally InfeasibleD, C, E--- [(2,2), (3,1), (3,3)]Maximally InfeasibleD, C, F--- [(2,3), (3,1), (3,1)]OKE, C, CIB-1 (Inverse) [(2,3), (3,1), (3,2)]Maximally InfeasibleE, C, E--- [(2,3), (3,1), (3,3)]Maximally InfeasibleE, C, F---

Logic Experiments Interactions presented as the set of interactions were encoded as drawn (no rotations) The interactions were selected pair-wise as submission to the Spatial-Logic The following data was collected –Number of physically possible interaction –Number of interactions possible for Maximal Features

Experimental Results 23 Interactions Compared (529 total pairs) –84 Completely Determined – 15.9% (78 No Interaction) –55 1 undetermined face – 10.4% –94 2 undetermined faces – 17.8% –124 3 undetermined faces – 23.4% –103 4 undetermined faces – 19.5% –60 5 undetermined faces – 11.3% –9 No faces determined 1.7% Maximal Feature Constraints Reduced The Number Of Possibilities an Additional 33.9%

User Interface System Overview Query In B-Rep Feature Extractor Spatial Logic Geometric Modeler Query Answer Spatial Logic Block Handler Query Evaluator Query Relaxation Component Database

Example Database An example database was generated to test out the process –Features were encoded as histograms of feature types Features used were Slots, Blind Slots, Steps, Blind Steps, and Pockets No other feature information was encoded Only maximal features were encoded –Interactions were encoded as histograms of interaction types present (I.e. PI-0, PI-1, etc.) –Two levels of abstraction were used for features and interactions Feature abstractions used the following abstraction scheme: –distinct features –combine blind and through of each type –combine all slots and steps Interaction abstractions used the following abstraction scheme: –Distinct interactions –Combine all proper or improper interactions of individual types –Combine all interactions of individual types (pass-through, intrusion, etc)

Example Database Components

Example Database Each Component was encoded along with any sub-parts. Each Component and Sub-part was then submitted to the database to find the closest match –Distances were calculated as the vector distance between the feature histogram plus the vector distance between the interaction histogram –For abstraction the histogram entries were reduced based on the abstraction scheme –Results for all combinations of feature and interaction abstraction levels were determined –Features and interactions were equally weighted

Example Database Selected Results Component 1 returned matches of components 10 and 25 –Sub part 1 returned component 10 –Sub part 2 returned components 11 and 25 Component 9 returned component 8 and both sub-parts from 7 Component 7 returned component 16 but sub parts returned component 8 Component 17 returned component 32 Component 28 returned components 20 and 23 Component 25 returned components 11, 20 and 26

Example Database Results Summary Generally reasonable results were achieved –The returned parts were qualitatively what would be expected Spatial Logic Not Utilized –Matching would be improved Interaction Type Lowest Level of Knowledge Encoded

Future Work Generate Database of More Complex Parts Implement Spatial Logic with Database Query Evaluation Unit Spatial Logic Symbology