University of Maribor 1 CADUI' June FUNDP Namur An Interactive Constraint-Based Graphics System with Partially Constrained Form-Features Borut Zalik Laboratory for Computer Graphics & Artificial Intelligence Faculty of Electrical Engineering & Computer Science MARIBOR (Slovenia)

University of Maribor 2 CADUI' June FUNDP Namur Introduction Problems which exist at the input of geometric modelling systems: the designers still have to use the most primitive approach of 'trials and errors' the engineering vocabulary is not supported spatial relationships cannot be expressed. Two promissing approaches: constrained-based and feature-based design of geometric objects

University of Maribor 3 CADUI' June FUNDP Namur 2D interactive constraint-based drawing system is considered. self-evident fact about geometric object are extracted automatically initial approximate data are used in the case of underdimensioning geometric constraints are specified in an interactive way.

University of Maribor 4 CADUI' June FUNDP Namur geometry is divided into two groups –visible geometry (related with topology) –auxiliary geometry (related with geometric constraints).

University of Maribor 5 CADUI' June FUNDP Namur Constraints refer only to the auxiliary geometry (points, lines, and circles).

University of Maribor 6 CADUI' June FUNDP Namur Constraints A constraint describes a relation that should be satisfied. Structural constraints Through (l i, p j )line l i passes through point p j HLine (l i )line l i is horizontal Parallel (l i, l j )lines l i and l j are parallel Dimensional constraints Distance (p i, p j, d)distance between points p i and p j is d Angle (l i, l j,  )angle between lines l i and l j is  Numerical constraints

University of Maribor 7 CADUI' June FUNDP Namur Problems at constraint description An efficient constraint solver has to be implemented. Inserting exact number of constraints. In real applications a huge number of constraints have to be specified. Constraining of free-form shapes is usually not considered.

University of Maribor 8 CADUI' June FUNDP Namur Constraint Solving A local propagation of known states –supports an interactive design –easy to implement. An implementation with BCDG.

University of Maribor 9 CADUI' June FUNDP Namur Form-Features A form-feature is a group of geometric and topolo- gical entities with functional meaning in a certain context. Parametrisation of a form-feature can be different.

University of Maribor 10 CADUI' June FUNDP Namur Solutions: more than one constraining schemes is prepared transformation algorithms are used. Our approach: The form-features are not constrained completely at the time of forming but during the process of combining of individual form-features.

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University of Maribor 12 CADUI' June FUNDP Namur Interactive Constraining Process An untrained user describes the serif as a feature having three line segments and two curves. Conclusion: The user describes the visible geometry. Description does not include spatial relations.

University of Maribor 13 CADUI' June FUNDP Namur The actions of the designer are observed by the system to generate all self-evident facts. Which facts are self-evident? Should we used an automatic detection of constraints based on the "small number  "?

University of Maribor 14 CADUI' June FUNDP Namur Demonstration of our system

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University of Maribor 21 CADUI' June FUNDP Namur Conclusions The system distinguishes between auxiliary and visible geometry By observing the actions of designer the self- evident information is extracted Bézier cubics are constrained in a natural way. Well-constrained and under-constrained objects are handled.

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