Eurographics Workshop on 3D Object Retrieval 2009
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Li Han
Mobility Exchange Report: GraphiTech -> Laboratory 3S, INPG (May 1 - October 31, 2006)
Research Summary
- Motivation:the available design tools still limit the designer's freedom through interaction modalities based on a constrained and unnatural language. They thus can't be capable to act directly on the designer's intent. Therefore, the divergence between stylist's conceptual model and the currently adopted modeling paradigm is still big. It therefore becomes essential to provide functional and higher-level operators for designers geared towards aesthetic product design. The aesthetic design activity conventionally starts by a sequence of curve-based 2D sketching. Those curve representations must incorporate geometric models e.g. B-Spline or NURBS-based curves. The higher-level shape operators should be able to convert the geometrical parameters of such curves, e.g. polygon control points, into a set of parameters that are meaningful for a designer, i.e. intuitive. As a result, the designer directly applies the aesthetic properties to the curve by using such semantics-based operators instead of the manipulation of tedious geometric parameters. Specifically this research work is trying to exploit the correlation of the semantic embedded NURBS curve operators with lower geometric parameters.
- Research Implementation:Leyton process grammar, which allows an exhaustive and intuitive classification of curves through intrinsic curvature extrema-based symbolic representation, has demonstrated that each shape can be obtained through a sequence of specific processes and that only six processes are necessary to obtain any 2D closed shape. This research work further expands this theory to the real-time case and it analyzes the curve properties while a set of geometric constraints are added. The quantitative parameters being used for the detection of the curve?s properties are proposed as well. Furthermore, an interactive environment is implemented through an user-driven interactive process, where the constraints are freely added to any selected characteristic point "CP" (curvature extrema point). More important, this work further highlights the correlation between geometric constraints and higher level aesthetic curve control.
- Research Results:This research work provides an implementation of the aesthetic design environment, focusing on shape characteristics and operators understandable by stylists, inside this shape grammar. The user can easily choose the operators in the interface; he/she can just impose the push/pull operations by dragging the selected curvature extrema points. The operator then automatically applies the corresponding constraint imposed by user?s dragging operation together with pre-defined constraint logics to obtain the predictable curve control. Meanwhile during the dragging process, the dynamical curvature analysis provides the stylist the real-time visual feedback for the appropriate control. In order to define the aesthetic operators, the research work analyses four typical characteristics by analyzing the curvature
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Analysis of the properties of curve:
- Small visibility:This characteristic is used to classify the details, considering that a characteristic point is a detail if it has both a small distance and a small curvature variation.
- Sharp corner:it is used to detect if there is dramatic curvature variation between two curvature extrema.
- Symmetric property: when the characteristic point CP has equivalent curvature variation between left and right curvature extremum, whilst they have the same codon.
- Redundant extrema: when the curve segment has frequent curvature variation within a small distance, it certainly causes unnecessary undulations
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Mapping between aesthetic operators and process grammar:
The concepts of acceleration, softness/sharpness, tension, convexity/concavity, flatness, crown, have been specified and valid in FIORES-II European project. This research further emphasizes the correlation between the properties with geometric constraints based on Leyton grammar and our analysis of curve properties. The details refer to the PhD thesis manuscript (Chapter 7). -
Sharpness operator:
It will produce a sharp corner property on the curve without inserting new characteristic points by:- Adding position constraint on the middle-codon curvature extremum "m-" or "M+";
- Fixing the left extrema point Pl and the right extrema point Pr. ;
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Concave/Convex operator:
This operator is used to transform a curve so that it becomes closer to the symmetric enclosing half-circle. The small visibility and symmetric properties are considered by:- Adding dynamic position constraint on the middle-codon curvature extremum "m+" or "M-";
- Analysing how meanwhile the changing of the middle-codon curvature extremum will produce the adjustment of two inflexion points along their normal vector direction n(u).
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Tension operator:
It can be perceived when one curvature minimum with a small curvature value in-between two curvature maxima with high curvature values. The inflexion point is then going to be produced by user-driven dragging produce by pplying the quantitative continuation operator C*m+ (C*M- depending of the initial stage) to decrease the curvature value of the curvature extremum to tend to 0. -
Acceleration operator:
The variation of the tangent is bigger around one end point, accelerating the extremum on the right means increasing the curvature value of the extremum without modifying the position of this point. The tangency constraint is added to one ending point to increase the value and to keep another ending point static.