A piecewise quintic G 1 spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular B ezier representation, is a ne invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G 1 continuously around a common vertex is solved by constructing C 2-consistent boundary curves. Piecewise C 1 boundary curves and a regular 4-split of the domain triangle make shape parameters available for controlling locally the boundary curves. A small number of free inner control points can be chosen for some additional local shape e ects.

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The display of space filling data is still a challenge for the community of visualization. Direct Volume Rendering (DVR) is one of the most important techniques developed to achieve direct perception of such volumetric data. It is based on semi-transparent representations, where the data are accumulated in a depth-dependent order. However, it produces images that may be difficult to understand, and thus several techniques have been proposed so as to improve its effectiveness, using for instance lighting models or simpler representations (e.g. Maximum Intensity Projection). In this paper we present two perceptual studies that question how DVR meets its goals, in either static or dynamic context. We show that a static representation is highly ambiguous, even in simple cases, but this can be counterbalanced by use of dynamic cues, i.e. motion parallax, provided that the rendering parameters are correctly tuned. Besides, perspective projections are demonstrated to provide relevant information to desambiguate depth perception in dynamic displays.

Triangular Bézier patches are an important tool for defining smooth surfaces over arbitrary triangular meshes. The previously introduced 4-split method interpolates the vertices of a 2-manifold triangle mesh by a set of tangent plane continuous triangular Bézier patches of degree five. The resulting surface has an explicit closed form representation and is defined locally. In this paper, we introduce a new method for visually smooth interpolation of arbitrary triangle meshes based on a regular 4-split of the domain triangles. Ensuring tangent plane continuity of the surface is not enough for producing an overall fair shape. Interpolation of irregular control-polygons, be that in 1D or in 2D, often yields unwanted undulations. Note that this undulation problem is not particular to parametric interpolation, but also occur with interpolatory subdivision surfaces. Our new method avoids unwanted undulations by relaxing the constraint of the first derivatives at the input mesh vertices: the tangent directions of the boundary curves at the mesh vertices are now completely free. Irregular triangulations can be handled much better in the sense that unwanted undulations due to flat triangles in the mesh are now avoided.

In this paper, we present a user study on the use of Depth of Field for depth perception in Direct Volume Rendering. Direct Volume Rendering with Phong shading and perspective projection is used as the baseline. Depth of Field is then added to see its impact on the correct perception of ordinal depth. Accuracy and response time are used as the metrics to evaluate the usefulness of Depth of Field. The on site user study has two parts: static and dynamic. Eye tracking is used to monitor the gaze of the subjects. From our results we see that though Depth of Field does not act as a proper depth cue in all conditions, it can be used to reinforce the perception of which feature is in front of the other. The best results (high accuracy & fast response time) for correct perception of ordinal depth is when the front feature (out of the users were to choose from) is in focus and perspective projection is used.

We describe a method for multiresolution deformation of closed planar curves that keeps the enclosed area constant. We use a wavelet based multiresolution representation of the curves that are represented by a finite number of control points at each level of resolution. A deformation can then be applied to the curve by modifying one or more control points at any level of resolution. This process is generally known as multiresolution editing to which we add the constraint of constant area. The key contribution of this paper is the efficient computation of the area in the wavelet decomposition form: the area is expressed through all levels of resolution as a bilinear form of the coarse and detail coefficients, and recursive formulas are developed to compute the matrix of this bilinear form. A similar result is also given for the bending energy of the curve. The area constraint is maintained through an optimization process. These contributions allow a real time multiresolution deformation with area constraint of complex curves.

The display of space filling data is still a challenge for the community of visualization. Direct Volume Rendering (DVR) is one of the most important techniques developed to achieve direct perception of such volumetric data. It is based on semi-transparent representations, where the data are accumulated in a depth-dependent order. However, it produces images that may be difficult to understand, and thus several techniques have been proposed so as to improve its effectiveness, using for instance lighting models or simpler representations (e.g. Maximum Intensity Projection). In this paper we present two perceptual studies that question how DVR meets its goals, in either static or dynamic context. We show that a static representation is highly ambiguous, even in simple cases, but this can be counterbalanced by use of dynamic cues, i.e. motion parallax, provided that the rendering parameters are correctly tuned.

Transforming an arbitrary mesh into a smooth G 1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G 1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces.