T. W. Sederberg, P. Gao, G. Wang, and H. Mu. 2-d shape blending: an intrinsic solution to the vertex path problem. In Proceedings of the 20th annual conference on Computer graphics and interactive techniques, pages 15--18. ACM Press, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of application, including image analysis, morphing, and cartography. Morphing, i.e. continuous transformation of one shape into another, is a particularly important area, due to the wide use in animation, modeling and computer graphics where it is also called shape blending or metamorphosis [4,15]. The problem of morphing polygons or planar triangulations has been attracting a lot of research [6 9,14,16] In Floater and Gotsman [6] an e cient approach for morphing compatible triangulations was introduced, which was further explored in Surazhsky and Gotsman [14] For an application in ....

T.W.Sederberg, P.Gao, G.Wang, H.Mu, 2D shape blending: an intrinsic solution to the vertex path problem. Computer Graphics (SIGGRAPH'93), 27 (1993), 1518.

....Shape Metamorphosis Metamorphosis is the blending of one shape into another. Work on 3D shape blending includes [8, 16] The blending of 2D shapes has widespread application in illustration, animation, etc. and simple (e.g. linear) interpolation techniques usually produce unsatisfactory results [29]. Shinagawa and Kunii [31] propose an method which interpolates differential properties of the 2D shape using the elastic surfaces of [37, 36] Motivated by their approach, we propose a new technique which exploits the properties of D NURBS surfaces. D NURBS provide minimal energy blends which are ....

....along u) interpolating between two closed elliptical curves. Fig. 7(b) shows a linear generalized cylinder obtained with high surface tension in the u direction: ff 1;1 = 1000 and ff 2;2 = fi i;j = 0. Note that the morphing ellipse shrinks as it rotates, a typical artifact of linear interpolation [29]. The rotational component can be preserved, however, by imposing a geometric constraint on the D NURBS which creates a helical surface in the u direction of the cylinder, as shown in Fig. 7(c) Here the only nonzero deformation energy parameter is the rigidity fi 1;1 = 1000. Note that the ....

T.W. Sederberg, P. Gao, G. Wang, and H. Mu. 2-D shape blending: An intrinsic solution to the vertex path problem. In Computer Graphics Proceedings, Annual Conference Series, Proc. ACM Siggraph'93 (Anaheim, CA, Aug.,

....requires manual assistance in order to achieve intuitive and accurate results. A major research challenge is thus to develop techniques that minimize the user assistance when it is not necessary. Morphing has been investigated for various shapes in two dimensions, including polygons, polylines [5,7,10 13], and freeform curves [9] It has also been investigated for images (see [14] for a survey) and in three dimensions (see [8] for a survey) Morphing requires the solutions to two subproblems. The first problem is to find a correspondence (matching) between features of the two shapes. The second ....

T. W. Sederberg, P. Gao, G. Wang, and H. Mu, 2D shape blending: an intrinsic solution to the vertex path problem, Computer Graphics (SIGGRAPH '93), 27 (1993), pp. 15--18.

....as the #rst polygon evolves into the second. Some papers have focused on solving the correspondence problem [3] and take the paths to be simple linear trajectories between corresponding points. Other papers assume that the correspondence is given and address the problem of #nding the vertex paths [8, 15, 16]. Clearly, a natural morph of two simple polygons is one which ensures that all the polygons in between are also simple but at the time of writing this appears to be an open problem. # Corresponding author. E mail: michael.#oater math.sintef.no. 0377 0427 99 see front matter c # 1999 ....

T.W. Sederberg, P. Gao, G. Wang, H. Mu, 2D shape blending: an intrinsic solution to the vertex path problem, Comput. Graphics 27 (1993) 15--18.

....object, through intermediate objects, into a target object. It has numerous applications, including scientific visualization and animation sequences in the film and advertising industries. Much of the work done in the area focused on two dimensional metamorphosis (e.g. 2] 4] 6] 10] 12] [24], 25] 28] Three dimensional morphing sequences are harder to compute, compared to their two dimensional counterparts. They have, however, many advantages over the two dimensional sequences. For instance, changes in the viewing position do not require a repeated computation of the entire ....

T.W. Sederberg, P. Gao, G. Wang, and H. Mu. 2--D shape blending: An intrinsic solution to the vertex path problem. In Proceedings of SIGGRAPH '93, volume 27, pages 15--18. ACM, August 1993.

....shrink during the morphing animation. In the preprocessing step, we construct dependency graphs for the both images. A dependency graph represents the feature curves and the connections among them. The features in the intermediate image are generated by applying the edge angle blending technique [22] on the two graphs. Our morphing system uses the field morphing technique [2] for the warp computation. The field morphing approach is very simple and easy to implement, yet it can generate impressive effects. Since the features of the images are represented using Bezier curves, we use pairs of ....

....circles. Merging the topologies of the projected objects and projecting them back to the original objects obtains the correspondence. In feature based morphing, feature interpolation is very important. This problem is similar to the vertex path problem in shape interpolation. Sederberg et al. [22] proposed an algorithm that blends the intrinsic definitions (edge lengths and vertex angles) of two polygonal shapes (edgeangle blending) In Shapira and Rappoport [23] they represent the interior of the two shapes by using star skeletons representation. Intermediate shapes are generated by ....

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T. Sederberg, P. Gao, G. Wang, and H. Mu. 2D shape blending: An intrinsic solution to the vertex path problem. In Proc. of SIGGRAPH'93, pages 15-18, 1993.

....into the warp that we describe. Lee et al. 10] have described a user interface based on snakes [9] that is useful for feature specification, as well as a new warp based on free form deformations [24] Warps have been applied in other domains as well, such as the work of Sederberg et al. [23] on 2 D curves, Witkin and Popovic[33]on motion curves for 3 D animation, and Lerios et al. 11] on volumes. This paper also presents a scheme for silhouette detection based on rendering the 3 D model into a frame buffer. In general, silhouette detection is closely related to hidden surface ....

Thomas W. Sederberg, Peisheng Gao, Guojin Wang, and Hong Mu. 2D Shape Blending: An Intrinsic Solution to the Vertex Path Problem. In James T. Kajiya, editor, SIGGRAPH 93 Conference Proceedings, Annual Conference Series, pages 15--18. ACM SIGGRAPH, Addison Wesley, August 1993.

....between shapes was first discussed for 2d models, more specifically polygons. Sederberg and Greenwood [Seder92a] propose a physically based approach to establish the correspondence between edges of two polygons. The transformation of the polygons was refined to use an implicit descripition in [Seder93a]. Shapira and Rappoprt make use of star skeleton represesentation of polygons [Shapi95a] The usefullness of morphing between polyhedral objects is known for a long time. First attempts can be found in [ChenP89a] HongM88a] and [KaulR91a] An almost general solution for genus 0 objects was ....

T.W. Sederberg, P. Gao, G. Wang, and H. Mu: 2-D Shape Blending: An intrinsic Solution to the Vertex Path Problem. Computer Graphics (SIGGRAPH `93 Proceedings), 27, 4, 15-18, 1993

....a correspondence alone does not guarantee a smooth transition from the source model to the target one, and the vertices paths have to avoid unpleasant situations such as self intersections. 2D shape blending techniques that deal with the vertices path problem are not easy to extend to 3D [7,9]. The problem of shape blending can also be considered as a problem of body reconstruction from cross sections [6,8] Some of the reconstruction methods use bivariate interpolation by finding a correspondence between the contours of two cross sections. Other methods use a univariate interpolation ....

T.W. Sederberg and P. Gao and G. Wang and H. Mu, 2-D Shape Blending: An Intrinsic Solution to the Vertex Path Problem, in Proceedings of SIGGRAPH '93, 27 (1993), 15-18.

....problem into three steps. In the first step, we introduce an anchor point in the shape and generate a trajectory for the anchor point. In the second step, we consider deformation of the shape along the trajectory of the anchor point. For this part, we use modified edge angle interpolation method [6]. In the third step, techniques from genetic algorithms are used to control the transformation process. A cost function is defined over a transformation process, taking into consideration the total path length, smoothness of the path, and collision freedom of the path. The shape blending problem ....

....by (1 Gamma u)P i uQ i , where 0 u 1. Sometimes, this approach produces undesirable effects such as self intersecting intermediate polygons. An improved approach, edge angle interpolation, was proposed in which 2 edge lengths and angles between the initial and final shapes are interpolated [6]. A modification of the edge angle interpolation is used in the first part of our shape transformation. Similar problems also arise in lofting used in geometric modeling, where a solid is to be constructed from a series of cross sections. Solutions using shortest path search in graphs [7] local ....

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T. W. Sederberg et al. 2d shape blending: An intrinsic solution to the vertex path problem. Computer Graphics (Proc. of SIGGRAPH), 27:15--18, 1993.

.... Animation, CAO, Interpolation, D eformation, Mod elisation g eom etrique A Geometrically Based Approach to 3D Skeleton Curve Blending 3 1 Introduction The animation and deformation of closed plane curves have been widely studied in image analysis [KWT87, KTZ92, ST94] and in computer graphics [SGWM93, SG92]. However, it seems that little attention has been paid in the computer graphics community, to the problem of the transformation of 3D open curves, even though there are many applications for this in animation techniques. For instance, generalized cylinders or implicit surfaces defined by skeleton ....

T.W. Sederberg, P. Gao, G. Wang, and H. Mu. 2D shape blending: An intrinsic solution to the vertex path problem. Computer Graphics (SIGGRAPH'93), 27(2):15--18, August 1993.

....Hug92] and is often used in movies. ffl In design, it is used to create new shapes by combining two objects ( CP89, KR91] Our concern is concentrated in the 3 D shape transformation problem; thus, we will not describe the 2 D approaches (the main approaches can be found in [CP89, BN92, SG92, SGWM93] The 3 D methods can be classified into two families according to the type of information used to compute the intermediate shapes. The volumic approaches [KR91, Hug92] As the volumic information is used to compute the shape transformation, there is no restriction for the topological ....

....two curves with the same number of points since they correspond to sampled values in the parameter space. Simply it is necessary to find a good interpolation process between the two polygonal lines. Henceforth, the terms axis, curve or polygonal line will designate the same entity. As noticed in [SGWM93] a linear interpolation of the two polygonal lines seems to be inadequate. For instance, the interpolation of two parallel segments oriented in opposite directions collapses for some interpolation value; this is not acceptable. Actually we consider the axis as a moving frame, which means that a ....

T.W. Sederberg, P. Gao, G. Wang, and H. Mu. 2D shape blending: An intrinsic solution to the vertex path problem. Computer Graphics (SIGGRAPH'93), 27(2):15--18, August 1993.

....popular approach makes the correspondence induced by the morphing scheme explicit. These techniques first compute correspondences between points (for instance, the vertices) of ff and fi and then creates intermediate shapes as defined by interpolated positions between the corresponding points [9, 18, 21, 22]. Since the interpolated positions are usually chosen to lie on the segments or splines joining corresponding points, these techniques usually find it very difficult to ensure that intermediate shapes do not self intersect. Surprisingly, this interesting problem has received very little attention ....

T. Sederberg, P. Gao, G. Wang, and H. Mu. 2-d shape blending: an intrinsic solution to the vertex path problem. Comput Graph., 27:15--18, 1993. Proc. SIGGRAPH '93.

....one geometric object into another is generally known as morphing, derived from the word metamorphosis , and has become important in computer graphics where geometric objects are used to generate computer images. Several methods are known for morphing two dimensional images [ 2 ] planar polygons [ 8,14,15,16 ], and three dimensional volume data [ 10,11 ] For simple polygons, a complete morph defines both a correspondence between the vertices of the two given polygons and a set of paths along which the corresponding vertices travel as the first polygon evolves into the second. Some papers have focused ....

....the first polygon evolves into the second. Some papers have focused on solving the correspondence problem [ 3 ] and take the paths to be simple linear trajectories between corresponding points. Other papers assume that the correspondence is given and address the problem of finding the vertex paths [ 8,15,16 ]. Clearly a natural morph of two simple polygons is one which ensures that all the polygons in between are also simple but at the time of writing this appears to be an open problem. In this paper we study the related problem of morphing two corresponding tilings. To the best of our knowledge the ....

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T. W. Sederberg, P. Gao, G. Wang, and H. Mu. 2D shape blending: An intrinsic solution to the vertex path problem, Computer Graphics 27 (1993), 15--18.

....are given only a small number of them at selected frames. Because the deformations are given sparsely and do not necessarily correspond to the underlying animation keyframes, we cannot interpolate between them directly (doing so would lead to the typical problems of object blending discussed in [Beie92, Leri95, Witk95, Sede93]) Instead of interpolating directly, we propagate the deformations throughout the underlying animation by factoring out the deformation offsets at the given frames, interpolating between these offsets, then adding the interpolated deformation offsets to the original animated model. This ....

Thomas Sederberg, Peisheng Gao, Guojin Wang, and Hong Mu. 2-D Shape Blending: An Intrinsic Solution to the Vertex Path Problem. In Proceedings of SIGGRAPH 93, pages 15-18. New York, July 1993. ACM.

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Sederberg, T. W., P. Gao, G. Wang, and H. Mu, 2#D shape blending: An intrinsic solution to the vertex path problem, Computer Graphics #Proc. SIGGRAPH# 27 #1993# 15#18. Acknowledgements. This work was supported under NSF grant DMC8657057 and by ONR under grantnumber N000-14-92-J-4064. Guojin Wang, Hong Mu, and Peisheng Gao served as an enthusiastic support team.

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T. W. Sederberg, P. Gao, G. Wang, and H. Mu. 2-d shape blending: an intrinsic solution to the vertex path problem. In Proceedings of the 20th annual conference on Computer graphics and interactive techniques, pages 15--18. ACM Press, 1993.

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T.W.Sederberg, P.S.Gao, G.J.Wang and H.Mu, 2D shape blending: an intrinsic solution to the vertex path problem,

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T. Sederberg, P. Gao, G. Wang, and H. Mu. 2-d shape blending: an intrinsic solution to the vertex path problem. Comput Graph., 27:15-18, 1993. Proc. SIGGRAPH '93.

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Sederberg, T. W., Gao, P., Wang, G., and Mu, H. 2-d shape blending: An intrinsic solution to the vertex path problem. In Computer Graphics (Annual Conference Proceedings), 1993, pp. 15--18.

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T. W. Sedeberg, P. Gao, G. Wang, and H. Mu. 2-D shape blending: An intrinsic solution to the vertex path problem. In Computer Graphics Proceedings, Annual Conference Series, pp 15--18, New York, NY, Aug. 1993. Conference Proceedings of SIGGRAPH '93.

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T. Sederberg, P. Gao, G. Wang, H. Mu. 2-D Shape Blending: An Intrinsic Solution to the Vertex Path Problem. Proc. SIGGRAPH'93, pp.15--18, 1993. 1

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Sederberg TW, Gao P, Wang G, Mu H. 2D shape blending: an intrinsic solution to the vertex path problem. Computer Graphics (SIGGRAPH '93) 1993;27:15}8.

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Sederberg TW, Gao P, Wang G, Mu H. 2D shape blending: an intrinsic solution to the vertex path problem. Computer Graphics (SIGGRAPH '93) 1993;27:15}8.

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T.W. Sederberg, P. Gao, G. Wang, and H. Mu. 2--D shape blending: An intrinsic solution to the vertex path problem. In Proceedings of SIGGRAPH '93, Vol 27, pp 15--18. ACM, August 1993.

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