Abstract
Three-dimensional mesh fusion provides an easy and fast way to create new mesh models from existing ones. We introduce a novel approach of mesh fusion in this paper based on functional blending. Our method has no restriction of disk-like topology or one-ring opening on the meshes to be merged. First of all, sections with boundaries of the under-fusing meshes are converted into implicit representations. An implicit transition surface, which joins the sections together while keeping smoothness at the boundaries, is then created based on cubic Hermite functional blending. Finally, the implicit surface is tessellated to form the resultant mesh. Our scheme is both efficient and simple, and with it users can easily construct interesting, complex 3D models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Adams, B., Dutré, P.: Interactive boolean operations on surfel-bounded solids. ACM Trans. on Graph. 22(3), 651–656 (2003)
Bajaj, C.L., Coyle, E.J., Lin, K.N.: Arbitrary topology shape reconstruction from planar cross sections. Graph. Models Image Process. 58(6), 524–543 (1996)
Barequet, G., Sharir, M.: Piecewise-linear interpolation between polygonal slices. Comput. Vis. Image Understanding 63(2), 251–272 (1994)
Barequet G., Shapiro D., Tal, A.: Multilevel sensitive reconstruction of polyhedral surfaces from parallel slices. Visual Comput. 16(2), 116–133 (2000)
Bedi, S.: Surface design using functional blending. Comput. Aided Des. 24(9), 505–511 (1992)
Bellman, R.E.: Introduction to Matrix Analysis. McGraw-Hill, New York (1960)
Biermann, H., Martin, I., Bernardini, F., Zorin, D.: A cut-and-paste editing of multiresolution surfaces. ACM Trans. on Graph. 21(3), 330–338 (2002)
Bloothmental, J.:An implicit surface polygonizer. Graphics Gems IV, 324–349 (1994)
Carr, J.C., Beaston, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R.: Reconstruction and representation of 3d objects with radial basis functions. In: Proc. of SIGGRAPH’2001, pp. 67–76 (2001)
Cong, G., Parvin, B.: Robust and efficient surface reconstruction from contours. Visual Comput. 17(4), 199–208 (2001)
Conte, S., de Boor, C.: Elementary Numerical Analysis: An Algorithm Approach. McGraw-Hill, New York (1980)
Elber, G.: Generalized filleting and blending operations toward functional and decorative applications. Graphical Models 67(3), 189–203 (2005)
Farin, G.: Curves and Surfaces for CAGD. Morgan Kaufmann, San Francisco (2002)
Funkhouser, T., Kazhdan, M., Shilane, P., Min, P., Kiefer, W., Tal A., Rusinkiewicz, S., Dobkin, D.: Modeling by example. ACM Trans. on Graph. 23(3), 652–663 (2004)
Fu, H., Tai, C.L., Zhang, H.: Topology-free cut-and-paste editing over meshes. Geometric Modeling and Processing’2004, IEEE Computer Society Press, pp. 173–184 (2004)
Kanai T., Suzuki, H., Kimura, F.: Three dimensional geometric metamorphosis based on harmonic maps. Visual Comput. 14(4), 166–176 (1998)
Kanai, T., Suzuki, H., Mitani, J., Kimura, F.: Interactive mesh fusion based on local 3D metamorphosis. In: Proc. of Graphics Interface’99, pp. 148–156 (1999)
Lorensen, W., Cline, H.: Marching cubes: A high resolution 3D surface construction algorithm. Comput. Graph. 21(4), 163–169 (1987)
Museth, K., Breen, D., Whitaker, R., Barr, A.: Level set surface editing operators. ACM Trans. on Graph. 21(3), 330–338 (2002)
Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.: Multi-level partition of unity implicits. ACM Trans. on Graph. 22(3), 463–470 (2003)
Pauly, M., Keiser, R., Kobbelt, K.P., Gross, M.: Shape modeling with point-sampled geometry. ACM Trans. on Graph. 22(3), 641–650 (2003)
Singh K., Parent, R.: Joining polyhedral objects using implicitly defined surfaces. Visual Comput. 17(7), 415–428 (2001)
Sorkine, O., Lipman, Y., Cohen-Or, D., Alexa, M., Rössl, C., Seidel, H.P.: Laplacian surface editing. In: Proc. of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, Eurographics Association, pp. 179–188 (2004)
Turk, G., O’Brien, J.: Shape transformation using variational implicit functions. In: Proc. of SIGGRAPH’1999, pp. 335–342 (1999)
Turk, G., O’Brien, J.: Modelling with implicit surfaces that interpolate. ACM Trans. on Graph. 21(4), 855–873 (2002)
Yu, Y., Zhou, K., Xu, D., Shi, X., Bao, H., Guo, B., Shum, H.: Mesh editing with Poisson-based gradient field manipulation. ACM Trans. on Graph. 23(3), 664–651 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jin, X., Lin, J., Wang, C. et al. Mesh fusion using functional blending on topologically incompatible sections. Visual Comput 22, 266–275 (2006). https://doi.org/10.1007/s00371-006-0004-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-006-0004-8