Abstract
A new model named the differential model is presented for representing the transformation of objects using differential information. Differential information refers to the curvature and torsion of a curve, the first and the second fundamental forms of a surface and the first fundamental form of a solid object. Given the initial and the final states in the transformation of an object, we compute the initial and the final values of these differential variables. Then, we interpolate the initial and the final values to obtain the in-between values. Finally, the in-between shapes with the desired values of the differential variables are reconstructed. It is possible to represent wide changes in the global shape with simple interpolation of differential variables. It is also easy to represent isometric (preserving the line length or the first fundamental form) transformation. Simulating the transformation of the coiled filamentous structure of the acrosome of an abalone sperm illustrates the efficiency of this method.
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© 1991 IFIP International Federation for Information Processing, 16 place Longemalle, CH-1204 Geneva, Switzerland
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Shinagawa, Y., Kunii, T.L. (1991). The Differential Model: A Model for Animating Transformation of Objects Using Differential Inforamtion. In: Kunii, T.L. (eds) Modeling in Computer Graphics. IFIP Series on Computer Graphics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68147-2_1
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DOI: https://doi.org/10.1007/978-4-431-68147-2_1
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-68149-6
Online ISBN: 978-4-431-68147-2
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