The Design of Physically Accurate Fluid Flow

We first review work in which a bivariate parametric polynomial is derived that maps one curve onto another and deforms regions about the curves conformally. The curves are defined in Bezier form. In this paper the approximation is extended to B-Spline curves that generate near-conformal maps. It is then applied to approximating and animating ideal fluid flows. The B-spline curve underpins the design approach. With it an interface is developed to design fluid flow applications which also incorporates potential field theory. We give parameter maps that set up the flow from the confomally designed regions. Examples of animated fluid flow include designed channel flows with obstacles.

[1]  Rida T. Farouki,et al.  Analytic properties of plane offset curves , 1990, Comput. Aided Geom. Des..

[2]  Gavin S. P. Miller,et al.  Globular dynamics: A connected particle system for animating viscous fluids , 1989, Comput. Graph..

[3]  L. Ahlfors.  Complex Analysis , 1979 .

[4]  Alain Fournier,et al.  A simple model of ocean waves , 1986, SIGGRAPH.

[5]  Jakub Wejchert,et al.  Animation aerodynamics , 1991, SIGGRAPH.

[6]  Alyn P. Rockwood,et al.  Blending parametric objects by implicit techniques , 1993, Solid Modeling and Applications.

[7]  Gavin S. P. Miller,et al.  Rapid, stable fluid dynamics for computer graphics , 1990, SIGGRAPH.

[8]  Eric L. Schwartz,et al.  Conformal image warping , 2018, IEEE Computer Graphics and Applications.

[9]  George Wolberg,et al.  Digital image warping , 1990 .

[10]  Darwyn R. Peachey,et al.  Modeling waves and surf , 1986, SIGGRAPH.

[11]  Rida T. Farouki,et al.  Algebraic properties of plane offset curves , 1990, Comput. Aided Geom. Des..

[12]  Gary Mastin,et al.  Fourier Synthesis of Ocean Scenes , 1987, IEEE Computer Graphics and Applications.

[13]  Murray R. Spiegel,et al.  Schaum's outline of theory and problems of complex variables , 1974 .

[14]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[15]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[16]  Alain Fournier,et al.  Conformal Texture Mapping , 1987, Eurographics.

[17]  Alyn P. Rockwood,et al.  Conformal maps defined about polynomial curves , 1998, Comput. Aided Geom. Des..

[18]  Murray R. Spiegel,et al.  Schaum's outline of theory and problems of complex variables : with an introduction to conformal mapping and its applications , 1964 .

[19]  Christopher Giertsen,et al.  Parallel volume rendering on a network of workstations , 1993, IEEE Computer Graphics and Applications.