Physics-Based B-spline Morphing
نویسندگان
چکیده
This paper presents a new method for automatically generating a transition between two given B-spline curves or surfaces. Rather than treating the curves or surfaces as purely geometric objects, we distribute mass, damping, elasticity onto them. For elastic objects, morphing can be formulated as a boundary-valued problem of ordinary differential equations. By using Modal Analysis, the boundary-valued problem can be solved analytically. As a result, we can create a morphing that simulates the shape transition with respect to physical properties or by appropriately choosing the physics parameter values we may create a visually pleasing morphing that has no self-intersection or unwanted wiggles. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Animation
منابع مشابه
Morphing Rational B-spline Curves and Surfaces Using Mass Distributions
A rational B-spline curve or surface is a collection of points associated with a mass (weight) distribution. These mass distributions can be used to exert local control over the morph between two rational B-spline curves or surfaces. Here we propose a technique for designing customized morphs by attaching appropriate mass distributions to target B-spline curves and surfaces. We also develop a u...
متن کاملInjectivity Conditions of 2D and 3D Uniform Cubic B-Spline Functions
Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is crucial to obtain desirable results in these areas. This paper considers the injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric inte...
متن کاملIntegrated geometry parametrization and grid movement using B-spline meshes
We propose an algorithm that integrates geometry parametrization and mesh movement using the control points of a B-spline mesh. An initial mesh is created using B-spline volumes in such a way that the control points mimic a coarse grid. The control points corresponding to the surface nodes are adopted as the design variables. Mesh movement is achieved by applying a standard movement algorithm t...
متن کاملLocal Injectivity Conditions of 2D and 3D Uniform Cubic B-Spline Functions
Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. This paper considers the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric i...
متن کاملA rational B-spline hypervolume for multidimensional multivariate modeling
This paper proposes a rational B-spline hypervolume that represents a volume object which has multiple attributes defined in a multidimensional space. This representation provides a mathematical framework for modeling and visualizing a multidimensional multivariate object as well as analyzing the object interiors to extract its intrinsic features that are directly inaccessible. We discuss the N...
متن کامل