Abstract—This paper proposes spherical product functions to
define implicit spherical product surfaces. A spherical product
function is composed of a contour function and a profile
function and its iso-surface’s shape is generated by modulating
and translating the iso-curve of the contour function through
the points on the iso-curve of the profile function. This paper
also shows if contour and profile functions are ray-linear, then
an implicit spherical product surface can be parameterized and
hence have both the advantages of implicit and parametric
surfaces. Moreover, this paper proposes ray-linear two-branch
and one-branch linear and super-hyperbolic functions that can
be used to construct new contour and profile functions with
asymmetric or symmetric iso-curves. Based on them, an
implicit spherical product surface can has asymmetric or
symmetric contour and profile and also has a parametric
representation.
Index Terms—Implicit surface, blending operations,
parametric surface.
Pi-Chung Hsu is with Department of Information Management, Shu-Te
University, Kaohsiung City, Taiwan (e-mail: pichung@stu.edu.tw).
[PDF]
Cite:Pi-Chung Hsu, "Asymmetric and Symmetric Spherical Product Surfaces
with both Implicit and Parametric Representations," International Journal of Modeling and Optimization vol. 3, no. 6, pp. 504-508, 2013.
