Abstract—In soft object modeling, a complex soft object is obtained by performing blending operations on primitive soft objects and primitive soft objects determine the shape of the complex soft object. To make the shapes of primitive soft objects more diverse, this paper proposes generalized erosion and dilation operations of distance functions to deform a primitive soft object. The proposed operations are able to increase and decrease the influential radius of the distance function of a soft object repeatedly via a sequence of dilating and eroding distance functions. Thus, unlike affine transform which deforms a surface by matrix multiplication, the proposed operations deform (dilate or erode) a soft object by a chosen dilating or eroding function, called dilation or erosion. In addition, because the proposed operations also allow more than two dilating and eroding functions to deform a soft object sequentially and successively, partial erosion and dilation, double or triple partial erosions and dilations are also allowed for local deformation. Thus, by using the proposed operations as a new distance function to redefine a soft object, a primitive soft object can be deformed for obtaining the following special deformation effects: concave, convex, point-dilation, disk-dilation, point-erosion, disk-erosion, four-ball-shaped, six-ball-shaped and UFO-shaped effects.

Index Terms—implicit surface, field function; soft object modeling, distance function

Cite: Pi-Chung Hsu, "Generalized Erosion and Dilation Operations of Distance Functions for Deforming Soft Objects," Journal of Image and Graphics, Vol. 3, No. 2, pp. 70-76, December 2015. doi: 10.18178/joig.3.2.70-76