A progressive lens produces a smooth increase in positive foca_or addition_ power from distance to near without any lines of demarcation. In order to provide this gradual change in power, the curvature of a convex progressive lens surface must become increasingly steeper toward the bottom of the lens (Figure 1). The addition power of a convex progressive lens surface is simply the result of the...

We compare curvature-based surface functionals by comparing the aesthetic properties of their minimizers. We introduce an enhancement to the original inline curvature variation functional. This new functional also considers the mixed cross terms of the normal curvature derivative and is a more complete formulation of a curvature variation functional. To give designers an intuitive feel for the ...

This paper proposes a mesh simplification algorithm using a discrete curvature norm. Most of the simplification algorithms are using a distance metric to date. The distance metric is very efficient to measure geometric error, but it is difficult to distinguish important shape features such as a high-curvature region even though it has a small distance metric. We suggest a discrete curvature nor...

This paper presents a method to compute curvatures of a surface patch S obtained from a degenerate representation defined over a rectangular domain. To compute curvatures at a point 4 in S where the surface representation is degenerate one has to assume that the point sef S has a tangent plane and well defined curvatures at the point 4 where the curvatures are to be computed. Our computation me...

BACKGROUND Tibial torsion is the angle between the transverse axes of the proximal and distal tibial articular surfaces. It measures the degree of twisting of the tibia around its own longitudinal axis. The accurate measurement on the magnitude of tibial torsion is of great use in monitoring derangements. It is also useful as a baseline in the event of surgical intervention. Various methods hav...

We observe and quantify wave-like characteristics of amoeboid migration. Using the amoeba Dictyostelium discoideum, a model system for the study of chemotaxis, we demonstrate that cell shape changes in a wave-like manner. Cells have regions of high boundary curvature that propagate from the leading edge toward the back, usually along alternating sides of the cell. Curvature waves are easily see...

Automatic detection of features in three-dimensional objects is a critical part of shape matching tasks such as object registration and recognition. Previous approaches to local surface matching have either focused on man-made objects, where features are generally well-defined, or required some type of user interaction to select features. Manual selection of corresponding features and subjectiv...

In 1998 1999 a team of researchers from the Computer Science Departments at the University of Stanford and the University of Washington digitized a number of Michelangelo’s sculptures, including the David statue, using a custom designed laser triangulation scanner. The resultant data has been made available to the research community. This paper explores the data structures and the inherent geom...

The spike proteins of a number of coronaviruses are able to bind to sialic acids present on the cell surface. The importance of this sialic acid binding ability during infection is, however, quite different. We compared the spike protein of transmissible gastroenteritis virus (TGEV) and the spike protein of infectious bronchitis virus (IBV). Whereas sialic acid is the only receptor determinant ...

Membrane organelles often have complicated shapes and differ in their volume, surface area and membrane curvature. The ratio between the surface area of the cytosolic and luminal leaflets (trans-membrane area asymmetry (TAA)) determines the membrane curvature within different sites of the organelle. Thus, the shape of the organelle could be critically dependent on TAA. Here, using mathematical ...