# Geometry

## 1406 Submissions

[2] **viXra:1406.0165 [pdf]**
*submitted on 2014-06-27 02:44:50*

### Latest Trends in Spherical Trigonometry

**Authors:** S.kalimuthu

**Comments:** 4 Pages. NA

According to Einstein and his followers space time geometry is gravity. Gravity is the manifestation of distortion of geometry of space due to presence of matter. The heart of these physical and cosmological phenomena is the line element or metric. This metric generated the field equation of Einstein general relative theory. Space time curvature, geodetic effect, frame tracking, gravitational lenses, gravitational red and blue shifts, block holes, dark matter, dark energy, big bang singularity, expansion of the universe and gravitational waves are the predictions of Einstein general relative theory. All these theoretical findings expect gravitational waves have been experimental test at to a very high degree of accuracy. In this work, the authors introduce an entirely new type of polar spherical triangle. The application of this triangle has been extended to Gabuzda- Wardle-Roberts superluminal motion equation and the consecution is noted

**Category:** Geometry

[1] **viXra:1406.0060 [pdf]**
*submitted on 2014-06-10 08:09:18*

### Volume Enclosed by Subdivision Surfaces with Sharp Creases

**Authors:** Jan Hakenberg, Ulrich Reif, Scott Schaefer, Joe Warren

**Comments:** 14 Pages.

Subdivision surfaces with sharp creases are used in surface modeling and animation. The framework that derives the volume formula for classic surface subdivision also applies to the crease rules. After a general overview, we turn to the popular Catmull-Clark, and Loop algorithms with sharp creases. We enumerate common topology types of facets adjacent to a crease. We derive the trilinear forms that determine their contribution to the global volume. The mappings grow in complexity as the vertex valence increases. In practice, the explicit formulas are restricted to meshes with a certain maximum valence of a vertex.

**Category:** Geometry