Surface of revolution never negative, the area is given by If the curve is described by the function , , then the integral becomes for revolution around the -axis, and for revolution around the "y"-axis (using ). These come from the above formula. For example, the spherical surface with unit radius is generated by the curve , , when ranges over . Its area is therefore For the case of the spherical curve with radius , rotated about the -axis A minimal surface of revolution is the surface of revolution of the curve between two given points which minimizes surface area. A basic
Volume Area Dihedral Angle Reporter Volume Area Dihedral Angle Reporter Volume, Area, Dihedral Angle Reporter (VADAR) is a freely available protein structure validation web server that was developed as a collaboration between Dr. Brian Sykes and Dr. David Wishart at the University of Alberta. VADAR consists of >15 different algorithms and programs for assessing and validating peptide and protein structures from their PDB coordinate data. VADAR is capable of determining secondary structure (using three different algorithms), identifying and classifying six different types of beta turns, determining and calculating the strength of C=O -- N-H hydrogen bonds, calculating residue-specific accessible surface areas (ASA), calculating residue volumes,