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 is calculated by dividing a given residue’s observed accessible surface areas by the calculated accessible surface areas for that residue in an extended Gly-Xaa-Gly tripeptide (where Xaa is the residue of interest). VADAR reports accessible surface are values both for the entire amino acid residue and for the amino acid side chains. The accessible surface areas is also calculated for charged atoms (N, O), polar (N, O, S) atoms and for non-polar atoms (C). This information can be used to calculate charged, polar and non-polar surface area. Accessible surface areas measurements/estimates are particularly useful in protein structure assessment, protein structure