Abstract: The disclosure provides a method of determining reflected irradiance for a surface point on a surface whose reflectance properties are represented by a measured BSDF. Additionally, the disclosure provides a renderer and a computer program product. In one embodiment, the method includes: (1) determining u, v and w coordinates in the measured BSDF for the surface point based on an incoming and an outgoing ray direction, (2) selecting a triangle for barycentric interpolation based on values of the v and the w coordinates at the surface point and (3) performing the barycentric interpolation for evaluating the measured BSDF for the surface point.

Abstract: The disclosure provides a method of determining reflected irradiance for a surface point on a surface whose reflectance properties are represented by a measured BSDF. Additionally, the disclosure provides a renderer and a computer program product. In one embodiment, the method includes: (1) determining u, v and w coordinates in the measured BSDF for the surface point based on an incoming and an outgoing ray direction, (2) selecting a triangle for barycentric interpolation based on values of the v and the w coordinates at the surface point and (3) performing the barycentric interpolation for evaluating the measured BSDF for the surface point.

Abstract: The present invention relates to a new process for obtaining fatty acids with improved color, odor and heat stability which is characterized in that: (a) in a first step the crude acids are fed to a rectification (“precut”) column in order to remove low boiling by-products being present in the starting material as a top fraction, and (b) in a second step the bottom fraction of the precut column is fed to a sidestream column in order to obtain the pure fatty acids as the side fraction, to remove low boiling by-products which have been formed in the course of the first distillation as a top fraction and to remove high boiling by-products, either being present from the starting material or formed during the first distillation, with the residue.

Abstract: The disclosed invention provides a process for the production of a benzoic acid ester by reaction of a benzoic acid component selected from benzoic acid or a benzoic acid ester with alcohol in the presence of a catalyst, characterized in that tin(II) oxide in combination with a phosphorus(I) compound is used as the catalyst. A phosphorus(I) acid or a salt thereof is preferably used as the phosphorus(I) compound. The resultant products can be used as constituents in cosmetic preparations.

Abstract: Disclosed is a new process for obtaining fatty acids with improved color, odor and heat stability which is characterized in that (a) in a first step the crude acids are fed to a rectification (“precut”) column in order to remove low boiling by-products being present in the starting material as a top fraction, and (b) in a second step the bottom fraction of the precut column is fed to a sidestream column in order to obtain the pure fatty acids as the side fraction, to remove low boiling by-products which have been formed in the course of the first distillation as a top fraction and to remove high boiling by-products, either being present from the starting material or formed during the first distillation, with the residue.