VRayFalloff produces a gradient texture based on the angular falloff of the surface of the geometry. The resulting map can simulate the falloff of opacity, reflection, and refraction for surfaces, where these properties vary depending on the surface's angle to the camera, such as curved glass or water.

VRayFalloff starts with two colors, usually black and white. Placement of these colors on the surface is based on the Falloff Type and Falloff Direction selected. The remainder of the map is generated as a gradient between these two colors, with a gradual falloff between the colors.

For the example shown on the right, VRayFalloff is used in the Diffuse channel of a V-Ray Material. The Falloff type is set to Perpendicular/Parallel with the falloff Direction set to World Y Axis. Solid colors of bright orange and dark green are used for the Front and Side Color parameters.

UI Path: Texture > V-Ray > VRayFalloff

Font/Side Color – Sets the extreme ends of the range of colors for the Falloff Map's gradient. The specific placement of these colors on the surface is determined by the Falloff Type and the Falloff Direction.

Falloff Type – Specifies the type of falloff:

Towards/Away – Based on the face normals' directions. Faces with normals that point in the Falloff Direction generate the Front Color while those facing in the opposite direction (180 degrees away from the falloff direction) generate the Side Color. 
Perpendicular/Parallel –Based on the face normals' directions. Faces with normals that point in the Falloff Direction generate the Front Color while those facing in a perpendicular direction (90 degrees away from the falloff direction) generate the Side Color.      
Fresnel –Based on changes to the index Of Refraction (IOR) over the surface, due to Fresnel calculations. Faces with normals that point in the Falloff Direction generate the  Front Color  and those facing in any other direction generate varying colors, depending on the IOR set by the Fresnel Index Of Reflection. 
Distance blend – Sets the falloff range based on distance from the camera, as specified by Distance Near and Distance Far. This option is useful for generating a Z-depth type of map when rendering a very large object such as terrain, where the Falloff Map can be used as a mask to dim distant details.

Falloff Direction – Specifies the falloff direction to be used by the Falloff Type. 

View Z – Uses the camera viewing direction. This is the most common selection.
View X / Y – Uses one of the camera's other axes.
Explicit – Uses the direction specified by the Explicit direction parameter.
Local X / Y / Z – Uses one of the object's local axes.
World X / Y / Z – Uses one of the world axes.

Fresnel IOR – Defines the IOR (Index of Refraction)when the Falloff Type is set to Fresnel.

Distance Extrapolate – When enabled, the effect continues beyond the range set by Distance Near and Distance Far. Parts of the surface nearer than Distance Near receive the Front Color, while parts farther from the camera than Distance Far receive the Side Color.

Distance Near – When the Falloff Type is set to Distance, parts of the surface at this distance from the camera and closer receive the Front Color.

Distance Far – When Falloff Type is set to Distance, parts of the surface at this distance from the camera and farther away receive the Side Color.

Explicit Direction – Specifies the direction for falloff when the Falloff Direction is set to Explicit.