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Texture Resolution – Determines the resolution of the displacement texture used by V-Ray. If the texture map is a bitmap, it would be best to match this resolution to the size of the bitmap. For procedural 2d maps, the resolution is determined by the desired quality and detail in the displacement. Note that V-Ray also automatically generates a normals map based on the displacement map, to compensate for details not captured by the actual displaced surface. 

Filter Texture – When enabled, the texture map is filtered before the actual displacement takes place.

Filter Blur – Specifies the amount of blur that is applied to the texture before the displacement takes place.

Precision – Related to the curvature of the displaced surface; flat surfaces can do with a lower precision (for a perfectly flat plane you can use 1), more curved surfaces require higher values. If the precision is not high enough you can get dark spots ("surface acne") on the displacement. Lower values compute faster.

Tight Bounds – Causes V-Ray to compute more precise bounding volumes for the displaced triangles, leading to slightly better rendering times. 

Multi Tile – When enabled, 2D Displacement can work with <UVTILE>/<UDIM> textures.

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Subdivision

 

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Enabled – Enables the object subdivision.

Geometry Generation – Determines when the geometry is compiled during rendering.

On the Fly  – The subdivision Geometry dynamically  goes into the dynamic memory pool during rendering from which it can later be removed if needed. This process is at the expense of some speed, but potentially saving on RAM. 
Pre-tessellated  – The subdivision geometry is pre-compiled into an acceleration structure at the beginning of the rendering and remains there until the end of the frame. This may speed up the rendering and increase the memory usage.

Preserve Map Borders – Specifies how to handle subdivisions of UV coordinates at UV seams when Subdivide UVs is enabled. The possible values are:

None – UVs are always subdivided regardless of whether they are on a UV seam or not.
Internal – Only preserve UVs if they are on an internal UV seam.
All – Does not subdivide UVs on UV seams.

Subdivide UVs – Enables the UVs of the object will be subdivided at the borders.

Preserve Geometry Borders – Specifies whether subdivision geometry borders are preserved or not.

Classic Catmull-Clark – When this option is enabled V-Ray uses the Classic Catmul-Clark method for subdividing the mesh instead of the hybrid one used by default. This option should be enabled only if the mesh is composed entirely of rectangular faces or it will not work.

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OpenSubdiv

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Enable Open Subdiv – When enabled, the object will be subdivided before rendering using the OpenSubdiv library.

Subdivision Level – The number of subdivision levels. This values is set to 0 by default.

Type – The type of subdivision used. Two types are currently supported by the OpenSubdiv library:

Catmull-Clark – The default subdivision method which can handle meshes with arbitrary polygons (triangles, quads etc);
Loop – This subdivision method works with triangles only.

Preserve Map Borders – Specifies how to handle subdivisions of UV coordinates at UV seams when Open Subdivide UVs is enabled. The possible values are:

None – UVs are always subdivided regardless of whether they are on a UV seam or not;
Internal – Only preserve UVs if they are on an internal UV seam;
All – Does not subdivide UVs on UV seams.

Subdivide UVsAllows you to choose whether or not the UVs of the object are subdivided at the borders.

Preserve Geometry Borders – Specifies whether geometry borders are preserved or not.

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Quality

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Use Global SettingsWhen enabled, the settings in the Geometry tab are overridden for the current object. This option is enabled by default.

View Dependent When enabled, Edge length determines the maximum length of a subtriangle edge, in pixels. A value of 1.0 means that the longest edge of each subtriangle is about one pixel long when projected on the screen. When View-dependent is off, Edge length is the maximum subtriangle edge length in world units. This options is disabled by default.

Edge LengthDetermines the quality of the displacement or subdivision. Each triangle of the original mesh is subdivided into a number of subtriangles. More subtriangles means more detail in the displacement, slower rendering times and more RAM usage. Less subtriangles mean less detail, faster rendering and less RAM. The meaning of Edge length depends on the View-dependent parameter above.

Max SubdivisionsControls the maximum subtriangles generated from any triangle of the original mesh. The value is in fact the square root of the maximum number of subtriangles. For example, a value of 256 means that at most 256 x 256 = 65536 subtriangles are generated for any given original triangle. It is not a good idea to keep this value very high. If you need to use higher values, it will be better to tessellate the original mesh itself into smaller triangles instead.

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