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Texture Mode – Specifies whether to use one or three textures for the different projection axes. 

Same texture on all axes – Projects the same texture along each local axis.
Different texture on each axis – Uses a different texture along each axis.

Texture X – The texture to project along the X axis when the texture mode is set to Different texture on each axis.

Texture Y – The texture to project along the Y axis when the texture mode is set to Different texture on each axis.

Texture Z – The texture to project along the Z axis when the texture mode is set to Different texture on each axis.

Size – Adjusts the size of the texture. 

Blend – Controls the blend between the different projections. Lower values produce sharper transitions between projections.

Frame Offset – Moves the point relative to which the textures are projected. 

Texture Rotation – Specifies rotation (in degrees) for the projected textures around the respective projection axis. If random texture rotation is enabled, non-zero components of this parameter specify increments for the rotation.

Reference Space – Specifies the type of projection space:

Local Object – The projection is done in local object space. When the object is moved/rotated/scaled, the texture moves with it.
Reference to Another Object – The projection is done in the local space of another object in the scene. If no reference object is specified, world space is used. This mode is useful when several objects need to be mapped with the same triplanar texture and to show consistent mapping.

Reference Object – Specifies the reference object, when the Reference Space is set to Reference to Another Object.

Use Displaced Surface – When enabled, uses the displaced geometry to calculate triplanar mapping, if there is displacement. When disabled, the triplanar considers the geometry before displacement.

Random Texture Offset – Randomizes the texture offset based on the Random mode.

Random Texture Rotation – Randomizes the texture rotation based on the Random mode. The rotation can be locked to specific increments (i.e. 45 degrees only, or 90 degrees only) by setting the Texture Rotation components to the desired increments for the different axes.

Random Axis – Randomly changes the projection axes based on the Random mode.

Random Frame Rotation – Randomly rotates the entire projection space based on the Random mode.

Random Mode  Specifies how to generate the random seed needed for the various randomizations: 

By face material ID – Computes the seed based on the face material ID of the mesh. 
By object render ID 
– Computes the seed based on the render ID of the objects.

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