Isotropic Virtual planes formulas
Length per unit volume
- p(box): Number of corners considered
- a(plane): Exact sampling area
- p(ref): Number of corners in region
: Total number of transects
Estimated total length
or 
, 
, 
- ssf: Section sampling fraction
- asf: Area sampling fraction
- hsf: Height sampling fraction
- psd: Probe sampling density
: Total number of transects- a(box): Area of sampling box
- h(box): Depth of sampling box
- d: Sampling plane separation
- dx, dy: Distances in XY
: Average section thickness- a(plane): Sampling plane area
- E: Expected value
- v(box): Volume of sampling box
Total plane area
- l: Number of layouts
- s: Number of sampling sites
- Ai,j: Plane area inside of each sampling box for each layout
Coefficient of error (Gundersen)
Poisson noise is 
- A,B,C: Covariogram values
: Particles counted
Plane areas
- A,B,C,D: Given constants
- d: Distance between planes
- i: Integer
- x0,y0,z0: Vertex of a sampling box
- bx,by,bz: Dimensions of a sampling box
Average number of counts
- p: Number of probes
- Lj: Number of layouts in each probe
- Qi j: Number of counts in each probe and layout
Total corners of sampling boxes inside the region of interest
- p: Number of probes
- Ci : Number of sampling boxes inside region of interest
References
Larsen, J. O., Gundersen, H.J.G., & Nielsen, J. (1998). Global spatial sampling with isotropic virtual planes: estimators of length density and total length in thick, arbitrarily orientated sections. Journal of Microscopy, 191, 238–248.