Shape correction function

The shape correction function is a ratio of the surface area of a growing organism and that of an isomorph as function of the volume. The shape of the isomorph is taken to be equal to that of the organism for a given reference volume, so for that particular volume the surface areas are also equal and the shape correction function has value one.

For volume $V$, reference volume $V_{d}$, the shape correction function $M(V)$ equal for

• V0-morphs: $M(V)=(V/V_{d})^{-2/3}$
• V1-morphs: $M(V)=(V/V_{d})^{1/3}$
• isomorphs: $M(V)=(V/V_{d})^{0}=1$
• static mixture between a V0- and a V1-morph: $M(V)=w(V/V_{d})^{-2/3}+(1-w)(V/V_{d})^{1/3}$ for $0<w<1$