Interpreting the projective hierarchy in expansions of the real line

We give a criterion when an expansion of the ordered set of real numbers defines the image of the expansion of the real field by the set of natural numbers under a semialgebraic injection. In particular, we show that for a non-quadratic irrational number a, the expansion of the ordered Q(a)-vector space of real numbers by the set of natural numbers defines multiplication on the real numbers

Biologically inspired simulation of livor mortis

We present a biologically motivated livor mortis simulation that is capable of modelling the colouration changes in skin caused by blood pooling after death. Our approach consists of a simulation of post mortem blood dynamics and a layered skin shader that is controlled by the haemoglobin and oxygen levels in blood. The object is represented by a layered data structure made of a triangle mesh for the skin and a tetrahedral mesh on which the blood dynamics are simulated. This allows us to simulate the skin discolouration caused by livor mortis, including early patchy appearance, fixation of hypostasis and pressure induced blanching. We demonstrate our approach on two different models and scenarios and compare the results to real world livor mortis photographic examples