The computational electromechanics of a contractile organ, such as the beating heart generates both scalar fields (e.g., intra- and extracellular, or transmembrane potentials, and intra- and extracellular ionic activities) and vector fields (e.g., ionic current densities, stresses and strains) within a moving, anisotropic and anatomically sculptured geometry. The dynamics of fluid enclosed by the organ, or vascular perfusion of the tissue itself, can also be obtained. This raises problems of visualisation of a number of different variables and derived quantities (such as action potential duration, or the filament around which re-entrant waves are propagating) within a complicated and moving geometry. Such visualisation may also be coupled with experimental or clinical data streams, and used for computational steering. Traditional scientific visualisation relies on surface representations, that are obtained by transforming field-based data sets. Volume graphics based on constructive volume geometry (CVG) uses field-based data sets as its intrinsic primitives, and is suited for depicting multiple structures, combinations of different data sets with heterogeneous interior structures by using opacity and combinational operators. CVG has been applied to virtual cardiac tissues (Chen et al., 2003a, b) and is applied to visualise the interior fibre structure that generates anisotropic propagation, to digitally dissect out fibre bundles, and to illustrate propagation in terms of scalar wavefront and vector current densities within a structured anisotropic three-dimensional geometry.