Shape conforming volumetric interpolation with interior distances

Source based heterogeneous modelling is a powerful way of defining gradient materials within a volume. The current solutions do not take into account the topology of the object and can provide counter intuitive results for complex objects. This paper presents a method to interpolate material properties and attributes based on the accessibility of the points in respect to the material features defined by the user. Our method requires the non overlapping source features with constant material to interpolate gradient materials, by using Voronoi diagrams on interior distances. It leads to intuitive material properties across the shape regardless of its topology or complexity. We show how the shape conforming field is defined inside the volume and can be extended outside the volume to create a valid operator for a heterogeneous modelling system dealing with scalar fields. The presented method is computationally efficient and has several applications, such as material property interpolation and shape aware procedural micro structures.