Shape conforming volumetric interpolation with interior distances

Abstract

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 conformal 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 e cient and has several applications, such as material property interpolation and shape aware procedural micro structures.Keywords: Heterogeneous modelling, material interpolation, shape conformal, interior distance, procedural texturing

Modeling and Visualization of Multi-material Volumes

“…The work [FSP15] employs specific spatial partitions based on a Voronoi diagram built for interior distance fields defined by material feature points introduced by the user. Transition zones to interpolate between materials are created by intersecting offsets of adjacent Voronoi cells.…”

“…User control is necessary for practical users of a modeling system (engineers, designers, artists) to create a material function which describes exactly their intent. The distance field is often necessary to provide predictability as argued in [BST04], [FST06] and [FSP15]. In addition, [SD01] argues that the lack of distance properties makes it difficult for the user to control or predict the material distribution.…”

“…Numerous approaches exist to compute interior distances, such as [RLF09] or [CWW13]. In [FSP15], interior distances were used in the combination with the transfinite interpolation [RSST01] to achieve shape conforming distribution of multiple materials defined by the user provided material sources.…”

“…More recently, it was also used to perform animation of heterogeneous object in [SFA*15]. Inverse distance weighting using natural neighbors was used to interpolate heterogeneous features in [FSP15], with the intrinsic distance (with respect to the solid) to the different features being used in the interpolation.…”

Sample-Based Design of Functionally Graded Material Structures

“…(b) -(d) show the interpolated target descriptors fields with the power of distance equals 4. For non-convex domains, interpolation with interior distances may be advantageous[71].Figure 6 (e) and (f) are generated bone structures from the (a) Two-phase femur bone structure (b) Perimeter field (c) Area field (d) Euler characteristic field (e) Reconstruction without Minkowski functionals fields (f) Reconstruction with Minkowski functionals fields Femur bone structure reconstruction. (a) shows a cross-section of a two-phase femur bone structure, (b) -(d) are Minkowski functionals fields of (a), (e) and (f) are reconstruction results without and with Minkowski functionals as descriptors fields.…”