To extend the subspace reduction technique for co-dimensional objects like thin plates or cloth, it is essential to adapt the embedding strategy to account for the unique geometric and physical properties of these objects. Unlike volumetric deformable bodies, co-dimensional objects have significantly different deformation characteristics, often involving bending and stretching rather than volumetric changes.
Defining a Suitable Subspace: The first step is to define a low-dimensional subspace that accurately captures the essential deformation modes of co-dimensional objects. This could involve using a combination of modal analysis and proper orthogonal decomposition (POD) to identify the most significant deformation patterns. For instance, in the case of cloth, the subspace could be constructed from the principal modes of deformation that represent bending and stretching.
Embedding Mesh Construction: The embedding mesh for co-dimensional objects should be designed to reflect their surface topology accurately. For thin plates, a surface mesh that captures the plate's geometry can be used, while for cloth, a mesh that allows for both in-plane and out-of-plane deformations is necessary. This may involve using a triangulated surface mesh that can adaptively refine based on the local curvature and deformation.
Incorporating Contact Dynamics: The contact dynamics for co-dimensional objects must be carefully modeled to prevent penetration and ensure realistic interactions. This can be achieved by integrating the Incremental Potential Contact (IPC) method with a focus on surface interactions, ensuring that contact forces are applied at the surface level rather than through volumetric assumptions.
Adaptive Resolution: Implementing an adaptive resolution mechanism can enhance the simulation of co-dimensional objects. This allows the simulation to dynamically adjust the level of detail based on the object's deformation state, ensuring that computational resources are allocated efficiently while maintaining accuracy.
By addressing these aspects, the subspace reduction technique can effectively handle co-dimensional objects, enabling realistic simulations of thin plates and cloth within the Embedded IPC framework.