A topology-preserving deformation method for three-dimensional models based on multi-body harmonic fields

By constructing a three-dimensional differential homoembryonic map based on multiple body harmonization fields, the problem of difficult construction and high computational cost of three-dimensional differential homoembryonic map is solved, and efficient differential homoembryonic mapping and topological deformation are achieved on complex geometric structures.

CN113129458BActive Publication Date: 2025-03-21DALIAN UNIV OF TECH
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Patent Information

Application Number
CN202110498133.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2021-05-08
Publication Date
2025-03-21
Estimated Expiration
2041-05-08

AI Technical Summary

Technical Problem

In three-dimensional situations, it is difficult to construct differential homoembryonic mapping, especially on low-deficiency surfaces with complex geometry. Existing methods such as large deformation differential homoembryonic metric mapping (LDDMM) are expensive to calculate and it is difficult to generate appropriate meshes at groove and cavity features.

Method used

By constructing a three-dimensional differential isomorphic map based on multiple body harmonic field, using multiple body harmonic field as the guiding field, the anisotropic body harmonic field is calculated, thereby generating a three-dimensional differential isomorphic map and induced topological deformation.

Benefits of technology

It realizes efficient three-dimensional differential homoembryonic mapping on complex geometric structures, and can deform the three-dimensional model under topological conditions, reducing the calculation cost, and solving the difficulty of grid generation in traditional methods at groove and cavity characteristics.

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Abstract

The present invention discloses a topology-preserving deformation method for a three-dimensional model based on a multi-body harmonic field, and belongs to the fields of computer graphics, computational mathematics, topology, and differential geometry. First, a tetrahedral mesh is constructed between the original three-dimensional model and the target three-dimensional model, and then the region where the topological transformation occurs during the deformation process is calculated based on the traditional one-body harmonic field, and a special multi-boundary condition is set, and then the multi-body harmonic field is calculated based on this, and finally a topology-preserving surface deformation is induced. The present invention can find the region where the topological transformation occurs during the deformation process based on the saddle point in the traditional body harmonic field, and adaptively construct a multi-body harmonic field that can induce topology-preserving deformation, thereby generating a topology-preserving deformation surface under the guidance of the multi-body harmonic field. The method is universal and efficient for the deformation of three-dimensional models with the same topology, requires less computational cost than the traditional large deformation differential homeomorphism metric mapping, and can be widely used.
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